back to list

Music Theory (was Re: How to keep discussions on-topic)

🔗Mike Battaglia <battaglia01@...>

6/7/2008 1:42:58 AM

> Charles Lucy is infamous for being of a proponent of a
> theory nobody other than himself can understand. He
> claims variously that:
> * He's discovered the long-lost tuning of John Harrison,
> which he's named after... himself.
> * He sometimes claims it's significantly different from
> other meantones even though nobody else agrees and he
> almost certainly couldn't tell the difference himself in
> a blind listening test. He sometimes backpedals on this
> only to re-assert it later.
> * That these special qualities are do to one or both of
> two facts:
> * The beat rates of irrational intervals based on pi
> entrain the brain in alpha states.
> * The irrational intervals based on pi capture something
> about the "spherical wavefronts" of sound.

Hahaha! Yeah, I've gotten that vibe. The concept of irrational
intervals standing on their own as musical entities, rather than being
"approximations" to rational ones, however, is something that needs to
be brought into consideration. There are huge inconsistencies in the
way microtonal music is often broken down... Starting with the notion
that 12tet "approximates" JI. And yet, it does...

> We tolerate him though because he's a resident eccentric.
> And he outranks me in microtonal seniority by a couple of
> decades.
>
> > From Charles Lucy:
> >
> > > I'm really glad to see that Rick is looking at this from a
> > > scientific POV.
> //
> > I suppose you should respond to Charles and tell him that
> > scientific POV's are "off-topic in this forum".
>
> LOL
>
> > Furthermore, why do you care? This is the current topic of
> > discussion on a tuning forum. You started pouting about it
> > being off topic as a reaction to -of all reasons- people
> > thinking that you thought the set of all irrationals was
> > countable. Who cares?
>
> Plenty of fine musicians and theorists have been driven off
> this list over the years due to the high message volume.
> And that was back when the messages did frequently contain
> exciting new discoveries. A tremendous amount of knowledge
> has been aggregated here, and it's worth caring about.
> There's a tremendous amount of potential here too, but as
> it stands I don't think this forum is ready for the rapid
> growth the topic of microtonal music is about to experience.
> Maybe it loses its central position, and maybe that's overdue
> anyway, I don't know.

I don't think it's going down, rather I think it's headed up. This
stuff is amazing. It is merely in its infancy.

I don't think that everything has been figured out at all yet, and
research further into the "why"'s and "how"'s of music, especially
microtonal music, will likely lead to breakthroughs in psychology and
other related fields as well as general music theory and the way it is
taught. Alternately, maybe we'll "re-realize" things that have been
realized in those fields, but within a musical context, and perhaps
revamp what I see as America's decrepit and aging theory system.

Honestly, it just plain sucks. I had to do years of independent
research into this stuff to explain just a few of the holes in the way
theory is usually taught in schools. If we could REALLY get at least
the CURRENT revelations of microtonal theory nailed into a consistent
axiomatic system, then we could teach it to the average music student
much more effectively. It might not be possible to represent every
possible musical statement in some kind of axiomatic "theory," but at
least we can fix the current one so that it isn't inconsistent.

Ironically, the current system is set up so that the people who have
the most natural talent are often screwed over the most. This is
because they realize that there are huge holes in the way theory is
often taught, and they start to struggle with that notion and of
self-doubt.

Take it this way: my Jazz piano teacher says that when formulating
chord voicings on the piano, that one shouldn't put any "b9"'s in the
voicing UNLESS it's over the root. So chords like this are bad:

C E G Bb D F

Since the E-F is a b9 over a note other than the root. But take this chord:

C E G Bb Db

That's okay, because the b9 is over the root.

The problem is that it doesn't make any f'ing sense. Yes, I agree that
the first chord sounds "weird" and in a jazz context "weak," but WHY?
The explanation is extremely, extremely poor. WHY does putting a
tempered b9 in a chord over any note but the root sound the way it
does?

Furthermore, this chord:

D F A d' f#'

has a very, very interesting sound that I have been getting into.
There is a b9 over the minor third - although maybe it's a #8. It
doesn't sound as week as the other chord above. Does it sound good
because it's a #8 instead of a b9? Does the numbering change reflect
some kind of "shift" in the way we perceive the JI intervals that the
notes are approximating? The whole system is ambiguous and in some
cases screwed up.

If we could do the hard work of not only making a consistent system
but one that builds off of what people already know, it would catch on
hugely and most likely be beneficial for everyone in a broad scale.
72tet is useful as a temperament because it builds off of people's
existing knowledge, and if we could somehow come up with a new and
improved "music theory" that doesn't require years of independent
research to understand (nobody wants to think of chords in terms of
4:5:6 except for guys like us), it would catch on.

At the very least, we might be able to free people from their
misconceptions about microtonal music consisting of "weird, dark,
dissonant quarter-tones."

-Mike

🔗Mike Battaglia <battaglia01@...>

6/7/2008 2:00:41 AM

[ Attachment content not displayed ]

🔗Kraig Grady <kraiggrady@...>

6/7/2008 2:25:14 AM

like most movements in art
( this one is strange
in that it is a technological
more than an aesthetic one)
that by the time it is all figured out,
it will be over.

but there is an underlying assumption that the world would be better dependent on how many people do microtones.
i prefer quality than quantity. When every MTV song is pitch corrected to microtones the life will be surely have been sucked out of it.

David Doty wrote a fine book to teach JI. Kyle Gann has info up also on his site.
There are already plenty of resources for anyone interested that is willing to go beyond having it handed to them without them having to think at all.
To add, subtract, multiply and divide will suffice

The wheel does not have to be reinvented every 6 months, with each new group of intonational born agains.

But if you insist, it is MUSIC that does it, not talk and theory! Useful, yes but only as supplements to the acts of the dreamers.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> > Charles Lucy is infamous for being of a proponent of a
> > theory nobody other than himself can understand. He
> > claims variously that:
> > * He's discovered the long-lost tuning of John Harrison,
> > which he's named after... himself.
> > * He sometimes claims it's significantly different from
> > other meantones even though nobody else agrees and he
> > almost certainly couldn't tell the difference himself in
> > a blind listening test. He sometimes backpedals on this
> > only to re-assert it later.
> > * That these special qualities are do to one or both of
> > two facts:
> > * The beat rates of irrational intervals based on pi
> > entrain the brain in alpha states.
> > * The irrational intervals based on pi capture something
> > about the "spherical wavefronts" of sound.
>
> Hahaha! Yeah, I've gotten that vibe. The concept of irrational
> intervals standing on their own as musical entities, rather than being
> "approximations" to rational ones, however, is something that needs to
> be brought into consideration. There are huge inconsistencies in the
> way microtonal music is often broken down... Starting with the notion
> that 12tet "approximates" JI. And yet, it does...
>
> > We tolerate him though because he's a resident eccentric.
> > And he outranks me in microtonal seniority by a couple of
> > decades.
> >
> > > From Charles Lucy:
> > >
> > > > I'm really glad to see that Rick is looking at this from a
> > > > scientific POV.
> > //
> > > I suppose you should respond to Charles and tell him that
> > > scientific POV's are "off-topic in this forum".
> >
> > LOL
> >
> > > Furthermore, why do you care? This is the current topic of
> > > discussion on a tuning forum. You started pouting about it
> > > being off topic as a reaction to -of all reasons- people
> > > thinking that you thought the set of all irrationals was
> > > countable. Who cares?
> >
> > Plenty of fine musicians and theorists have been driven off
> > this list over the years due to the high message volume.
> > And that was back when the messages did frequently contain
> > exciting new discoveries. A tremendous amount of knowledge
> > has been aggregated here, and it's worth caring about.
> > There's a tremendous amount of potential here too, but as
> > it stands I don't think this forum is ready for the rapid
> > growth the topic of microtonal music is about to experience.
> > Maybe it loses its central position, and maybe that's overdue
> > anyway, I don't know.
>
> I don't think it's going down, rather I think it's headed up. This
> stuff is amazing. It is merely in its infancy.
>
> I don't think that everything has been figured out at all yet, and
> research further into the "why"'s and "how"'s of music, especially
> microtonal music, will likely lead to breakthroughs in psychology and
> other related fields as well as general music theory and the way it is
> taught. Alternately, maybe we'll "re-realize" things that have been
> realized in those fields, but within a musical context, and perhaps
> revamp what I see as America's decrepit and aging theory system.
>
> Honestly, it just plain sucks. I had to do years of independent
> research into this stuff to explain just a few of the holes in the way
> theory is usually taught in schools. If we could REALLY get at least
> the CURRENT revelations of microtonal theory nailed into a consistent
> axiomatic system, then we could teach it to the average music student
> much more effectively. It might not be possible to represent every
> possible musical statement in some kind of axiomatic "theory," but at
> least we can fix the current one so that it isn't inconsistent.
>
> Ironically, the current system is set up so that the people who have
> the most natural talent are often screwed over the most. This is
> because they realize that there are huge holes in the way theory is
> often taught, and they start to struggle with that notion and of
> self-doubt.
>
> Take it this way: my Jazz piano teacher says that when formulating
> chord voicings on the piano, that one shouldn't put any "b9"'s in the
> voicing UNLESS it's over the root. So chords like this are bad:
>
> C E G Bb D F
>
> Since the E-F is a b9 over a note other than the root. But take this > chord:
>
> C E G Bb Db
>
> That's okay, because the b9 is over the root.
>
> The problem is that it doesn't make any f'ing sense. Yes, I agree that
> the first chord sounds "weird" and in a jazz context "weak," but WHY?
> The explanation is extremely, extremely poor. WHY does putting a
> tempered b9 in a chord over any note but the root sound the way it
> does?
>
> Furthermore, this chord:
>
> D F A d' f#'
>
> has a very, very interesting sound that I have been getting into.
> There is a b9 over the minor third - although maybe it's a #8. It
> doesn't sound as week as the other chord above. Does it sound good
> because it's a #8 instead of a b9? Does the numbering change reflect
> some kind of "shift" in the way we perceive the JI intervals that the
> notes are approximating? The whole system is ambiguous and in some
> cases screwed up.
>
> If we could do the hard work of not only making a consistent system
> but one that builds off of what people already know, it would catch on
> hugely and most likely be beneficial for everyone in a broad scale.
> 72tet is useful as a temperament because it builds off of people's
> existing knowledge, and if we could somehow come up with a new and
> improved "music theory" that doesn't require years of independent
> research to understand (nobody wants to think of chords in terms of
> 4:5:6 except for guys like us), it would catch on.
>
> At the very least, we might be able to free people from their
> misconceptions about microtonal music consisting of "weird, dark,
> dissonant quarter-tones."
>
> -Mike
>
>

🔗Kraig Grady <kraiggrady@...>

6/7/2008 3:06:48 AM

there are allot of philosophy that rely on the person.
look at cage. what worked for him seems not to produce the same results for others.
Terrence McKenna is maybe a better example as pointed out by Rubert Sheldrake

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

🔗Cameron Bobro <misterbobro@...>

6/7/2008 3:47:55 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
> At the very least, we might be able to free people from their
> misconceptions about microtonal music consisting of "weird, dark,
> dissonant quarter-tones."
>
> -Mike
>

Doing that is on the one hand very simple, and on the other,
impossible. At least, this has been my experience. For on the one
hand, it is as easy as pie to make very microtonal music that is
downright pretty and immediately appealing to plenty of people, and
on the other, if you do mention that it's "microtonal", you get
variations on a theme which boils down to "no it couldn't be because
it doesn't sound weird, dark, and dissonant" (or sometimes "not
Indian/Arabic/etc").

So as far as I have seen the real problem might be a definition of
"microtonal" which is simply going to move about in order to retain a
negative connotation. By negative connotation I don't just mean
"bad", but exclusive, cf. the term "xenharmonic".

-Cameron Bobro

🔗Kraig Grady <kraiggrady@...>

6/7/2008 3:54:24 AM

The best way to answer this is to give it to a string or wind or brass group and see what they play.I think you will find that whoever has the third will lower it so 5/4 is at least 'informing' the intonation. but if we ran the chord throughout a big variety of music we would find different intonation used in different times depending on , for one, the emotional characteristic of the passage. At least this is what i hear and/or imagine i hear. I also think different composers imply different intonation and i think gene smith was on the right course here, whether his conclusions would be completely consistent by what players do, might not be the case. Joe Monzo has also implied such ideas. I would only add that when these composers overlapped with passages that were like others before them, it seems an ensemble might revert to that way of thinking in part. That intonation can vary all the time and moment to moment might be exactly what humans are doing.....making our knowledge of what we are doing endless.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> To further the discussion, this is something I posted a while ago in > one of Charles Lucy's threads and before that in various spinoffs of > the Rick Ballan thread... But I'll repost it here for tidiness, > modified to be slightly clearer:
>
> ____________________________________________________________________________
>
>
> Rick has been talking recently about how maybe we're hearing 3 steps > of 12tet as being an only slightly out-of-tune 19/16 ratio rather than > a really out-of-tune 6/5 ratio. 19/16, however, has an entirely > different /*character*/ than 6/5. Which begs the question: what ARE we > hearing? What is the nature of this change in character, and what does > this character mean?
>
> What is it that we hear when we hear a 12tet major chord? Often this > chord is cited as having a relatively in-tune 3/2 and a slightly > out-of-tune 5/4... But is there some other way that we are really > hearing it?
>
> Do we psychologically "move" these ratios to the nearest JI one, or > the simplest one, or...? If I play a JI minor chord with the minor > third as 19/16 am I hearing THAT as an out of tune 6/5?
>
> I think the context of it might matter. There is definitely some > difference between 11-tet and 12-tet, for example. 12-tet offers > better "matches" to intervals in the harmonic series. So to SOME > extent, imposing some kind of JI-related structure on equal > temperaments offers useful results.
>
> Take the following 2 chords:
>
> 1:2:3:4:5:6
>
> and
>
> 100:200:300:400:504:600
>
> You will still most likely hear the resemblence to the overtone series > and hear that context superimposed over the second chord. The > sharpened "5" will cause some beating that you may or may not like, > depending on the context. I hear the second one as "vibrant," > "exciting," etc. You might also view it as "dissonant" and an > "out-of-tune" version of 1:2:3:4:5:6. However, you might ALSO view > that second chord as an "inversion" of a completely different JI > chord, which would presumably act in a different way if you take into > account the "traditional" ways that chord inversions and such are > viewed - and these ways were groundbreaking in their own time and > evolved out of their own realizations.
>
> I.E.: the two approaches give differing results, and thus something in > the overall theory is inconsistent. All known musical truths will > never be accessible through any axiomatic system - but it might be > useful to at least make the current one consistent. As I see it (and I > feel this is a fairly common perspective), the way many of us have > been taught music theory in school fails to explain microtonal theory > (see above for the b9 example), and the way many of us currently see > microtonal theory fails to explain good ol' fashioned 12tet music > theory from school (the areas in which it DOES work). If these two > could be reconciled, I think it would be good.
>
>
> So to restate the question:
>
> Why do we sometimes hear intervals "guided" to their nearest match in > a harmonic series, and why do we sometimes hear them as new entities > in their own right with different feelings and characters to them?
>
> Or, in a more general sense, what causes someone to hear a certain > interval as a mistuned form of another interval?
>
> OR, in its /broadest/ sense, what causes someone, when experiencing a > phenomenon, to view that phenomenon as an altered version of another > phenomenon?
>
> Sometimes we get into "well the brain does this" or "the brain does > that," and I think those answers often fall short of the truth.
>
> -Mike
>
>

🔗Mike Battaglia <battaglia01@...>

6/7/2008 6:08:50 AM

> David Doty wrote a fine book to teach JI. Kyle Gann has info up also on
> his site.
> There are already plenty of resources for anyone interested that is
> willing to go beyond having it handed to them without them having to
> think at all.
> To add, subtract, multiply and divide will suffice

There are a lot of people who are amazing musicians who don't even
think in terms of theory. They can play amazingly well entirely by
ear. Most of the popular musicians to come out of the 20th century, in
fact. We should make it easy for THESE people to get into microtonal
music as well - simply because it will brighten everyone's life. In
addition, there are the musicians who think in terms of theory but
eschew the mathematics involved in JI as being "too complicated"... as
well as the fact that most of us don't have an instrument to play on.
Even though you and I think that JI is simple and fairly straight
forward, as soon as I mention "the 3rd overtone of the 7th overtone,
so the 21st overall overtone" these people are already lost.

And it isn't because they are lazy or poor musicians. It has to do
with some kind of deficiency in their education that they doubt
themselves mathematically. but that's okay, because they're still good
musicians.

There are a lot of different kinds of musicians... I think it to be a
worthwhile pursuit to make and popularize a system that is accessible
to -everyone-. At least, accessible in the sense that it builds off of
what we have now, rather than the alternative, which is to discard the
whole system in favor of something new.

In other words, note names like C D E F... etc should have some kind
of place in JI. Maybe 72-tet is the way to go after all.

🔗Mike Battaglia <battaglia01@...>

6/7/2008 6:27:34 AM

> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
> > At the very least, we might be able to free people from their
> > misconceptions about microtonal music consisting of "weird, dark,
> > dissonant quarter-tones."
> >
> > -Mike
> >
> Doing that is on the one hand very simple, and on the other,
> impossible. At least, this has been my experience. For on the one
> hand, it is as easy as pie to make very microtonal music that is
> downright pretty and immediately appealing to plenty of people, and
> on the other, if you do mention that it's "microtonal", you get
> variations on a theme which boils down to "no it couldn't be because
> it doesn't sound weird, dark, and dissonant" (or sometimes "not
> Indian/Arabic/etc").

Haha, yeah. My goal is to make microtonal music that is pretty and
appealing, but different enough to sound "new" and "interesting" while
not necessarily sounding "weird" and "dark." Of course, explaining
this to most people proves to be pretty difficult, as you usually hear
with "I think it'll sound weird no matter what because what we like is
all a cultural thing and we're used to 12tet" and blah blah.

> So as far as I have seen the real problem might be a definition of
> "microtonal" which is simply going to move about in order to retain a
> negative connotation. By negative connotation I don't just mean
> "bad", but exclusive, cf. the term "xenharmonic".

Yeah, I'm a bit confused about that - is a 6:7:9 subminor triad, for
example, "xenharmonic?" On the one hand, it sounds quite harmonic and
pleasing and consonant, and yet it is still a "new" sound that isn't
available in 12tet. On the other hand, it isn't like completely
foreign and different either. Which one of these is commonly
considered "xenharmonic?" I hear the definition tossed around to
incorporate both of these.

🔗Caleb Morgan <calebmrgn@...>

6/7/2008 6:47:02 AM

--- On Sat, 6/7/08, Mike Battaglia <battaglia01@...> wrote:

> From: Mike Battaglia <battaglia01@...>
> Subject: [tuning] Music Theory (was Re: How to keep discussions on-
> Furthermore, this chord:
>
> D F A d' f#'
...
...
> -Mike

(of course jazz theory "sucks"--it's purpose is simply to enable communication between musicians who share a common practice. It's a communicative, not an explanatory or generative kind of theory...)

this chord: > D F A d' f#

the lower the original D, the more of a root it is...
high enough, and the root here is Bb, (A is 15) and F# is perhaps 25

or if the lowest D is high enough, the root could be G, and then F approximates 7 and f#' approximates 15

or it's just a good old sweet-and-sour major-minor third 014-ish thingy, ala Stravinsky. Don't play this in a jazz session. Assert frequently, and it will sound right.

There are limits to how low a root can be--I'd put the limit around 16 hz--the approximate "flicker fusion" threshold.

I'm all for multipersectivismthingamajigglism, but when I read "quantum" I reach for the little button that gets me to the next post...I've never regretted this, but maybe someone will find some connection between things quantum and music theory.

🔗Mike Battaglia <battaglia01@...>

6/7/2008 6:54:09 AM

On Sat, Jun 7, 2008 at 6:54 AM, Kraig Grady <kraiggrady@...> wrote:
>
> The best way to answer this is to give it to a string or wind or brass
> group and see what they play.I think you will find that whoever has the
> third will lower it so 5/4 is at least 'informing' the intonation. but
> if we ran the chord throughout a big variety of music we would find
> different intonation used in different times depending on , for one, the
> emotional characteristic of the passage. At least this is what i hear
> and/or imagine i hear. I also think different composers imply different
> intonation and i think gene smith was on the right course here, whether
> his conclusions would be completely consistent by what players do, might
> not be the case. Joe Monzo has also implied such ideas. I would only add
> that when these composers overlapped with passages that were like others
> before them, it seems an ensemble might revert to that way of thinking
> in part. That intonation can vary all the time and moment to moment
> might be exactly what humans are doing.....making our knowledge of what
> we are doing endless.

Definitely. I've heard choirs sing in 7-limit just before, and Jazz
bands often play in up to 11-limit just (if a horn section is playing
a C7#11 chord, for example, that F# will often be a full quarter tone
flat to be in line with the 11th harmonic.

And so the question is, is there anything that determines -WHY-
certain intervals sound the way that do? I hear string quartets play
minor chords as both having 19/16 in it and as having 6/5 in it -
sometimes even as having 7/6 in it (although that one's more rare).
But when we hear C-Eb on a piano, what determines how we hear it? Do
we go towards the nearest JI ratio? Which is the nearest JI ratio? Is
it the nearest 5-limit one? Or the nearest ratio under a certain
threshold of perceptibility? Or what?

-Mike

🔗Mike Battaglia <battaglia01@...>

6/7/2008 6:56:57 AM

> (of course jazz theory "sucks"--it's purpose is simply to enable
> communication between musicians who share a common practice. It's a
> communicative, not an explanatory or generative kind of theory...)

Indeed it does. If we could make microtonal music so communicative so
as to expedite its use in jazz... or at least find a way to not have
to discard the current jazz vocabulary... that would be great.
Unfortunately, the two approaches often give different results and
predictions as to how things "should" sound.

> this chord: > D F A d' f#
>
> the lower the original D, the more of a root it is...
> high enough, and the root here is Bb, (A is 15) and F# is perhaps 25
>
> or if the lowest D is high enough, the root could be G, and then F
> approximates 7 and f#' approximates 15
>
> or it's just a good old sweet-and-sour major-minor third 014-ish thingy, ala
> Stravinsky. Don't play this in a jazz session. Assert frequently, and it
> will sound right.

I play it in a jazz session sometimes just for that sound - definitely
not if I'm trying to play old-school "traditional" jazz. It's a more
modern sound. What do you mean by "014"?

-Mike

🔗Mike Battaglia <battaglia01@...>

6/7/2008 7:04:23 AM

I think the problem is that if we're describing things in terms of
rational multiples, then we have to take chords like 16:19:24 and
factor prime numbers back out of them and such to see how they're
related. Which is hard. If I had a complicated chord I wanted someone
to play and I wrote 31:49:59:68:72:75, that's going to take a pretty
long time to figure out what it is. That kind of notation is useful
for describing theoretical chords on this forum, but not so for more
fast-paced or improvisational music (such as jazz). And I don't mean
jazz in its "traditional" sense as in what chords are classically used
in the genre and such -- I mean real, down to earth jazz where
experimentation is the driving force and people are looking for new
sounds to play with in real time.

It's hard to read numbers like 31:49:59:68:72:75 because you have to
do all of this work of factoring different numbers and such. Actually,
it might be easy if it turns out that P=NP. We'll see.

-Mike

🔗Kraig Grady <kraiggrady@...>

6/7/2008 7:19:37 AM

Mircotones is already easy enough, just down load a tuning from scala and let it rip. one doesn't have to know anything.
but 31 is way easier than 72. first it makes sharps and flats different then puts a note between the natural and the sharp , a plus. between a natural and a flat , a minus. no one should have a problem understanding that. i have never had a problem explaining harmonics to people. Here at the local university of wollongong, you have students that can't read music writing in just intonation with PD, so i don't buy it. it isn't that hard and the school teaches this stuff to all the students.
how many soft synth have harmonic controls already . people can use these things and that isn't any easier than tuning.

Add to the easy books Lou harrison's music primer. It has lots on intonation and maybe it is good to start with pentatonics. if fact i have gone back to them, and i can tell you, they are not as understood as one would think, especially if you look at how different ones interact within a larger tuning.

Maybe everyone should be taught an easy way to write for orchestra.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> > David Doty wrote a fine book to teach JI. Kyle Gann has info up also on
> > his site.
> > There are already plenty of resources for anyone interested that is
> > willing to go beyond having it handed to them without them having to
> > think at all.
> > To add, subtract, multiply and divide will suffice
>
> There are a lot of people who are amazing musicians who don't even
> think in terms of theory. They can play amazingly well entirely by
> ear. Most of the popular musicians to come out of the 20th century, in
> fact. We should make it easy for THESE people to get into microtonal
> music as well - simply because it will brighten everyone's life. In
> addition, there are the musicians who think in terms of theory but
> eschew the mathematics involved in JI as being "too complicated"... as
> well as the fact that most of us don't have an instrument to play on.
> Even though you and I think that JI is simple and fairly straight
> forward, as soon as I mention "the 3rd overtone of the 7th overtone,
> so the 21st overall overtone" these people are already lost.
>
> And it isn't because they are lazy or poor musicians. It has to do
> with some kind of deficiency in their education that they doubt
> themselves mathematically. but that's okay, because they're still good
> musicians.
>
> There are a lot of different kinds of musicians... I think it to be a
> worthwhile pursuit to make and popularize a system that is accessible
> to -everyone-. At least, accessible in the sense that it builds off of
> what we have now, rather than the alternative, which is to discard the
> whole system in favor of something new.
>
> In other words, note names like C D E F... etc should have some kind
> of place in JI. Maybe 72-tet is the way to go after all.
>
>

🔗Kraig Grady <kraiggrady@...>

6/7/2008 7:25:40 AM

when i hear the piano i hear 12 ET intervals, and they often confuse me as i am not sure what it is supposed to be

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> On Sat, Jun 7, 2008 at 6:54 AM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>> wrote:
> >
> > The best way to answer this is to give it to a string or wind or brass
> > group and see what they play.I think you will find that whoever has the
> > third will lower it so 5/4 is at least 'informing' the intonation. but
> > if we ran the chord throughout a big variety of music we would find
> > different intonation used in different times depending on , for one, the
> > emotional characteristic of the passage. At least this is what i hear
> > and/or imagine i hear. I also think different composers imply different
> > intonation and i think gene smith was on the right course here, whether
> > his conclusions would be completely consistent by what players do, might
> > not be the case. Joe Monzo has also implied such ideas. I would only add
> > that when these composers overlapped with passages that were like others
> > before them, it seems an ensemble might revert to that way of thinking
> > in part. That intonation can vary all the time and moment to moment
> > might be exactly what humans are doing.....making our knowledge of what
> > we are doing endless.
>
> Definitely. I've heard choirs sing in 7-limit just before, and Jazz
> bands often play in up to 11-limit just (if a horn section is playing
> a C7#11 chord, for example, that F# will often be a full quarter tone
> flat to be in line with the 11th harmonic.
>
> And so the question is, is there anything that determines -WHY-
> certain intervals sound the way that do? I hear string quartets play
> minor chords as both having 19/16 in it and as having 6/5 in it -
> sometimes even as having 7/6 in it (although that one's more rare).
> But when we hear C-Eb on a piano, what determines how we hear it? Do
> we go towards the nearest JI ratio? Which is the nearest JI ratio? Is
> it the nearest 5-limit one? Or the nearest ratio under a certain
> threshold of perceptibility? Or what?
>
> -Mike
>
>

🔗Jon Szanto <jszanto@...>

6/7/2008 8:30:06 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> But if you insist, it is MUSIC that does it, not talk and theory!
> Useful, yes but only as supplements to the acts of the dreamers.

There is strong evidence to support the fact that Kraig and I were
separated at birth. Except for the fact that we don't look much alike,
and are different ages. Nonetheless, I am in total concurrence with
his thoughts above.

🔗Carl Lumma <carl@...>

6/7/2008 12:44:11 PM

Mike wrote:
> > Plenty of fine musicians and theorists have been driven off
> > this list over the years due to the high message volume.
> > And that was back when the messages did frequently contain
> > exciting new discoveries. A tremendous amount of knowledge
> > has been aggregated here, and it's worth caring about.
> > There's a tremendous amount of potential here too, but as
> > it stands I don't think this forum is ready for the rapid
> > growth the topic of microtonal music is about to experience.
> > Maybe it loses its central position, and maybe that's overdue
> > anyway, I don't know.
>
> I don't think it's going down, rather I think it's headed up.
> This stuff is amazing. It is merely in its infancy.
>
> I don't think that everything has been figured out at all yet,

It is in its infancy and there lots of important open questions.
But we do have a very solid foundation that allows us to frame
the most powerful questions. It was built from the shared
knowledge and experiences of dozens of people, including killer
players, choir directors, composers, physicists, mathematicians,
computer programmers, historians, wikipedians, independent
researchers, and at least one world-class neuroscientist.

> Honestly, it just plain sucks. I had to do years of independent
> research into this stuff to explain just a few of the holes in
> the way theory is usually taught in schools.

That's a common way people arrive here. They've done a ton
of independent research and don't know anyone else who knows
anything about the subject at all, so they assume they're an
expert. Honestly, that's the opinion I had when I joined.
I was quickly put in my place, and 11 years later I actually
am an expert, although there are still many concepts I don't
understand.

> At the very least, we might be able to free people from their
> misconceptions about microtonal music consisting of "weird,
> dark, dissonant quarter-tones.

The best way to do that is by making music. And it's
happening. There's a lot to be said for experimenting with
new tunings, but I think theory has a big role to play too.
You can hear as much in the music of artists like Petr Parizek,
Gene Ward Smith, Igliashon Jones, Aaron Johnson, Kraig Grady,
Marcus Satellite, and Stephen James Taylor to name a few.
That said there is also such a thing as too much theory, and
what we here there is silence.

-Carl

🔗Carl Lumma <carl@...>

6/7/2008 12:53:06 PM

> So to restate the question:
>
> Why do we sometimes hear intervals "guided" to their nearest
> match in a harmonic series, and why do we sometimes hear them
> as new entities in their own right with different feelings and
> characters to them?
>
> Or, in a more general sense, what causes someone to hear a
> certain interval as a mistuned form of another interval?
>
> OR, in its *broadest* sense, what causes someone, when
> experiencing a phenomenon, to view that phenomenon as an
> altered version of another phenomenon?
>
> Sometimes we get into "well the brain does this" or "the brain
> does that," and I think those answers often fall short of
> the truth.
>
> -Mike

Hi again Mike! I'm a practical guy. I believe that if you
ask a question, you ought to be prepared to hear an answer.
Not everyone is like that though. In particular, some schools
of philosophy have carved out a niche by asking questions and
being forever unsatisfied with answers of any kind. That's
apparently good enough to get by in some university departments
but it won't cut the mustard here. So let me first ask you
if you can imagine a hypothetical answer that would satisfy
you. In other words: what form of answer are you looking for?
If you can imagine being satisfied by *some* answer, let me
know what shape that answer might hav and I can check if the
answer that satisfies me might also satisfy you. If I think
it does I'll let you know and I'm happy to try to explain it
to you. You're still under no obligation to like it of course.
If it doesn't, then I can let you know that your question is
still an open problem and maybe we can pursue afresh.

-Carl

🔗Carl Lumma <carl@...>

6/7/2008 1:19:54 PM

Mike wrote:
> There are a lot of people who are amazing musicians who don't even
> think in terms of theory. They can play amazingly well entirely by
> ear.

Absolutely. But they all play in 12! Their astonishing ears
have the benefit of centuries of music theory in the form of
the instruments they play, and the music they hear around them.

We have jazz because the piano embodies a very powerful music
theory. Drop it in front of someone who isn't boxed in by
the existing repertoire and you'll get wonders. But no such
instruments exist for microtonal music. With the possible
exception of refretted guitars. But you still have to know
which divisions to pick. We're just starting to see keyboards
arrive and it will take a generation or two to get the first
William Byrd. You could say Scott Joplin was the Byrd of jazz,
Tatum the Bach, and Monk the Beethoven.

As stated in my previous message, I think if you compare the
music of quartertone composers, or microtonal musicians who
aren't using the theory of Partch, Erv Wilson, or the "regular
mapping paradigm" of this list (which includes the theories
of Partch and Wilson), or something similar... if you compare
that stuff with the output of people who ARE using those
theories... you'll find it sucks in comparison. That's my
opinion anyway, and I'd be interested if you agree. I can
point you to mp3s if you like.

> We should make it easy for THESE people to get into microtonal
> music as well - simply because it will brighten everyone's life.

Yes. And the way to do it is by building new instruments
and creating inspiring music and having a group of theorists
who are happy to field questions.

> In other words, note names like C D E F... etc should have
> some kind of place in JI. Maybe 72-tet is the way to go
> after all.

Well the sagittal notation system developed here is one
attempt at that. But personally I doubt there will be a
successful standard. Notation isn't popular enough to
drive one. Instead I think we should have score editing
software that is flexible enough to support custom
notations.

-Carl

🔗Herman Miller <hmiller@...>

6/7/2008 1:24:22 PM

Mike Battaglia wrote:

> Hahaha! Yeah, I've gotten that vibe. The concept of irrational
> intervals standing on their own as musical entities, rather than being
> "approximations" to rational ones, however, is something that needs to
> be brought into consideration. There are huge inconsistencies in the
> way microtonal music is often broken down... Starting with the notion
> that 12tet "approximates" JI. And yet, it does...

One of the useful innovations that, so far as I know, originated on this list is the idea of EDO (equal divisions of the octave). If 12-ET is an "equal temperament", that implies an approximation. But on the other hand, you can think of 12-EDO as simply dividing the octave into 12 equal parts (on a logarithmic pitch scale).

> Honestly, it just plain sucks. I had to do years of independent
> research into this stuff to explain just a few of the holes in the way
> theory is usually taught in schools. If we could REALLY get at least
> the CURRENT revelations of microtonal theory nailed into a consistent
> axiomatic system, then we could teach it to the average music student
> much more effectively. It might not be possible to represent every
> possible musical statement in some kind of axiomatic "theory," but at
> least we can fix the current one so that it isn't inconsistent.

Much of the work on the tuning-math list is centered around the idea of building a unified system that encompasses JI, ET, and everything in between. Paul Erlich's paper in Xenharmonikï¿½n 18 ("A Middle Path") is a first step in that direction. Dave Keenan and George Secor's paper on Sagittal notation in the same issue provides a means of notating JI and ET in a single, unified system that can also be adapted for notating the kinds of tunings described in Paul's Middle Path paper. Erv Wilson's golden-ratio-based scales don't fit neatly into this system, but they do share enough similarities with what we're now calling "rank two temperaments" that many of the same ideas can be applied to both. The main thing that's missing is a simple, readable introduction to the more recent developments since those papers were published.

🔗Carl Lumma <carl@...>

6/7/2008 1:54:32 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
> I think the problem is that if we're describing things in terms of
> rational multiples, then we have to take chords like 16:19:24 and
> factor prime numbers back out of them and such to see how they're
> related. Which is hard. If I had a complicated chord I wanted
> someone to play and I wrote 31:49:59:68:72:75, that's going to
> take a pretty long time to figure out what it is.

Takes about 0.001 seconds on a computer.

-Carl

🔗Torsten Anders <torstenanders@...>

6/7/2008 2:05:47 PM

Dear Carl,

On Jun 7, 2008, at 9:19 PM, Carl Lumma wrote:
> As stated in my previous message, I think if you compare the
> music of quartertone composers, or microtonal musicians who
> aren't using the theory of Partch, Erv Wilson, or the "regular
> mapping paradigm" of this list (which includes the theories
> of Partch and Wilson), or something similar... if you compare
> that stuff with the output of people who ARE using those
> theories... you'll find it sucks in comparison. That's my
> opinion anyway, and I'd be interested if you agree. I can
> point you to mp3s if you like.

Please do :)

Thanks!

Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

🔗Carl Lumma <carl@...>

6/7/2008 2:06:27 PM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> Mircotones is already easy enough, just down load a tuning from scala
> and let it rip. one doesn't have to know anything.

Why have you spent hundreds of hours analyzing patterns
in the eikosany then?

-Carl

🔗Torsten Anders <torstenanders@...>

6/7/2008 2:07:41 PM

Dear Herman,

On Jun 7, 2008, at 9:24 PM, Herman Miller wrote:
> Much of the work on the tuning-math list is centered around the
> idea of
> building a unified system that encompasses JI, ET, and everything in
> between. Paul Erlich's paper in Xenharmonikôn 18 ("A Middle Path")
> is a
> first step in that direction. Dave Keenan and George Secor's paper on
> Sagittal notation in the same issue provides a means of notating JI
> and
> ET in a single, unified system that can also be adapted for
> notating the
> kinds of tunings described in Paul's Middle Path paper. Erv Wilson's
> golden-ratio-based scales don't fit neatly into this system, but
> they do
> share enough similarities with what we're now calling "rank two
> temperaments" that many of the same ideas can be applied to both. The
> main thing that's missing is a simple, readable introduction to the
> more
> recent developments since those papers were published.

I am one of those guys who feels that he likely missed those "recent
developments". Could you just name a few of these new concepts, so I
could dig into the archive for details.

Thanks!

Best
Torsten

🔗Carl Lumma <carl@...>

6/7/2008 3:41:52 PM

> Dear Carl,
//
> Please do :)
>
> Thanks!
>
> Torsten

OK, to start let's talk CDs. I firmly believe that
buying CDs is still warranted if they're microtonal. :)
Here are the CDs everyone on this list should own:

http://lumma.org/music/theory/Top12MicrotonalAlbums.html

Start with the last album here -- you can purchase and
download it as DRM-free mp3s from cdbaby and I personally
guarantee it's on par with any classical masterpiece you
can think of -- especially if you like Nancarrow.

Now let's have a look at the artists I mentioned in my
earlier post...

> artists like Petr Parizek, Gene Ward Smith,
> Igliashon Jones, Aaron Johnson, Kraig Grady,
> Marcus Satellite, and Stephen James Taylor
> to name a few.

It's tragic that Gene's music is no longer on the internet,
but I've temporarily placed one of his pieces here:
http://lumma.org/stuff/Chromosounds.mp3
It's like a deep tissue ear and brain massage. Try it with
headphones! It demonstrates a command of pitch space that
simply cannot be achieved without the hard-hitting theory
Gene used to achieve it.

Petr usually distributes his stuff via yousendit, which is
only temporary. I'd like to take this opportunity to
encourage him to find a more permanent place for his
stuff (perhaps on Google Pages?).

Here's the SoundClick page of one of Igliashon's projects:
http://www.soundclick.com/bands/default.cfm?bandID=376205
(follow the link to the "music" page... you may need to
register to download, I'm not sure)

Here's Aaron Johnson's signature piece:
http://www.akjmusic.com/audio/juggler.mp3
Lots of other good stuff can be found by going to the root
domain there.

Kraig's best CD is on my list above. You can hear a sample:
http://www.anaphoria.com/creation.mp3
All of Kraig's stuff is great. He's a visionary artist and
his music is satisfying on both an entrancing level and an
intellectual level. Quite a feat.

Marcus is also on my CDs list, and you can again buy DRM-free
mp3s from the Amazon link I provided there. His stuff is
also available on iTunes and cdbaby. His website is:
http://marcussatellite.com

Stephen James Taylor is getting to be a big-shot Hollywood
composer. You may have already heard his mircotonal music
in films or on TV! You can hear excerpts in this excellent
radio interview that I'm temporarily hosting here:
http://lumma.org/stuff/SJTonKPFK.mp3

That should keep you busy.

-Carl

🔗Torsten Anders <torstenanders@...>

6/7/2008 4:44:01 PM

Thank you very much for this list!

Best
Torsten

On Jun 7, 2008, at 11:41 PM, Carl Lumma wrote:
> > Dear Carl,
> //
> > Please do :)
> >
> > Thanks!
> >
> > Torsten
>
> OK, to start let's talk CDs. I firmly believe that
> buying CDs is still warranted if they're microtonal. :)
> Here are the CDs everyone on this list should own:
>
> http://lumma.org/music/theory/Top12MicrotonalAlbums.html
>
> Start with the last album here -- you can purchase and
> download it as DRM-free mp3s from cdbaby and I personally
> guarantee it's on par with any classical masterpiece you
> can think of -- especially if you like Nancarrow.
>
> Now let's have a look at the artists I mentioned in my
> earlier post...
>
> > artists like Petr Parizek, Gene Ward Smith,
> > Igliashon Jones, Aaron Johnson, Kraig Grady,
> > Marcus Satellite, and Stephen James Taylor
> > to name a few.
>
> It's tragic that Gene's music is no longer on the internet,
> but I've temporarily placed one of his pieces here:
> http://lumma.org/stuff/Chromosounds.mp3
> It's like a deep tissue ear and brain massage. Try it with
> headphones! It demonstrates a command of pitch space that
> simply cannot be achieved without the hard-hitting theory
> Gene used to achieve it.
>
> Petr usually distributes his stuff via yousendit, which is
> only temporary. I'd like to take this opportunity to
> encourage him to find a more permanent place for his
> stuff (perhaps on Google Pages?).
>
> Here's the SoundClick page of one of Igliashon's projects:
> http://www.soundclick.com/bands/default.cfm?bandID=376205
> (follow the link to the "music" page... you may need to
> register to download, I'm not sure)
>
> Here's Aaron Johnson's signature piece:
> http://www.akjmusic.com/audio/juggler.mp3
> Lots of other good stuff can be found by going to the root
> domain there.

🔗Kraig Grady <kraiggrady@...>

6/7/2008 5:05:04 PM

My answer was for the idea that microtones be accessible to those who want to just jump in. one could download the eikosany any just play around with it.
i spent hours with the eikosany cause i prefer to go deeper into something as opposed to going outside of it:)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> > Mircotones is already easy enough, just down load a tuning from scala
> > and let it rip. one doesn't have to know anything.
>
> Why have you spent hundreds of hours analyzing patterns
> in the eikosany then?
>
> -Carl
>
>

🔗Mike Battaglia <battaglia01@...>

6/7/2008 7:20:26 PM

> That's a common way people arrive here. They've done a ton
> of independent research and don't know anyone else who knows
> anything about the subject at all, so they assume they're an
> expert. Honestly, that's the opinion I had when I joined.
> I was quickly put in my place, and 11 years later I actually
> am an expert, although there are still many concepts I don't
> understand.

By no means do I think I'm an "expert." Why do your interactions with
me have to always take the form of how long you've been here and how
short I have? I have done some research, but there is a lot I don't
understand. I know who a lot of the "well-known"'s are around here,
e.g. you and Graham and George Secor and Charles Lucy and Neil
Haverstick and Aaron Krister Johnson and the list could go on for
quite a long time. I am just trying to learn as much as I can here; I
have my own goals as to the applications I see with this stuff.

> Hi again Mike! I'm a practical guy. I believe that if you
> ask a question, you ought to be prepared to hear an answer.
> Not everyone is like that though. In particular, some schools
> of philosophy have carved out a niche by asking questions and
> being forever unsatisfied with answers of any kind. That's
> apparently good enough to get by in some university departments
> but it won't cut the mustard here. So let me first ask you
> if you can imagine a hypothetical answer that would satisfy
> you. In other words: what form of answer are you looking for?
> If you can imagine being satisfied by *some* answer, let me
> know what shape that answer might hav and I can check if the
> answer that satisfies me might also satisfy you. If I think
> it does I'll let you know and I'm happy to try to explain it
> to you. You're still under no obligation to like it of course.
> If it doesn't, then I can let you know that your question is
> still an open problem and maybe we can pursue afresh.

I don't understand what you mean. I don't know what the answer is.
What is the answer you have arrived at? I have a few different ideas,
but I'm not sure which one it is.

My current guess is that a human being has to be "shown" the way that
a new tone could fit in a chord somehow, or else he/she will be apt to
hear it as a mistuning of something they already know. I think that
the cognitive labeling of it as such is something that changes over
the course of a lifetime - babies are likely to be much more open to
it, adults less so, but older adults perhaps more so again.

Sorry, I'm still waking up right now - my brain's kind of fried. I'll
restate it more precisely once I get the ol motor fired up.

> Absolutely. But they all play in 12! Their astonishing ears
> have the benefit of centuries of music theory in the form of
> the instruments they play, and the music they hear around them.

Absolutely. They know the "intuitive" aspects of music theory. I
suppose what I am trying to do here is to take all of the jumble of
theory ideas that have accumulated over centuries and find places
where there are holes. My above example about how my teacher said I
have to avoid b9's and such over any note except for the root is one
of them. He is right in some cases, not others, and furthermore, WHY
is that the case? What is it about a tempered b9 that's going to cause
this? I would really like to know why, and I don't think there is
anything wrong with that.

Musicians often say that it's bad to ask "why." They say that it's
just better to accept and listen. While when you play, it definitely
is better to accept and listen, there is also no harm in asking "why."

> We have jazz because the piano embodies a very powerful music
> theory. Drop it in front of someone who isn't boxed in by
> the existing repertoire and you'll get wonders. But no such
> instruments exist for microtonal music. With the possible
> exception of refretted guitars. But you still have to know
> which divisions to pick.

Exactly! That is why I'm frustrated. I want to bring microtonality to
jazz, and to the songwriters, and to the rock musicians and the little
kids. I want to come up with a way that makes it easy for musicians
out there to get into this stuff. It is extremely hard to do that
right now for a variety of reasons:

1) Different tuning systems need to be weighed to find out which ones
are best suited for the task. The ideal candidate will be easy to
adjust to, easy to understand, and expressive in its harmonic output.
72tet might be the candidate. It's a great system, in my opinion, but
you can forget about ever making a 72tet guitar (unless it's
fretless). And we need 72tet trumpets and saxes and horns with extra
keys and such to get that rolling.

As for a 72tet keyboard... I haven't found one that I really like yet,
except for the "Z-board" i think it's called was pretty decent.

2) There is currently a lot of math and such involved if you even want
to start playing around with this stuff at all. Assuming you go the
Partch/harmonic series route, you might first get into higher-limit
JI, and JI is math, hah. Another common notion is that 31tet or 53tet
or 72tet are just too many "notes" to deal with per octave, when that
isn't really how it works.

So I suppose the science of pedagogy has to be brought into it.

I had some more reasons, but as stated above, my brain is dead right
now. I was going to say something along the lines of how 31tet might
not be the best idea for specifically "jazz" as it gains better 3rds
at the cost of its fifths, and so all of the quartal voicings that we
know and love will sound pretty warbly. I remember minor 9 chords
being like that.

> We're just starting to see keyboards
> arrive and it will take a generation or two to get the first
> William Byrd. You could say Scott Joplin was the Byrd of jazz,
> Tatum the Bach, and Monk the Beethoven.

And Bill Evans the Debussy, and Herbie the Liszt.

> As stated in my previous message, I think if you compare the
> music of quartertone composers, or microtonal musicians who
> aren't using the theory of Partch, Erv Wilson, or the "regular
> mapping paradigm" of this list (which includes the theories
> of Partch and Wilson), or something similar... if you compare
> that stuff with the output of people who ARE using those
> theories... you'll find it sucks in comparison. That's my
> opinion anyway, and I'd be interested if you agree. I can
> point you to mp3s if you like.

I agree as well. I think that's because "music" to us, as we live in a
western culture, is very harmonic in nature and thus related to the
harmonic series. Partch and Wilson simply expanded the small range of
the harmonic series that we were using, and so it sounds like an
"extension" of the stuff we already know. When I listen to
"quartertone composers," they usually don't strike me as having that
same harmonic quality to them, and so the stuff is more atonal - and
while it's often great anyway, it's only one possible flavor of what's
possible.

Please do point me to some MP3's. I've heard only a handful of
examples that I really like - a few songs off of Easley Blackwood's
Etudes did it for me, but there's this Joel Mandelbaum piece on
youtube that is awesome, and Aaron Johnson has some amazing songs too
(I always liked Melancholic). Hook it up!

> Yes. And the way to do it is by building new instruments
> and creating inspiring music and having a group of theorists
> who are happy to field questions.

And changing the way theory is taught in schools so that it comes from
the perspective of music IN 12tet, not that 12tet is all that there
is.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/7/2008 7:26:07 PM

> Much of the work on the tuning-math list is centered around the idea of
> building a unified system that encompasses JI, ET, and everything in
> between. Paul Erlich's paper in Xenharmonikôn 18 ("A Middle Path") is a
> first step in that direction. Dave Keenan and George Secor's paper on
> Sagittal notation in the same issue provides a means of notating JI and
> ET in a single, unified system that can also be adapted for notating the
> kinds of tunings described in Paul's Middle Path paper. Erv Wilson's
> golden-ratio-based scales don't fit neatly into this system, but they do
> share enough similarities with what we're now calling "rank two
> temperaments" that many of the same ideas can be applied to both. The
> main thing that's missing is a simple, readable introduction to the more
> recent developments since those papers were published.

THAT sounds interesting. Do you have links to those papers or to any
of the "recent developments?" Are they to be found on the tuning-math
list?

-Mike

🔗Mike Battaglia <battaglia01@...>

6/7/2008 7:28:30 PM

> Thank you very much for this list!
>
> Best
> Torsten

Here are a few more:

My favorite Aaron Johnson work: http://www.akjmusic.com/audio/melancholic.mp3

Joel Mandelbaum's 31tet Woodwind Quintet:
http://www.youtube.com/results?search_query=joel+mandelbaum&search_type=&aq=f

🔗Mike Battaglia <battaglia01@...>

6/7/2008 7:40:23 PM

> It's tragic that Gene's music is no longer on the internet,
> but I've temporarily placed one of his pieces here:
> http://lumma.org/stuff/Chromosounds.mp3
> It's like a deep tissue ear and brain massage. Try it with
> headphones! It demonstrates a command of pitch space that
> simply cannot be achieved without the hard-hitting theory
> Gene used to achieve it.

Just curious - I really liked this one. What "theory" did Gene use for
this? I'd really like to know. Why is his music no longer on the
internet? These are the noobish questions I seek release from.

-Mike

🔗Graham Breed <gbreed@...>

6/7/2008 7:45:18 PM

Mike Battaglia wrote:
>> Much of the work on the tuning-math list is centered around the idea of
>> building a unified system that encompasses JI, ET, and everything in
>> between. Paul Erlich's paper in Xenharmonikï¿½n 18 ("A Middle Path") is a
>> first step in that direction. Dave Keenan and George Secor's paper on
>> Sagittal notation in the same issue provides a means of notating JI and
>> ET in a single, unified system that can also be adapted for notating the
>> kinds of tunings described in Paul's Middle Path paper. Erv Wilson's
>> golden-ratio-based scales don't fit neatly into this system, but they do
>> share enough similarities with what we're now calling "rank two
>> temperaments" that many of the same ideas can be applied to both. The
>> main thing that's missing is a simple, readable introduction to the more
>> recent developments since those papers were published.
> > THAT sounds interesting. Do you have links to those papers or to any
> of the "recent developments?" Are they to be found on the tuning-math
> list?

Paul Erlich Middle Path (second hit from Google):

http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-MiddlePath.pdf

George Secor, The Miracle Temperament (another key paper from the same Xenharmonikon):

http://xenharmony.wikispaces.com/space/showimage/Miracle.pdf

Sagittal website:

http://dkeenan.com/sagittal/

Graham

🔗Herman Miller <hmiller@...>

6/7/2008 8:20:08 PM

Torsten Anders wrote:
> Dear Herman,
> > On Jun 7, 2008, at 9:24 PM, Herman Miller wrote:
>> Much of the work on the tuning-math list is centered around the >> idea of
>> building a unified system that encompasses JI, ET, and everything in
>> between. Paul Erlich's paper in Xenharmonikï¿½n 18 ("A Middle Path") >> is a
>> first step in that direction. Dave Keenan and George Secor's paper on
>> Sagittal notation in the same issue provides a means of notating JI >> and
>> ET in a single, unified system that can also be adapted for >> notating the
>> kinds of tunings described in Paul's Middle Path paper. Erv Wilson's
>> golden-ratio-based scales don't fit neatly into this system, but >> they do
>> share enough similarities with what we're now calling "rank two
>> temperaments" that many of the same ideas can be applied to both. The
>> main thing that's missing is a simple, readable introduction to the >> more
>> recent developments since those papers were published.
> > I am one of those guys who feels that he likely missed those "recent > developments". Could you just name a few of these new concepts, so I > could dig into the archive for details.

Graham Breed's page at http://x31eq.com/paradigm.html "The Regular Mapping Paradigm" is a good introduction to some of the ideas and the notation system we've settled on for describing these temperaments. He's also been working on a set of papers that describe the mathematical details of various error and complexity measures. See e.g. "Prime Weighted Errors and Complexity" from June 2006, "More prime errors and complexities" from Jan. 2007, "Parametric scalar badness" from Feb. 2008, "Complete Rank 2 Temperament Searches" from Mar. 2008, "Composite Errors and Complexities" from Apr. 2008.

George Secor and Dave Keenan have continued to revise and update the Sagittal notation system, providing new definitions for extreme precision (Olympian) Sagittal notation and others. I've been attempting to work out the details of how Sagittal notation can be applied to notating different sorts of rank 2 temperaments, including the ones mentioned in Paul's paper. (See the threads on proposed Sagittal notations starting around Dec. 2007.)

🔗Carl Lumma <carl@...>

6/7/2008 8:55:29 PM

Mike wrote:
> > Hi again Mike! I'm a practical guy. I believe that if you
> > ask a question, you ought to be prepared to hear an answer.
> > Not everyone is like that though. [snip]
> > can imagine a hypothetical answer that would satisfy
> > you? [snip]
>
> I don't understand what you mean. I don't know what the answer
> is. What is the answer you have arrived at? I have a few
> different ideas, but I'm not sure which one it is.

You've asked these general questions here several times in
several different messages. I'm trying to figure out why you
keep asking them without modification, despite that I think
I've already tried to answer them. And why don't answers of
the form 'the brain does such and such' satisfy you? Because
those are the kind of answers I tend to give.

> > Absolutely. But they all play in 12! Their astonishing ears
> > have the benefit of centuries of music theory in the form of
> > the instruments they play, and the music they hear around them.
>
> Absolutely. They know the "intuitive" aspects of music theory. I
> suppose what I am trying to do here is to take all of the jumble
> of theory ideas that have accumulated over centuries and find
> places where there are holes. My above example about how my
> teacher said I have to avoid b9's and such over any note except
> for the root is one of them. He is right in some cases, not
> others, and furthermore, WHY is that the case? What is it about
> a tempered b9 that's going to cause this?

Cause what? You seem to be saying the rule doesn't hold.
If that's the case then there's nothing to explain.

> > We have jazz because the piano embodies a very powerful music
> > theory. Drop it in front of someone who isn't boxed in by
> > the existing repertoire and you'll get wonders. But no such
> > instruments exist for microtonal music. With the possible
> > exception of refretted guitars. But you still have to know
> > which divisions to pick.
>
> Exactly! That is why I'm frustrated. I want to bring
> microtonality to jazz, and to the songwriters, and to the rock
> musicians and the little kids. I want to come up with a way
> that makes it easy for musicians out there to get into this
> stuff.

If you want to take jazz chords and retune them (in JI or some
other way), that's a very powerful paradigm to work in and it
could keep lots of people busy for a long time. But you can
only ever come up with a small fraction of what's possible in
microtonality that way. It's more than OK if that's where you
want to go but if you really want to explain why 12-ET theory
is the way it is you may find it very helpful to step outside
12-ET theory for a bit.

> It is extremely hard to do that right now for a variety
> of reasons:
>
> 1) Different tuning systems need to be weighed to find out
> which ones are best suited for the task. The ideal candidate
> will be easy to adjust to, easy to understand, and expressive
> in its harmonic output. 72tet might be the candidate. It's
> a great system, in my opinion, but you can forget about ever
> making a 72tet guitar (unless it's fretless). And we need
> 72tet trumpets and saxes and horns with extra keys and such
> to get that rolling.

Why do we need to pick one system?

Woodwinds generally have plenty of keys to play microtonally
already. The addition of one more valve and/or more precise
slide triggers would make it a lot *easier* to control the
intonation of the trumpet. French horns and trombones and of
course strings are really flexible as is. The main thing
that's lacking is the consciousness. For that, nothing beats
a discrete-pitch generator that a single person can play
polyphonically, i.e. a keyboard. It gets sounds into the ears,
hands, and even the eyes (watching a player piano can be
educational for instance, and generalized keyboards make even
better music visualizers than the halberstadt).

> > As stated in my previous message, I think if you compare the
> > music of quartertone composers, or microtonal musicians who
> > aren't using the theory of Partch, Erv Wilson, or the "regular
> > mapping paradigm" of this list (which includes the theories
> > of Partch and Wilson), or something similar... if you compare
> > that stuff with the output of people who ARE using those
> > theories... you'll find it sucks in comparison. That's my
> > opinion anyway, and I'd be interested if you agree. I can
> > point you to mp3s if you like.
>
> I agree as well. I think that's because "music" to us, as we
> live in a western culture, is very harmonic in nature and thus
> related to the harmonic series. Partch and Wilson simply expanded
> the small range of the harmonic series that we were using,

Partch not only expanded the range of harmonics used, he
threw out the diatonic scale. That's a pretty big step.
Wilson created a system for classifying scales and their
corresponding keyboard mappings and notations, and further
elucidated what goes on when we extend the range of
harmonics used. Among other things.

> and so it sounds like an "extension" of the stuff we
> already know.

It's a *generalization* of what we already know. And if you
do it right, you can indeed explain most everything in common
practice theory (some things are just down to "frozen
accidents").

> Please do point me to some MP3's. I've heard only a handful
> of examples that I really like - a few songs off of Easley
> Blackwood's Etudes did it for me, but there's this
> Joel Mandelbaum piece on youtube that is awesome, and
> Aaron Johnson has some amazing songs too (I always liked
> Melancholic). Hook it up!

See my reply to Torsten.

-Carl

🔗Carl Lumma <carl@...>

6/7/2008 9:08:50 PM

Mike wrote:

> > It's tragic that Gene's music is no longer on the internet,
> > but I've temporarily placed one of his pieces here:
> > http://lumma.org/stuff/Chromosounds.mp3
> > It's like a deep tissue ear and brain massage. Try it with
> > headphones! It demonstrates a command of pitch space that
> > simply cannot be achieved without the hard-hitting theory
> > Gene used to achieve it.
>
> Just curious - I really liked this one. What "theory" did Gene use
> for this? I'd really like to know. Why is his music no longer on
> the internet? These are the noobish questions I seek release from.

Generally speaking, he used the "regular mapping paradigm", to
which Paul's "Middle Path" paper is an introduction:
http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-MiddlePath.pdf

You may also find my TCTMO helpful:
http://lumma.org/music/theory/tctmo

Gene had many different techniques, many of which he shared on
the tuning-math list over the years. Not all of them were ever
understood by anyone else. To give you an idea, his main
composition environment was Maple.

Gene would often work by picking an ET and then writing around
the various linear temperaments available in it. Chromosounds
is in 46-ET; I don't remember the particular linear temperament(s)
used (one could look it up).

Gene left the lists last year and let his domain registration
lapse. I don't know exactly why. He's got lots of other good
music but until I get permission to post it I won't.

-Carl

🔗Graham Breed <gbreed@...>

6/7/2008 9:34:41 PM

Mike Battaglia wrote:

> Exactly! That is why I'm frustrated. I want to bring microtonality to
> jazz, and to the songwriters, and to the rock musicians and the little
> kids. I want to come up with a way that makes it easy for musicians
> out there to get into this stuff. It is extremely hard to do that
> right now for a variety of reasons:

This is where we hit what I call the complexity problem. A lot of us are looking for scales with more and more accurate consonances. Naturally they end up more complex than 12-equal or meantone diatonics. As musicians in general have no problems with the scales they know they'll quite rightly ask why they should worry about anything more complicated.

I think a lot of musicians really have no need to go beyond what they know and there's no point in pushing them. A lot of musicians, for that matter, have no need for equal temperament and are happy with diatonics or even pentatonics. But a certain proportion of musicians will be able to deal with the additional complexity and in a global community there are enough of them to sustain a healthy sub-genre. A lot of jazz musicians will fall into this category, and prog rockers as well.

In some cases the increase in complexity is an advantage. People are actually looking for more subtlety. Why else would the quartertone movement have taken off?

> 1) Different tuning systems need to be weighed to find out which ones
> are best suited for the task. The ideal candidate will be easy to
> adjust to, easy to understand, and expressive in its harmonic output.
> 72tet might be the candidate. It's a great system, in my opinion, but
> you can forget about ever making a 72tet guitar (unless it's
> fretless). And we need 72tet trumpets and saxes and horns with extra
> keys and such to get that rolling.

A blackjack guitar, tuned to 72tet, is perfectly viable. I don't remember if anybody has one yet. Guitars are all we need for rock music. Most orchestral instruments are already very flexible with regards to pitch and quartertone instruments all the better for reaching arbitrary intervals.

Still, blackjack isn't my ideal guitar fretting. It's a bit too complicated. But I'm very interested in magic19 -- see below.

> As for a 72tet keyboard... I haven't found one that I really like yet,
> except for the "Z-board" i think it's called was pretty decent.

Blackjack (miracle21) can work on a remapped halberstadt. Not ideal by any means but enough to explore the territory. For a performance you may even find you don't need that many notes and you can use a special case mapping with exactly the ones you need.

I have a pipe dream of a miracle ensemble. Each instrument plays a different subset of canasta (miracle31) or 72tet if you like. Some will play "pygmy" pentatonics, with chains of approximate 8:7s. Six of those can handle 30 notes between them. Some instruments will play mohajira (7 notes generated by neutral thirds). Three such cover the 21 notes of blackjack. Some instruments will handle the full decimal scale, and four such give canasta with a bit of overlap. Maybe some of the instruments will be able to handle the full 31 note gamut. But the idea is to share the notes around so that each instrument and each instrumental part is relatively simple.

It helps that miracle breaks down into some interesting subsets. Pygmy pentatonics and mohajira are good, simple scales in their own right. Great for musicians who find 12tet already has too many notes.

> 2) There is currently a lot of math and such involved if you even want
> to start playing around with this stuff at all. Assuming you go the
> Partch/harmonic series route, you might first get into higher-limit
> JI, and JI is math, hah. Another common notion is that 31tet or 53tet
> or 72tet are just too many "notes" to deal with per octave, when that
> isn't really how it works.

The "too many notes" argument is why I use linear temperaments. Miracle works fine with 21 notes. You only need to teach those 21 notes. Sure, it's more complicated than 12 notes, but the more adventurous musicians can handle it. It has some really cool intervals. You can teach it much the way you do any other super-scale -- nice chords, nasty chords, scales, melodies. There are more consonances to remember but that's the whole point.

Magic works with only 19 notes and you can do a fair bit with 16. That means it isn't significantly more complex than meantone in the 7-limit. It doesn't naturally break down into simpler scales but I've cracked the notation problem now. It naturally supports chords built by chaining thirds. There are more of them than in 12tet and more ways of connecting them but not so difficult compared to the outer reaches of jazz harmony.

In both cases you can tie chords to the harmonic series if you want to. If your students object to that you can talk about different thirds: subminor-minor-neutral-major-supermajor.

> So I suppose the science of pedagogy has to be brought into it.

Experience is what we need. Experience of making music and experience of passing the knowledge to other musicians.

> I had some more reasons, but as stated above, my brain is dead right
> now. I was going to say something along the lines of how 31tet might
> not be the best idea for specifically "jazz" as it gains better 3rds
> at the cost of its fifths, and so all of the quartal voicings that we
> know and love will sound pretty warbly. I remember minor 9 chords
> being like that.

I agree that meantone (of which 31tet is almost optimal) doesn't work for 9th chords. That's why I draw a distinction between 7-limit and 9-limit temperaments. Meantone is, to me, a 7-limit temperament. Magic (22&19) is the simplest 9-limit temperament. So for mainstream jazz harmony the next step is magic. I've got 19 notes tuned up now, and they work well enough. It means chords sound familiar but smoother than in 12tet. For mainstream harmony the problem is that you can't chain many fifths before you run off the edge. For me the problem is that I miss those spicy 11-limit intervals. There are some approximate 11:8s though and one neutral third!

If you want more fifths the solution seems to be schismatic/garibaldi (12&29). 29 notes work well enough and fit a halberstadt layout although it's a stretch. It is more complex than magic. Maybe the familiarity of a fifth generator will make up for that. It's the great neverwozzer of temperament classes -- implied in theories of different cultures but never properly taken up.

For more exotic intervals or more accuracy the answer is miracle. It looked like the holy grail of 11-limit harmony when it was re-discovered in 2001 and I don't think any recent developments have changed that.

You may also have a look at orwell (22&31). It doesn't have a unique selling point in the 9-limit but it's similar to the other ones I mentioned and simpler than miracle in the 11-limit.

>> As stated in my previous message, I think if you compare the
>> music of quartertone composers, or microtonal musicians who
>> aren't using the theory of Partch, Erv Wilson, or the "regular
>> mapping paradigm" of this list (which includes the theories
>> of Partch and Wilson), or something similar... if you compare
>> that stuff with the output of people who ARE using those
>> theories... you'll find it sucks in comparison. That's my
>> opinion anyway, and I'd be interested if you agree. I can
>> point you to mp3s if you like.
> > I agree as well. I think that's because "music" to us, as we live in a
> western culture, is very harmonic in nature and thus related to the
> harmonic series. Partch and Wilson simply expanded the small range of
> the harmonic series that we were using, and so it sounds like an
> "extension" of the stuff we already know. When I listen to
> "quartertone composers," they usually don't strike me as having that
> same harmonic quality to them, and so the stuff is more atonal - and
> while it's often great anyway, it's only one possible flavor of what's
> possible.

We don't all live in a western culture :-P

My rather hubristic opinion is that although I'm not even a competent musician I do have a great theory. And that theory's good enough to lead me to some worthwhile music if nobody gets there first. It's naturally difficult to interest musicians without musical examples.

Graham

🔗Mike Battaglia <battaglia01@...>

6/7/2008 10:54:09 PM

> You've asked these general questions here several times in
> several different messages. I'm trying to figure out why you
> keep asking them without modification, despite that I think
> I've already tried to answer them. And why don't answers of
> the form 'the brain does such and such' satisfy you? Because
> those are the kind of answers I tend to give.

Sorry, I don't remember your answering them in previous threads. But
rather than bicker back and forth forever about this, let me just
clarify what I am asking:

The paradigm in which the "brain" is solely responsible for these
effects, while useful for part of the answer, is incomplete because it
ignores the huge role that psychology plays in music.

If I go and play, let's say, Pachelbel's Canon in 5-limit just (I've
heard this done before), then let's say when the A major chord goes to
B minor (a root movement of a minor whole tone), a lot of people who
aren't used to the sound find that root movement particularly
offensive.

What is happening is that they hear it as a "flat" or "out-of-tune"
version of the tempered version. They don't hear it as a new entity in
its own right. What causes this?

And the reason I don't think the answer lies SOLELY within the "brain"
is that babies, for example, are much more likely to view new things
as actually being "new" rather than as altered versions of previously
experienced things.

I think that the temperament (no pun intended) of the individual has a
lot to do with how open they are to new forms of music and the like.
In fact, I think the direct answers to these questions are probably
psychological or even spiritual in nature and have nothing to do with
music. My specific question is how much of the way this works is the
"brain," and how much is the person's bias? How does that work, what
is that fine line, and how do the two elements interplay?

> Cause what? You seem to be saying the rule doesn't hold.
> If that's the case then there's nothing to explain.

It does hold. If you play C E G Bb D F that F will sound pretty "weak"
in a straight ahead jazz context, although in modern forms of jazz
where experimentation is law then that chord is fairly common. There
are situations where a b9 over the m3 in a minor chord will sound
good, although that might be better expressed as a #8, and the two may
only be enharmonically equivalent in 12tet. So is it only b9's...? Is
it a certain JI interval here that is causing this phenomenon?

I don't know why equal tempered b9's often sound weak if played over
something that isn't the root. I suspect the answer has to do
something with beat frequencies that interfere with the stability of
the chord, but I'm not sure why. But it would be nice to elucidate
concepts like that so that in schools they are taught with more
clarity.

> If you want to take jazz chords and retune them (in JI or some
> other way), that's a very powerful paradigm to work in and it
> could keep lots of people busy for a long time. But you can
> only ever come up with a small fraction of what's possible in
> microtonality that way.

It's more that I want to develop or utilize a consistent microtonal
system, whether blackjack or 72tet or otherwise, build instruments
using that system, give these instruments to improvisational
musicians, and stand back and watch sparks fly. This field of music is
currently dominated by computer-generated, preplanned compositions as
that is really the only place for now that one can get at that stuff.
It would be amazing to see what this stuff would sound like for on the
spot, improvised music between other musicians... That's what jazz is
about to me, not so much taking traditional jazz and retuning it to a
different system. Jazz musicians are always in the spirit of
experimenting with new sounds, and I think it would be amazing to give
someone like Ralph Alessi or Kurt Rosenwinkel and their respective
groups access to new sounds like these.

We are starting to see microtonal keyboards come out, which is
exciting, although for a lot of musicians they are prohibitively
expensive (for me as well right now). But the progress being made is
exciting.

> It's more than OK if that's where you
> want to go but if you really want to explain why 12-ET theory
> is the way it is you may find it very helpful to step outside
> 12-ET theory for a bit.

Hence my problem with the way music theory is taught in schools. The
b9 over yada yada example above is just the most convenient example of
this I could remember. It screwed my mental model of harmony entirely
up when I heard that "b9 rule" above, as it wasn't taught in terms of
music, but in terms of 12tet steps.

> The main thing that's lacking is the consciousness. For that, nothing beats
> a discrete-pitch generator that a single person can play
> polyphonically, i.e. a keyboard. It gets sounds into the ears,
> hands, and even the eyes (watching a player piano can be
> educational for instance, and generalized keyboards make even
> better music visualizers than the halberstadt).

Alas, if only they were less expensive...

> It's a *generalization* of what we already know. And if you
> do it right, you can indeed explain most everything in common
> practice theory (some things are just down to "frozen
> accidents").

Interesting. If work has been done in extending common practice theory
to non-meantone 7- and 11-limit music, I am very interested in seeing
it. How does a 7/6 subminor 7th tetrad fit into common practice
theory? How do 4-part chord voicings and voice leading techniques
extend out to the 7-limit realm, or 5-part techniques out to the
11-limit realm?

The main place where common practice theory breaks down for me is that
it fails to explain why certain chords are heard the way they are. It
doesn't explain why the JI Pachelbel's canon root movement by minor
whole tone from V to vi sounds as weird as it does. This concept of
things sounding "good" or "bad" has been used sometimes in common
practice theory (you aren't supposed to double the third in a major
chord, for example) because that was felt to destabilize the chord.
Nowadays that doesn't sound so bad. So I think that rather than add
random corollaries to common practice theory about what sounds good or
bad, we should take the concept up to a higher level of abstraction
and figure out WHY things sound good or bad, and how the psychology
involved works. Obviously it couldn't be used to generate music, but
it is still something to think about, and would offer an improvement
on the current system.

🔗Carl Lumma <carl@...>

6/8/2008 12:23:23 AM

Hi Mike,

> The paradigm in which the "brain" is solely responsible for
> these effects, while useful for part of the answer, is
> incomplete because it ignores the huge role that psychology
> plays in music.

Human psychology varies greatly by individual and by trial
(what kind of day you're having), so it's difficult to
formalize anything about it in a music theory.

Another thing that's usually not formalized are priming
effects -- otherwise known as musical context. These effects
again will vary by listener and by trial. In adaptive tuning
schemes, one can treat past notes just like simultaneous
notes but subject to a decay process that weakens the
interactions. IIRC John deLaubenfels' system did something
like that, and other adaptive tuning schemes probably do
too (my own pet adaptive tuning scheme makes use of it).

Finally, at the level of cognitive psychology and
psychoacoustics (a branch of cog psy actually), effects are
largely listener-invariant. So I think it's a good place
to start.

> If I go and play, let's say, Pachelbel's Canon in 5-limit
> just (I've heard this done before), then let's say when the
> A major chord goes to B minor (a root movement of a minor
> whole tone), a lot of people who aren't used to the sound
> find that root movement particularly offensive.
>
> What is happening is that they hear it as a "flat" or
> "out-of-tune" version of the tempered version. They don't
> hear it as a new entity in its own right. What causes this?

Assuming that people do complain about this and that it is
because of the smaller whole step, what you have is a
tendency to hear *melodic* intervals in terms of other melodic
intervals. This is very different from the whole
16:19 v. 6:5 thing. The theory of harmonic approximation is
on solid footing at this point. Our understanding of a similar
concept for melodic intervals is more formative.

However, a guy named David Rothenberg has published papers
about it. The basic idea is that the human memory can't cope
with all the pitches in a melody directly, but it can accurately
measure the size of melodic intervals as they come in and deduce
the scale that way. It hears Adown Bup Aup and it knows the
last note should be B above the first. The catch is, this is
a skill like riding a bike. Takes a while to learn but you
never forget. But you have to do it for every different scale.
Say the diminished scale is a recumbent and Paul Erlich's
pajara scales are like unicycles. The first time you get on a
unicycle you might try to ride it like a regular bike, but
you'll fall on your ass. You may then complain about unicycles.
But if you practice until you can do it you then may praise
unicycles.

Rothenberg's model actually makes predictions. For example,
as you morph one scale to another (by sliding the pitches
around), it predicts when you'll start to call it some tuning
of the new scale instead of some tuning of the old. These
predictions can be tested experimentally, but so far haven't
been (to my knowledge).

> > Cause what? You seem to be saying the rule doesn't hold.
> > If that's the case then there's nothing to explain.
>
> It does hold.

You gave cases where it doesn't. It's so incredibly easy
to make up music rules that hold sometimes and not others
that they're usually not worth thinking about.

> If you play C E G Bb D F that F will sound
> pretty "weak" in a straight ahead jazz context,

C E G Bb D is a nice 4:5:6:7:9 chord in 12. The F is
pretty far from the 21 that might sound nice in the chord.

> although in
> modern forms of jazz where experimentation is law then that
> chord is fairly common.

Sure, you can use any perception -- positive or negative --
to create a good musical effect. That doesn't invalidate
the perception though.

> There are situations where a b9 over the m3 in a minor
> chord will sound good, although that might be better
> expressed as a #8, and the two may only be enharmonically
> equivalent in 12tet. So is it only b9's...? Is it a
> certain JI interval here that is causing this phenomenon?

I will say that one reason I don't like the rule is that
it talks about one interval alone without considering the
rest of the intervals in the chord. When evaluating chords,
generally there are two things I consider: 1. how strong is
the harmonic series interp (e.g. 4:5:7:9) and 2. how many
of the dyads within the chord are consonant. Both of these
necessitate looking at the *whole chord*, not just which
root some interval is built on top of.

> It's more that I want to develop or utilize a consistent
> microtonal system, whether blackjack or 72tet or otherwise,
> build instruments using that system, give these instruments
> to improvisational musicians, and stand back and watch
> sparks fly.

You and me both. We could buy a bunch of AXiSes and refretted
guitars and pitch a workshop to Berklee. I'd bet they'd go
for it. Might even give us some money.

> This field of music is currently dominated by
> computer-generated, preplanned compositions as that is really
> the only place for now that one can get at that stuff.

Petr's music is generally improvisational in nature.

> > It's more than OK if that's where you
> > want to go but if you really want to explain why 12-ET theory
> > is the way it is you may find it very helpful to step outside
> > 12-ET theory for a bit.
>
> Hence my problem with the way music theory is taught in schools.
> The b9 over yada yada example above is just the most convenient
> example of this I could remember. It screwed my mental model of
> harmony entirely up when I heard that "b9 rule" above, as it
> wasn't taught in terms of music, but in terms of 12tet steps.

The very term "b9" is completely tied to the diatonic scale if
not to the 12-ET kernel as well and if you're using it in your
line of questioning you haven't stepped outside 12 in the way
I'm suggesting here.

> > The main thing that's lacking is the consciousness. For that,
> > nothing beats a discrete-pitch generator that a single person
> > can play polyphonically, i.e. a keyboard. It gets sounds into
> > the ears, hands, and even the eyes (watching a player piano
> > can be educational for instance, and generalized keyboards
> > make even better music visualizers than the halberstadt).
>
> Alas, if only they were less expensive...

The AXiS is competitively priced with halberstadt MIDI keyboards.
I looked at several by Kawai and Yamaha that were as expensive
just the other day. They were also total junk FWIW.

> > It's a *generalization* of what we already know. And if you
> > do it right, you can indeed explain most everything in common
> > practice theory (some things are just down to "frozen
> > accidents").
>
> Interesting. If work has been done in extending common practice
> theory to non-meantone 7- and 11-limit music, I am very
> interested in seeing it.

Fokker and the Dutch 31-toners did a bit of this, and some
of the effects of 7-limit harmony on voice leading are
understood by barbershop arrangers. But if you're looking
for a detailed approach to extended JI and the diatonic
scale, I'd say the the door is fairly open. Have at it and
post your results here as you go! Oh, you might want to
search in the 1/1 archives if that's possible (journal of
the JI Network).

But again, I didn't say extending common practice theory,
I said generalizing it. Probably best to have a look at
the papers you've been referred to at this point if you're
interested in that route.

> I think that rather than add random corollaries to common
> practice theory about what sounds good or bad, we should take
> the concept up to a higher level of abstraction and figure
> out WHY things sound good or bad

Well you've come to the right place then!

-Carl

🔗Mike Battaglia <battaglia01@...>

6/8/2008 2:00:34 AM

> Paul Erlich Middle Path (second hit from Google):
>
> http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-MiddlePath.pdf
>
> George Secor, The Miracle Temperament (another key paper
> from the same Xenharmonikon):
>
> http://xenharmony.wikispaces.com/space/showimage/Miracle.pdf
>
> Sagittal website:
>
> http://dkeenan.com/sagittal/
>
> Graham

Much appreciated.

> This is where we hit what I call the complexity problem. A
> lot of us are looking for scales with more and more accurate
> consonances. Naturally they end up more complex than
> 12-equal or meantone diatonics. As musicians in general
> have no problems with the scales they know they'll quite
> rightly ask why they should worry about anything more
> complicated.

Ah, yeah. Those people might screw around with it if we yelled "HEADS
UP" and forcefully threw a 17- or 19-tone guitar directly at them.
They are also the people least likely to like the way it sounds, as if
these people are already burned into 12-equal, then they're unlikely
to like the sound of much else short of 36-equal or 72-equal or
something. And those are considerably more difficult to get into.

> I think a lot of musicians really have no need to go beyond
> what they know and there's no point in pushing them. A lot
> of musicians, for that matter, have no need for equal
> temperament and are happy with diatonics or even
> pentatonics. But a certain proportion of musicians will be
> able to deal with the additional complexity and in a global
> community there are enough of them to sustain a healthy
> sub-genre. A lot of jazz musicians will fall into this
> category, and prog rockers as well.

Definitely. There is also an interesting shade of musician that can
deal with the added complexity provided it is explained to them in a
certain way that they don't have mental defenses against. For me, math
and scientific-sounding theories were never a problem, so I find
what's going on here to be fascinating. But if I talk about the
overtones and 7-limit music and god forbid I even HINT at something
like "72 notes per octave," a lot of my friends' minds shut down. And
I'm talking about people who are obviously good at math enough to play
extremely complicated jazz patterns in 16th notes at quarter note =
300, but it's just that they don't want to have to think about music
in the way that we often describe it here.

Some people jump right into that kind of thinking, and some don't. But
if I gave these people a 31-tone instrument and let them play on it, I
bet they'd come up with extremely interesting sounds and chords that
maybe we wouldn't have even thought of. Maybe they'd start playing C
Eb G Bb and then see what the difference between that and C D# G A#
is, and "discover" 7-limit music for themselves. Hell, maybe they
wouldn't even ever know it has anything to do with the 7th overtone,
just like many current musicians don't know that major chords have
anything to do with the 3rd and fifth overtones.

> In some cases the increase in complexity is an advantage.
> People are actually looking for more subtlety. Why else
> would the quartertone movement have taken off?

Yeah, these musicians I'm talking about always want to get started
with quartertones. I always tell them that if that's what they want
then maybe to try sixth-tones instead, that is, to try 36tet rather
than 24tet. I try to explain that it will allow them better
approximations to the 7th harmonic, whereas quarter tones skips that
and goes up to the 11th harmonic, which is an often weird sound that
they might not like. They ignore me and/or don't understand and say
"nah man, we'll do quarter tones first and then we'll get up to third
tones later." Then they hear quartertones and they're like "ahh, this
sucks. I guess I'm just used to 12tet and it's a cultural thing and it
will never change and blah blah." Sorry, I'm slightly ranting here.

> A blackjack guitar, tuned to 72tet, is perfectly viable. I
> don't remember if anybody has one yet. Guitars are all we
> need for rock music. Most orchestral instruments are
> already very flexible with regards to pitch and quartertone
> instruments all the better for reaching arbitrary intervals.

Interesting. My beef with non-equal temperaments being used as a
widespread system is just that you can't write in any key. Maybe it's
just my bias - I hear different keys as having different colors, and
if every song to come out were in only two or three keys because of a
non-equal system, I'd be really sad. It's like the only colors you see
for the rest of your life are red. Or, like if any time you saw blue
from then on, it was really dirty blue because blue suddenly has
terrible wolf fifths that threaten the harmonic stability of your
state of mind and the entire world. I may be ranting again.

Plus, it would be quite difficult to compose Debussy-ish pieces that
use interesting modulations and such. Jazz as well has a history of
composers and songwriters trying to come out with more and more
interesting chord progressions, so that would be limiting there as
well. I'm sure I'm gonna get hammered for clinging to my equal
temperaments on a forum about tuning, but I've always had that feeling
about it.

> I have a pipe dream of a miracle ensemble. Each instrument
> plays a different subset of canasta (miracle31) or 72tet if
> you like. Some will play "pygmy" pentatonics, with chains
> of approximate 8:7s.

Interesting description. Would 5-equal satisfy what you would call a
"pygmy" pentatonic in one particular key?

> Six of those can handle 30 notes
> between them. Some instruments will play mohajira (7 notes
> generated by neutral thirds). Three such cover the 21 notes
> of blackjack. Some instruments will handle the full decimal
> scale, and four such give canasta with a bit of overlap.
> Maybe some of the instruments will be able to handle the
> full 31 note gamut. But the idea is to share the notes
> around so that each instrument and each instrumental part is
> relatively simple.

That's a really interesting idea - I'd be very interested in hearing
what that would sound like.

I think it would be worthwhile to put some of these ideas through
Vienna Symphonic Library or EastWest or some "hyper-realistic"
orchestral sample program to hear what this stuff would sound like.
EWQL Ra would undoubtedly be a good idea as well.

> The "too many notes" argument is why I use linear
> temperaments. Miracle works fine with 21 notes. You only
> need to teach those 21 notes. Sure, it's more complicated
> than 12 notes, but the more adventurous musicians can handle
> it. It has some really cool intervals. You can teach it
> much the way you do any other super-scale -- nice chords,
> nasty chords, scales, melodies. There are more consonances
> to remember but that's the whole point.

That's a really interesting idea. To teach someone with blackjack and
then have them jump up to canasta and then the 41-note one (I forget
the name now) and then up to 72-equal. That might be a really good way
to teach this stuff.

Sometimes though, no matter what my friends say about "too many
notes," I feel like if I gave them 72-equal sax with the full range of
notes, they'd figure it out pretty quickly. They already know to drop
the major third in a horn ensemble so that it sounds closer to a 5/4 -
they would basically then have a key to do that. I also hear them
playing 4:5:6:7 for dominant 7 chords sometimes, but only sometimes -
it's amazing how many different ways a horn section will approach a C7
chord depending on whether it's the tonic (mixolydian) or a 5 chord to
a major chord or to a minor chord. But either way, rather than have to
lip that 7 down a third of a half step, they'll have a key for that.

And if I ever hear a trumpet play a #11 over a dominant 7 chord,
chances are he's a full quartertone flat and is hitting 11/4. So
there'd just be a valve for that as well. I find that it's really easy
to get musicians to adjust to 72-equal if they think of it as just a
formalized system of things they already know. Like maybe as
quartertones with a few intermediate steps that have various uses in
terms of currently existing music. So instead of having to learn
72-12=60 new notes, it becomes much more simple to conceptualize.
Usually the term 72-equal is intimidating, but it doesn't have to be.
People don't have to think of all 12 of the notes now when they're
playing major 7 chords and such.

I think it would be like they'd stick to 12-equal mostly, then they'd
"wander out" into 72 a little bit by comma-adjusting for major thirds
here and there, and then they'd eventually get comfortable that way.
Then they'll comma adjust for other things in 72 as well, then try new
chords and modulations and such. Then someone will come along who's
spent time on it and has learned and invented all kinds of new
symmetric scales, and the bar will be raised, and it could take off
that way as well.

> Magic works with only 19 notes and you can do a fair bit
> with 16. That means it isn't significantly more complex
> than meantone in the 7-limit. It doesn't naturally break
> down into simpler scales but I've cracked the notation
> problem now. It naturally supports chords built by chaining
> thirds. There are more of them than in 12tet and more ways
> of connecting them but not so difficult compared to the
> outer reaches of jazz harmony.

I'll have to check magic out again. 19-tet is magic, isn't it? Maybe
19-tet is too limiting for the full range of what magic can do. Or is
magic just the linear temperament generated by dividing 3/1 into 5
equal parts?

> In both cases you can tie chords to the harmonic series if
> you want to. If your students object to that you can talk
> about different thirds: subminor-minor-neutral-major-supermajor.

Yeah. I find 31-equal to be a great introduction to the whole thing,
honestly. 19-equal is a decent introduction as well, but the fact that
7/6 and 8/7 are represented by the same interval is a little confusing
for people, not to mention that a subm7 triad in 19-equal doesn't
really sound too much like a JI subm7 triad. The concept then goes out
the window though because 31-tet's extremely handy and useful
note-naming system really only applies to 31-tet. 53-tet has it so
that the sharps are higher than the flats, and none of it makes any
sense in terms of 72-tet at all.

> Experience is what we need. Experience of making music and
> experience of passing the knowledge to other musicians.

Amen.

> I agree that meantone (of which 31tet is almost optimal)
> doesn't work for 9th chords. That's why I draw a
> distinction between 7-limit and 9-limit temperaments.
> Meantone is, to me, a 7-limit temperament. Magic (22&19) is
> the simplest 9-limit temperament. So for mainstream jazz
> harmony the next step is magic. I've got 19 notes tuned up
> now, and they work well enough. It means chords sound
> familiar but smoother than in 12tet. For mainstream harmony
> the problem is that you can't chain many fifths before you
> run off the edge. For me the problem is that I miss those
> spicy 11-limit intervals. There are some approximate 11:8s
> though and one neutral third!

Alright, I've got to look into magic more deeply. When you talk about
22 and 19, are you saying 22 and 19 equal? Or just a linear
temperament of 22 and 19 notes?

Also, do you have any recordings of this stuff? What tools do you use
to play around with all of this? This is fascinating.

> If you want more fifths the solution seems to be
> schismatic/garibaldi (12&29). 29 notes work well enough and
> fit a halberstadt layout although it's a stretch. It is
> more complex than magic. Maybe the familiarity of a fifth
> generator will make up for that. It's the great neverwozzer
> of temperament classes -- implied in theories of different
> cultures but never properly taken up.

Yeah. Schismatic temperament interests me quite a bit. The left
hemisphere of my brain might love 72-tet, but the right hemisphere is
obsessed with 53-tet. Somehow neither of them really likes 41-equal
all that much though. I don't know why. It just never sounded all that
good to me. Maybe the flat major third is what does it. 53-equal
amazes me in that it even exists though.

> For more exotic intervals or more accuracy the answer is
> miracle. It looked like the holy grail of 11-limit harmony
> when it was re-discovered in 2001 and I don't think any
> recent developments have changed that.
>
> You may also have a look at orwell (22&31). It doesn't have
> a unique selling point in the 9-limit but it's similar to
> the other ones I mentioned and simpler than miracle in the
> 11-limit.

Ah yeah, orwell. That and semisixth I hear I need to probe more deeply into.

What software do you use to get into all of this? I've been using
Scala but it seems incapable of being used for actual composition,
unless maybe I just don't know how to use it.

> We don't all live in a western culture :-P

...What? Non...western...culture? Dunno what you're talking about here

> My rather hubristic opinion is that although I'm not even a
> competent musician I do have a great theory. And that
> theory's good enough to lead me to some worthwhile music if
> nobody gets there first. It's naturally difficult to
> interest musicians without musical examples.

Yeah, I've been reading your "regular mapping paradigm" as I've been
writing this post... I started writing it at like 3 AM and now it's 5
AM. I don't think I'll be sleeping tonight.

-Mike

🔗Torsten Anders <torstenanders@...>

6/8/2008 2:50:39 AM

Thank you!

Torsten

On Jun 8, 2008, at 4:20 AM, Herman Miller wrote:

> Torsten Anders wrote:
> > Dear Herman,
> >
> > On Jun 7, 2008, at 9:24 PM, Herman Miller wrote:
> >> Much of the work on the tuning-math list is centered around the
> >> idea of
> >> building a unified system that encompasses JI, ET, and
> everything in
> >> between. Paul Erlich's paper in Xenharmonikôn 18 ("A Middle Path")
> >> is a
> >> first step in that direction. Dave Keenan and George Secor's
> paper on
> >> Sagittal notation in the same issue provides a means of notating JI
> >> and
> >> ET in a single, unified system that can also be adapted for
> >> notating the
> >> kinds of tunings described in Paul's Middle Path paper. Erv
> Wilson's
> >> golden-ratio-based scales don't fit neatly into this system, but
> >> they do
> >> share enough similarities with what we're now calling "rank two
> >> temperaments" that many of the same ideas can be applied to
> both. The
> >> main thing that's missing is a simple, readable introduction to the
> >> more
> >> recent developments since those papers were published.
> >
> > I am one of those guys who feels that he likely missed those "recent
> > developments". Could you just name a few of these new concepts, so I
> > could dig into the archive for details.
>
> Graham Breed's page at http://x31eq.com/paradigm.html "The Regular
> Mapping Paradigm" is a good introduction to some of the ideas and the
> notation system we've settled on for describing these temperaments.
> He's
> also been working on a set of papers that describe the mathematical
> details of various error and complexity measures. See e.g. "Prime
> Weighted Errors and Complexity" from June 2006, "More prime errors and
> complexities" from Jan. 2007, "Parametric scalar badness" from Feb.
> 2008, "Complete Rank 2 Temperament Searches" from Mar. 2008,
> "Composite
> Errors and Complexities" from Apr. 2008.
>
> George Secor and Dave Keenan have continued to revise and update the
> Sagittal notation system, providing new definitions for extreme
> precision (Olympian) Sagittal notation and others. I've been
> attempting
> to work out the details of how Sagittal notation can be applied to
> notating different sorts of rank 2 temperaments, including the ones
> mentioned in Paul's paper. (See the threads on proposed Sagittal
> notations starting around Dec. 2007.)
>
>
>

🔗Torsten Anders <torstenanders@...>

6/8/2008 3:32:30 AM

On Jun 8, 2008, at 3:20 AM, Mike Battaglia wrote:
> Please do point me to some MP3's. I've heard only a handful of
> examples that I really like - a few songs off of Easley Blackwood's
> Etudes did it for me, but there's this Joel Mandelbaum piece on
> youtube that is awesome, and Aaron Johnson has some amazing songs too
> (I always liked Melancholic). Hook it up!

What I really like very much is Ben Johnston, e.g., his string quartets. I very much hope that the Kepler Quartet will record all of them in the end, as announced. Here is one of their CDs.

http://www.amazon.com/Ben-Johnston-String-Quartets/dp/B000CSUMYY/ref=pd_bbs_sr_1?ie=UTF8&s=music&qid=1212916852&sr=8-1

More Johnston recordings are listed on his wikipedia page.
http://en.wikipedia.org/wiki/Ben_Johnston_%28composer%29

Some are seemingly out of print, but an out-out print LP is available as mp3s for download at
http://www.avantgardeproject.org/AGP9/index.htm

Naturally, I am also happy to mention my former teacher Wolfgang von Schweinitz. For example, he recently wrote a piece for orchestra in extended JI (Plainsound-Sinfonie, 11-limit for orchestra and 23-limit of soloist). Unfortunately, there are no commercial CDs of his recent JI pieces. Still, the first pages of the score and an mp3 of the intro of this work are available online -- like several others.

http://www.plainsound.org/WSwork.html

http://www.plainsound.org/music/sinfonie.m3u
http://www.plainsound.org/pdfs/sinfonie.pdf

BTW: ww.plainsound.org lists the work of more interesting composers and some papers can be downloaded. For example, Marc Sabat (http://www.plainsound.de/MSscores.html) and W v Schweinitz intonated some classical pieces in JI. These include highly chromatic pieces like the Tristan prelude and the Ricercar from Bach's Musikalisches Oper. The ricercar is available online

http://www.plainsoundmusic.org/videos/Ricercar.mov
http://www.plainsound.de/scores/ricercar.pdf
http://www.plainsound.de/research/ricercartext.pdf

Best
Torsten

🔗Mike Battaglia <battaglia01@...>

6/8/2008 3:33:33 AM

> Human psychology varies greatly by individual and by trial
> (what kind of day you're having), so it's difficult to
> formalize anything about it in a music theory.

Difficult but necessary. These concepts already factor into Gestalt
psychology anyway. It isn't that hard - assuming that you're writing
music for a certain audience, you would first have in mind the mood of
the audience as they sat down. You would then use that to your
advantage in composing the opening movement of your piece. It would be
something to shift the mood and of your audience so that no matter
what mood they're in, they get dragged along with you so they are on
the same page as you. The way they view the "gestalt" of your
performance would change on your terms. You would then, knowing what
mood they are in, then work their emotions perhaps more subtly in
different ways and eventually lead them where you want.

You may have noticed I have basically just written out the workings of
a good composer. Good composers do this all of the time. They might
even take it a step further and have an overture in there as the
audience comes in to even further entice the audience, and then the
opening movement usually is something that easily gets the audience's
interest.

Good composers know this intuitively. They already have their own
theory. I merely suggest we formalize it and replace the old, coarse
one.

That way we don't have the extremely coarse common practice system
where doubling the third supposedly just "sounds bad." It sounded bad
back then, perhaps, but we're more than used to it nowadays. There are
plenty of times when doubling the thirds sounds really good imo. If
this theory could be generalized to include the gestalt of the
listener, then we would see that given the tuning system and mindset
of the average listener during the common practice period, doubling
the third WOULD sound like a weird version of something they were
already used to, and nowadays it stands out as an entity in its own
right.

If you think about it, common practice theory is already partially
tied in with psychology because of its attempts to label certain
things as sounding "good" or "bad." We're already into it. And if
we're going to go into it at all, then we'll have to take the concept
a step further, as imo it's currently pretty sketchy at places. The
other option is to avoid it and make no attempt in any music theory to
predict how things will sound.

Alternatively, a third option would be to leave it the way it is as a
weird oddity so that those interested will eventually give up on it
and do some research into how music REALLY works and end up at this
group like I did. :P But I think there's a better way.

A good music theory will simply be a formalized system to represent
the thinking of a good, intuitive musician.

> Another thing that's usually not formalized are priming
> effects -- otherwise known as musical context. These effects
> again will vary by listener and by trial. In adaptive tuning
> schemes, one can treat past notes just like simultaneous
> notes but subject to a decay process that weakens the
> interactions. IIRC John deLaubenfels' system did something
> like that, and other adaptive tuning schemes probably do
> too (my own pet adaptive tuning scheme makes use of it).

Ah, wow. An extension of the concept that if you leave out the 3rd in
a chord, your mind will "fill it in" based on what third was heard
before...? Perhaps even in a different chord? Like if I play C and G,
but a little while ago there was an Eb major chord, I'll likely hear
that dyad as having a "minor" quality.

> Finally, at the level of cognitive psychology and
> psychoacoustics (a branch of cog psy actually), effects are
> largely listener-invariant. So I think it's a good place
> to start.

Yeah. That's where things like beat frequencies and such come into it.
Perhaps it's split up this way:

Psychoacoustics is a good way to look at beat frequencies,
sum-and-difference tones, phantom fundamental tones, etc... And then
where gestalt psychology enters into it is how one reacts to the beat
frequencies and such.

I think my main point about psychology is that even as gestalt
psychology predicts certain things about how someone will perceive a
chord or phrase, there will be those whose gestalts differ. Different
expectations yield different gestalts. And different expectations
usually stem from different cultures. So ethnomusicology should be
brought into the fold as well.

I envision a theory that gives a decent prediction of how a piece in
some tuning system will sound to someone used to some other tuning
system. It will be able to predict that on the first listen, for
Americans, the second chord in AKJ's "The Juggler" it will sound
weird, but after repeated listens, it starts to become natural. It
might even go further and predict that it sounds weird for some people
and "interesting" for others, and why that would be.

It might also predict ways to get people into the fold of hearing
something new without it sounding like a messed up version of
something old. Again, most people have theories of their own floating
around in their heads anyway, so they might as well be formalized and
made consistent.

> Assuming that people do complain about this and that it is
> because of the smaller whole step, what you have is a
> tendency to hear *melodic* intervals in terms of other melodic
> intervals. This is very different from the whole
> 16:19 v. 6:5 thing. The theory of harmonic approximation is
> on solid footing at this point. Our understanding of a similar
> concept for melodic intervals is more formative.

Ah yeah, that's interesting. Harmony is different. You are right. Why
the schism in harmony and melody here, I wonder...

> However, a guy named David Rothenberg has published papers
> about it. The basic idea is that the human memory can't cope
> with all the pitches in a melody directly, but it can accurately
> measure the size of melodic intervals as they come in and deduce
> the scale that way. It hears Adown Bup Aup and it knows the
> last note should be B above the first. The catch is, this is
> a skill like riding a bike. Takes a while to learn but you
> never forget. But you have to do it for every different scale.
> Say the diminished scale is a recumbent and Paul Erlich's
> pajara scales are like unicycles. The first time you get on a
> unicycle you might try to ride it like a regular bike, but
> you'll fall on your ass. You may then complain about unicycles.
> But if you practice until you can do it you then may praise
> unicycles.

Interesting. So that makes quite a bit of sense. And then the lazy
musicians who don't want to do work never get the point block
themselves off from perfecting this skill except for the scales that
they already know.

> Rothenberg's model actually makes predictions. For example,
> as you morph one scale to another (by sliding the pitches
> around), it predicts when you'll start to call it some tuning
> of the new scale instead of some tuning of the old. These
> predictions can be tested experimentally, but so far haven't
> been (to my knowledge).

Do you have a link to his model? This is really interesting. Does this
apply to harmony as well?

It seems interrelated to the fact that if I play a minor triad, and
then a neutral triad, the neutral triad takes on a slightly major
quality. But, if I play a major triad and then a neutral triad, the
neutral triad takes on a slightly minor quality.

> You gave cases where it doesn't. It's so incredibly easy
> to make up music rules that hold sometimes and not others
> that they're usually not worth thinking about.

Yeah. And they are being taught in schools.

But I'm more trying to figure out why when that rule DOES hold, it
works. Is there some physical basis for that rule, or is it describing
a cultural expectation that alters our gestalt of the chord?

>> If you play C E G Bb D F that F will sound
>> pretty "weak" in a straight ahead jazz context,
>
> C E G Bb D is a nice 4:5:6:7:9 chord in 12. The F is
> pretty far from the 21 that might sound nice in the chord.

Yeah, but the 21 is closer to the F than the 7 is to the Bb. There has
to be another explanation...

> Sure, you can use any perception -- positive or negative --
> to create a good musical effect. That doesn't invalidate
> the perception though.

I mean that the C E G Bb D F gives a negative perception in some
contexts and a positive one in others. Sometimes it sounds "floaty."
And sometimes it sounds "unstable". See? Half full, half empty.
Gestalt. Furthermore, if you're a musician who knows this extremely
rough "no b9" rule, and you hear that chord, your impression of the
chord might be "bad musician." I think that a decent music theory
would somehow incorporate all of this. Maybe it would leave out
people's personal biases so that it describes a mental space that is
completely free of biases -- one that any human being could
hypothetically get to. So it would be more universal.

> I will say that one reason I don't like the rule is that
> it talks about one interval alone without considering the
> rest of the intervals in the chord. When evaluating chords,
> generally there are two things I consider: 1. how strong is
> the harmonic series interp (e.g. 4:5:7:9) and 2. how many
> of the dyads within the chord are consonant. Both of these
> necessitate looking at the *whole chord*, not just which
> root some interval is built on top of.

I think that's what my teacher is doing. He checks every dyad of the
chord, and he has determined a 12tet "b9" dyad to be dissonant unless
it's over the root. So the question can be reformulated as thus: what
makes a dyad consonant or dissonant?

> You and me both. We could buy a bunch of AXiSes and refretted
> guitars and pitch a workshop to Berklee. I'd bet they'd go
> for it. Might even give us some money.

Hey, why not :P You buy the AXiSes, I'll write Berklee...

> Petr's music is generally improvisational in nature.

Ah, neat. I'll have to check that out.

> The very term "b9" is completely tied to the diatonic scale if
> not to the 12-ET kernel as well and if you're using it in your
> line of questioning you haven't stepped outside 12 in the way
> I'm suggesting here.

I have. I was just reiterating how it is being taught in schools. I
still don't know the answer to why a 12tet b9 sometimes sounds bad
over a non-rootnote in a chord. I'm not sure what the corresponding JI
question is, as I don't know what the corresponding JI interval to a
12-tet "b9" is in this particular context. There are a lot around that
area. I'm trying to figure it out though.

> The AXiS is competitively priced with halberstadt MIDI keyboards.
> I looked at several by Kawai and Yamaha that were as expensive
> just the other day. They were also total junk FWIW.

Yeah, it's $1700. It's almost twice as expensive as a Fender Rhodes
and 2 and slightly less expensive than an Access TI Polar, both of
which are far more than just MIDI controllers. All of this and you
still have to connect it to a computer and set up your some tuning
software and deal with that if you ever want to play it live. Never
mind the fact that if you want decent samples to play it through, such
as if you want to run it through Native Instrument's Elektric Piano or
something, you're going to have to go through hell to get that
running, and possibly have to deal with latency issues. So it isn't
exactly the "all-in-one" package I'd hope for to turn someone onto
microtonality :P But I'm sure that's in the works somewhere.

> Fokker and the Dutch 31-toners did a bit of this, and some
> of the effects of 7-limit harmony on voice leading are
> understood by barbershop arrangers.

And choirs. I heard these Sibelius choral works being sung by a group
called "Jubilate" choir - they use 7:4 all the time. Sounds perfectly
natural and yet, exotic.

> But if you're looking for a detailed approach to extended JI and the diatonic
> scale, I'd say the the door is fairly open. Have at it and
> post your results here as you go! Oh, you might want to
> search in the 1/1 archives if that's possible (journal of
> the JI Network).

Haha, will do. Just talking about it on this group is certainly
expanding my mind about the whole thing. I definitely like the
Sims-Maneri notation for 72-tet as a starting point, although that
still takes into account the pythagorean comma, so it does break down
eventually and in certain cases. Sagittal notation is pretty decent
too, but I still find Sims-Maneri to be clearer and much more easy to
adjust to.

> But again, I didn't say extending common practice theory,
> I said generalizing it. Probably best to have a look at
> the papers you've been referred to at this point if you're
> interested in that route.

Yeah, I've lost my life to the regular mapping paradigm at this point.

>> I think that rather than add random corollaries to common
>> practice theory about what sounds good or bad, we should take
>> the concept up to a higher level of abstraction and figure
>> out WHY things sound good or bad
>
> Well you've come to the right place then!

Yeah man! I think we just need to formalize all of these ideas. We
already have ideas about why things sound the way they do, what things
will sound like in this or that culture, what it'll sound like to
someone in this or that mood... And I think everyone knows somewhere
where traditional "music theory," whether jazz theory or common
practice theory breaks down or is inconsistent with reality. So if we
had a formal axiomatic theory to represent the new ideas we've got
floating around, and made sure the axioms were consistent, we'd be one
huge step ahead of where music theory is now. I think that it would be
a huge, huge help for music education in America.

Hell, maybe one of the axioms would be that the theory is incomplete,
a la Godel... Unnecessary, sure, but would certainly serve to remind
people to keep developing, exploring, and thinking, and not fall into
the same traps that they do with the current system.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/8/2008 3:36:57 AM

Yeah, I wish all of this stuff was on Napster. I pay $20 a month for a
subscription, but the majority of microtonal music on there is in the
form of guitar feedback... :D Does have some good stuff though.

I'll have to check out those links for sure. Any acoustic microtonal
stuff is already on my list as "must-hear."

-Mike

On Sun, Jun 8, 2008 at 6:32 AM, Torsten Anders <torstenanders@...> wrote:
> On Jun 8, 2008, at 3:20 AM, Mike Battaglia wrote:
>> Please do point me to some MP3's. I've heard only a handful of
>> examples that I really like - a few songs off of Easley Blackwood's
>> Etudes did it for me, but there's this Joel Mandelbaum piece on
>> youtube that is awesome, and Aaron Johnson has some amazing songs too
>> (I always liked Melancholic). Hook it up!
>
> What I really like very much is Ben Johnston, e.g., his string
> quartets. I very much hope that the Kepler Quartet will record all of
> them in the end, as announced. Here is one of their CDs.
>
> http://www.amazon.com/Ben-Johnston-String-Quartets/dp/B000CSUMYY/
> ref=pd_bbs_sr_1?ie=UTF8&s=music&qid=1212916852&sr=8-1
>
> More Johnston recordings are listed on his wikipedia page.
> http://en.wikipedia.org/wiki/Ben_Johnston_%28composer%29
>
> Some are seemingly out of print, but an out-out print LP is available
> as mp3s for download at
> http://www.avantgardeproject.org/AGP9/index.htm
>
> Naturally, I am also happy to mention my former teacher Wolfgang von
> Schweinitz. For example, he recently wrote a piece for orchestra in
> extended JI (Plainsound-Sinfonie, 11-limit for orchestra and 23-limit
> of soloist). Unfortunately, there are no commercial CDs of his recent
> JI pieces. Still, the first pages of the score and an mp3 of the
> intro of this work are available online -- like several others.
>
> http://www.plainsound.org/WSwork.html
>
> http://www.plainsound.org/music/sinfonie.m3u
> http://www.plainsound.org/pdfs/sinfonie.pdf
>
> BTW: ww.plainsound.org lists the work of more interesting composers
> and some papers can be downloaded. For example, Marc Sabat (http://
> www.plainsound.de/MSscores.html) and W v Schweinitz intonated some
> classical pieces in JI. These include highly chromatic pieces like
> the Tristan prelude and the Ricercar from Bach's Musikalisches Oper.
> The ricercar is available online
>
> http://www.plainsoundmusic.org/videos/Ricercar.mov
> http://www.plainsound.de/scores/ricercar.pdf
> http://www.plainsound.de/research/ricercartext.pdf
>
> Best
> Torsten
>
> --
> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586227
> Private: +44-1752-558917
> http://strasheela.sourceforge.net
> http://www.torsten-anders.de
>
>

🔗Torsten Anders <torstenanders@...>

6/8/2008 3:59:22 AM

On Jun 8, 2008, at 11:32 AM, Torsten Anders wrote:
> the Ricercar from Bach's Musikalisches Oper.
> The ricercar is available online
>
> http://www.plainsoundmusic.org/videos/Ricercar.mov
> http://www.plainsound.de/scores/ricercar.pdf
> http://www.plainsound.de/research/ricercartext.pdf

Perhaps I should mention that this is at least 7-limit adaptive JI, it also includes higher limits such as 17 and 19. I find downright crazy what they did here -- its actually a new piece.

Best
Torsten

🔗Graham Breed <gbreed@...>

6/8/2008 8:56:21 AM

Me:
>> This is where we hit what I call the complexity problem. A
>> lot of us are looking for scales with more and more accurate
>> consonances. Naturally they end up more complex than
>> 12-equal or meantone diatonics. As musicians in general
>> have no problems with the scales they know they'll quite
>> rightly ask why they should worry about anything more
>> complicated.

Mike:
> Ah, yeah. Those people might screw around with it if we yelled "HEADS
> UP" and forcefully threw a 17- or 19-tone guitar directly at them.
> They are also the people least likely to like the way it sounds, as if
> these people are already burned into 12-equal, then they're unlikely
> to like the sound of much else short of 36-equal or 72-equal or
> something. And those are considerably more difficult to get into.

Even so far as I'm a musician I wear different hats. I own a few diatonic instruments and there's plenty of great diatonic music to play on them. I shun chromatic mouth organs as too complicated. I also have a standard guitar I use to do songs in my English lessons. 12-equal's great for that because it has all the notes you need to accompany pop songs and nothing superfluous.

> Definitely. There is also an interesting shade of musician that can
> deal with the added complexity provided it is explained to them in a
> certain way that they don't have mental defenses against. For me, math
> and scientific-sounding theories were never a problem, so I find
> what's going on here to be fascinating. But if I talk about the
> overtones and 7-limit music and god forbid I even HINT at something
> like "72 notes per octave," a lot of my friends' minds shut down. And
> I'm talking about people who are obviously good at math enough to play
> extremely complicated jazz patterns in 16th notes at quarter note =
> 300, but it's just that they don't want to have to think about music
> in the way that we often describe it here.

Mental defences can be a real problem. I think of it as the psychological immune system. If it encounters a foreign idea the first action is to repulse it. Over time, if the idea proves to be benign, the reaction fades. I know it's something I'm guilty of -- I often argue against things on a knee jerk and then change my mind after mulling it over for a few hours.

> Some people jump right into that kind of thinking, and some don't. But
> if I gave these people a 31-tone instrument and let them play on it, I
> bet they'd come up with extremely interesting sounds and chords that
> maybe we wouldn't have even thought of. Maybe they'd start playing C
> Eb G Bb and then see what the difference between that and C D# G A#
> is, and "discover" 7-limit music for themselves. Hell, maybe they
> wouldn't even ever know it has anything to do with the 7th overtone,
> just like many current musicians don't know that major chords have
> anything to do with the 3rd and fifth overtones.

For those kind of musicians, yes, try that! Others will be overwhelmed with the complexity.

>> A blackjack guitar, tuned to 72tet, is perfectly viable. I
>> don't remember if anybody has one yet. Guitars are all we
>> need for rock music. Most orchestral instruments are
>> already very flexible with regards to pitch and quartertone
>> instruments all the better for reaching arbitrary intervals.
> > Interesting. My beef with non-equal temperaments being used as a
> widespread system is just that you can't write in any key. Maybe it's
> just my bias - I hear different keys as having different colors, and
> if every song to come out were in only two or three keys because of a
> non-equal system, I'd be really sad. It's like the only colors you see
> for the rest of your life are red. Or, like if any time you saw blue
> from then on, it was really dirty blue because blue suddenly has
> terrible wolf fifths that threaten the harmonic stability of your
> state of mind and the entire world. I may be ranting again.

Are you the one with perfect pitch then? A guitar's already like that for me because I can only play in 2 or 3 keys :-P And it does get harder the more frets you add. But, still, 31's about doable (some have done it) so you could fret to canasta and have 10 different keys of blackjack.

> Plus, it would be quite difficult to compose Debussy-ish pieces that
> use interesting modulations and such. Jazz as well has a history of
> composers and songwriters trying to come out with more and more
> interesting chord progressions, so that would be limiting there as
> well. I'm sure I'm gonna get hammered for clinging to my equal
> temperaments on a forum about tuning, but I've always had that feeling
> about it.

Miracle temperament naturally supports modulations by seconds because they're the simplest intervals. The 10 note scale is almost equal. If you can't do an exact modulation it's often a question of trading one consonance for another. There are still more notes than 12-equal and different places to start so you have more opportunity for interesting progressions.

Mystery temperament deserves a mention here. It has two scales of 29-equal about 16 cents apart. Not that simple, but once you tune it up you can modulate freely to 29 different degrees. And it's very good for 15-limit harmony. One way to realize it would be with a guitar fretted to 29-equal.

>> I have a pipe dream of a miracle ensemble. Each instrument
>> plays a different subset of canasta (miracle31) or 72tet if
>> you like. Some will play "pygmy" pentatonics, with chains
>> of approximate 8:7s.
> > Interesting description. Would 5-equal satisfy what you would call a
> "pygmy" pentatonic in one particular key?

The true Pygmy scale (from the Scala archive) is in just intonation. It can be approximated in miracle, in which case it's an MOS of Margo Schulter's wonder temperament -- every other note of miracle and no 5s. In that case, yes, 5-equal is a tuning.

There's another interesting scale you get by tuning the other way from 5-equal. The generator is a compromise between 7:6 and 8:7 so two of them give a 4:3. It works with 19-, 24-, and 29-equal. Not a great approximation but in so far as it works every interval is in the 9-limit. (Also a property of the traditional meantone pentatonic.)

I used both scales with custom timbres in my MMM Day submission, which I think is on my website now.

>> Six of those can handle 30 notes
>> between them. Some instruments will play mohajira (7 notes
>> generated by neutral thirds). Three such cover the 21 notes
>> of blackjack. Some instruments will handle the full decimal
>> scale, and four such give canasta with a bit of overlap.
>> Maybe some of the instruments will be able to handle the
>> full 31 note gamut. But the idea is to share the notes
>> around so that each instrument and each instrumental part is
>> relatively simple.
> > That's a really interesting idea - I'd be very interested in hearing
> what that would sound like.
> > I think it would be worthwhile to put some of these ideas through
> Vienna Symphonic Library or EastWest or some "hyper-realistic"
> orchestral sample program to hear what this stuff would sound like.
> EWQL Ra would undoubtedly be a good idea as well.

It's a bit eccentric to design a virtual orchestra around the limitations of acoustic insruments but perhaps I will one day. I don't have any of these samples... The pentatatonic instruments would logically be gu zhengs, which aren't symphonic. Maybe bamboo flutes for the mohajiras.

>> The "too many notes" argument is why I use linear
>> temperaments. Miracle works fine with 21 notes. You only
>> need to teach those 21 notes. Sure, it's more complicated
>> than 12 notes, but the more adventurous musicians can handle
>> it. It has some really cool intervals. You can teach it
>> much the way you do any other super-scale -- nice chords,
>> nasty chords, scales, melodies. There are more consonances
>> to remember but that's the whole point.
> > That's a really interesting idea. To teach someone with blackjack and
> then have them jump up to canasta and then the 41-note one (I forget
> the name now) and then up to 72-equal. That might be a really good way
> to teach this stuff.

There's no particular need to go beyond canasta. But if you do the next one's called stud loco.

>> Magic works with only 19 notes and you can do a fair bit
>> with 16. That means it isn't significantly more complex
>> than meantone in the 7-limit. It doesn't naturally break
>> down into simpler scales but I've cracked the notation
>> problem now. It naturally supports chords built by chaining
>> thirds. There are more of them than in 12tet and more ways
>> of connecting them but not so difficult compared to the
>> outer reaches of jazz harmony.
> > I'll have to check magic out again. 19-tet is magic, isn't it? Maybe
> 19-tet is too limiting for the full range of what magic can do. Or is
> magic just the linear temperament generated by dividing 3/1 into 5
> equal parts?

Magic can be 19 notes. The optimal tuning is very close to 41-tet, which you say you don't like :-O But you can make it more 19-like if you want. Yes, it divides the 3/1 into 5 parts, each of which approximates a 5:4.

>> In both cases you can tie chords to the harmonic series if
>> you want to. If your students object to that you can talk
>> about different thirds: subminor-minor-neutral-major-supermajor.
> > Yeah. I find 31-equal to be a great introduction to the whole thing,
> honestly. 19-equal is a decent introduction as well, but the fact that
> 7/6 and 8/7 are represented by the same interval is a little confusing
> for people, not to mention that a subm7 triad in 19-equal doesn't
> really sound too much like a JI subm7 triad. The concept then goes out
> the window though because 31-tet's extremely handy and useful
> note-naming system really only applies to 31-tet. 53-tet has it so
> that the sharps are higher than the flats, and none of it makes any
> sense in terms of 72-tet at all.

The thirds are only equally spaced in 31-equal. But throw away the neutral third and the ones you have left are equally spaced in magic temperament. You may not want to call them "thirds" then. Whatever you call them you can talk about them in any regular temperament.

>> I agree that meantone (of which 31tet is almost optimal)
>> doesn't work for 9th chords. That's why I draw a
>> distinction between 7-limit and 9-limit temperaments.
>> Meantone is, to me, a 7-limit temperament. Magic (22&19) is
>> the simplest 9-limit temperament. So for mainstream jazz
>> harmony the next step is magic. I've got 19 notes tuned up
>> now, and they work well enough. It means chords sound
>> familiar but smoother than in 12tet. For mainstream harmony
>> the problem is that you can't chain many fifths before you
>> run off the edge. For me the problem is that I miss those
>> spicy 11-limit intervals. There are some approximate 11:8s
>> though and one neutral third!
> > Alright, I've got to look into magic more deeply. When you talk about
> 22 and 19, are you saying 22 and 19 equal? Or just a linear
> temperament of 22 and 19 notes?

A linear temperament with MOS scales of 19 or 22 notes.

> Also, do you have any recordings of this stuff? What tools do you use
> to play around with all of this? This is fascinating.

My original magic demonstration is on my website:

http://x31eq.com/music/

It's both partly improvised and entirely computer generated!

I also have a cover version of the Fleetwood Mac song the name "magic" comes from that involves both magic and miracle temperaments. But it isn't on the website because of its obvious unoriginality.

These days I have a Miditech Midistart-2 input keyboard plugged into Csound. With, so far, some very boring timbres in magic because the clever ones are all designed for decimal tunings.

> What software do you use to get into all of this? I've been using
> Scala but it seems incapable of being used for actual composition,
> unless maybe I just don't know how to use it.

Csound these days. I used Kyma before but I can't carry the hardware around with me.

>> We don't all live in a western culture :-P
> > ...What? Non...western...culture? Dunno what you're talking about here

I live in a city with so few westerners that people stare at me as I walk past.

As it happens there was a programme on the television tonight celebrating Chinese culture. And the triumphalist ending was -- set to music entirely based on western harmony. Which confirms somebody's point: harmony is a very successful European export. Folk tunes around the world are being set to a soupy 5-limit backing and losing the original intonation. One thing I hope to get across with the regular mapping paradigm is that there are other ways to do harmony. Some of them may suit other cultures even if the principles follow from European considerations.

Graham

🔗Carl Lumma <carl@...>

6/8/2008 11:17:43 AM

Mike wrote:

> > Human psychology varies greatly by individual and by trial
> > (what kind of day you're having), so it's difficult to
> > formalize anything about it in a music theory.
>
> Difficult but necessary.

Nah.

> assuming that you're writing music for a certain audience,
> you would first have in mind the mood of the audience as
> they sat down.

That's what DJing is all about. But see:
http://lumma.org/microwave/#2005.09.21

A related idea also features prominently in Indian classical
music, but from a more religious angle.

> Good composers do this all of the time.

Yes. It's nothing specific to microtonality that I can see.

> If you think about it, common practice theory is already partially
> tied in with psychology because of its attempts to label certain
> things as sounding "good" or "bad." We're already into it.

Nah. You can derive most of the common-practice rules
from psychoacoustics.

> > Another thing that's usually not formalized are priming
> > effects -- otherwise known as musical context. These effects
> > again will vary by listener and by trial. In adaptive tuning
> > schemes, one can treat past notes just like simultaneous
> > notes but subject to a decay process that weakens the
> > interactions. IIRC John deLaubenfels' system did something
> > like that, and other adaptive tuning schemes probably do
> > too (my own pet adaptive tuning scheme makes use of it).
>
> Ah, wow. An extension of the concept that if you leave out
> the 3rd in a chord, your mind will "fill it in" based on what
> third was heard before...?

No. That's to do with simultaneities.

> Perhaps even in a different chord? Like if I play C and G,
> but a little while ago there was an Eb major chord, I'll likely
> hear that dyad as having a "minor" quality.

More like it, yes.

> > Finally, at the level of cognitive psychology and
> > psychoacoustics (a branch of cog psy actually), effects are
> > largely listener-invariant. So I think it's a good place
> > to start.
>
> Yeah. That's where things like beat frequencies and such come
> into it.

It's much more than beat frequencies.

> I think my main point about psychology is that even as gestalt
> psychology predicts certain things about how someone will
> perceive a chord or phrase, there will be those whose gestalts
> differ. Different expectations yield different gestalts. And
> different expectations usually stem from different cultures.

If you know a way to get falsifiable predictions out of
gestalt psychology you should submit to Nature now.

> So ethnomusicology should be brought into the fold as well.

You could say that the regular mapping paradigm is the
resulting of turning ethnomusicology on Western music.

> > Assuming that people do complain about this and that it is
> > because of the smaller whole step, what you have is a
> > tendency to hear *melodic* intervals in terms of other melodic
> > intervals. This is very different from the whole
> > 16:19 v. 6:5 thing. The theory of harmonic approximation is
> > on solid footing at this point. Our understanding of a similar
> > concept for melodic intervals is more formative.
>
> Ah yeah, that's interesting. Harmony is different. You are
> right. Why the schism in harmony and melody here, I wonder...

It's because the former doesn't require memory. Harmonies
are processed directly by the virtual pitch detector in the
auditory midbrain.

> > Rothenberg's model actually makes predictions. For example,
> > as you morph one scale to another (by sliding the pitches
> > around), it predicts when you'll start to call it some tuning
> > of the new scale instead of some tuning of the old. These
> > predictions can be tested experimentally, but so far haven't
> > been (to my knowledge).
>
> Do you have a link to his model? This is really interesting.

Yes. I should warn you it's heavy going.
http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf

> Does this apply to harmony as well?

No. :)

> It seems interrelated to the fact that if I play a minor triad, and
> then a neutral triad, the neutral triad takes on a slightly major
> quality. But, if I play a major triad and then a neutral triad, the
> neutral triad takes on a slightly minor quality.

Yeah, that's related to:
http://en.wikipedia.org/wiki/Anchoring_effect

> > You gave cases where it doesn't. It's so incredibly easy
> > to make up music rules that hold sometimes and not others
> > that they're usually not worth thinking about.
>
> Yeah. And they are being taught in schools.

Oh, it gets far worse that that! Know anything about
"music set theory"?

> >> If you play C E G Bb D F that F will sound
> >> pretty "weak" in a straight ahead jazz context,
> >
> > C E G Bb D is a nice 4:5:6:7:9 chord in 12. The F is
> > pretty far from the 21 that might sound nice in the chord.
>
> Yeah, but the 21 is closer to the F than the 7 is to the Bb.
> There has to be another explanation...

The field of attraction of 7 is effectively much broader
than the field of attraction of 21, because 21 runs into
the nearby very strong field of 4/3.
Or it could be that you want to hear 11 there. The point
is that F doesn't fit into the harmonic series interp as
well as the other notes, so it weakens the interp. If we
had hexadic harmonic entropy, you could actually calculate
that the harmonic entropy goes down as you go from C E
to C E G to C E G Bb to C E G Bb D and then pops up when
you add the F.

> > Sure, you can use any perception -- positive or negative --
> > to create a good musical effect. That doesn't invalidate
> > the perception though.
>
> I mean that the C E G Bb D F gives a negative perception in
> some contexts and a positive one in others. Sometimes it
> sounds "floaty." And sometimes it sounds "unstable". See?
> Half full, half empty.

Yes. That's musical context and its study is really out of
the scope of tuning theory. But if you want to post your
findings here people will probably be receptive, especially
if you use alternate tunings in your experiments. But if
you just want to ask about it here it's probably not the
right venue.

> > I will say that one reason I don't like the rule is that
> > it talks about one interval alone without considering the
> > rest of the intervals in the chord. When evaluating chords,
> > generally there are two things I consider: 1. how strong is
> > the harmonic series interp (e.g. 4:5:7:9) and 2. how many
> > of the dyads within the chord are consonant. Both of these
> > necessitate looking at the *whole chord*, not just which
> > root some interval is built on top of.
>
> I think that's what my teacher is doing. He checks every dyad
> of the chord, and he has determined a 12tet "b9" dyad to be
> dissonant unless it's over the root.

No. When you check every dyad you don't care where they are
in the chord (checking the harmonic series interp takes care
of that). For intance, the dyads in C E G Bb approximate:

5/4
6/5
7/6
3/2
7/5
7/4

All of those are 7-limit consonances. So assuming the
approximations are any good, the chord will be consonant.

> So the question can be reformulated as thus: what
> makes a dyad consonant or dissonant?

There are two things: low harmonic entropy and low roughness.
You can have one, the other, or both. Consonance is actually
two different perceptions. But for harmonic timbres usually
used in Western music, these two components of consonance
usually move together. When you get into adaptive synthesis
like Bill Sethares, you can make timbres that are beatless
in 10-ET, but at the cost of increasing harmonic entropy
somewhat. So you can begin to hear one without the other
in that case.

But probably the best way to hear one without the other is
by playing extended utonalities -- try a subharmonic
4:5:6:7:9:11 chord. It's should be just as beatless as the
harmonic version because all its dyads are the same. But
the harmonic series interp skyrockets, which means the
harmonic entropy does too. And the chord by most accounts
sounds waay less consonant.

> > You and me both. We could buy a bunch of AXiSes and refretted
> > guitars and pitch a workshop to Berklee. I'd bet they'd go
> > for it. Might even give us some money.
>
> Hey, why not :P You buy the AXiSes, I'll write Berklee...

We could write a grant, or suggest to Berklee that they
pay us for giving the workshop.

> > Petr's music is generally improvisational in nature.
>
> Ah, neat. I'll have to check that out.

Drop him a line or make a post asking to hear his stuff.

> > The AXiS is competitively priced with halberstadt MIDI keyboards.
> > I looked at several by Kawai and Yamaha that were as expensive
> > just the other day. They were also total junk FWIW.
>
> Yeah, it's $1700. It's almost twice as expensive as a Fender Rhodes

How you figure? Rhodeses are total money pits. You could buy
several AXiSes for one in any kind of condition.

> and 2 and slightly less expensive than an Access TI Polar,

By the way, I believe the Access TI has built-in Hermode
tuning. (www.hermode.com)

> both of which are far more than just MIDI controllers

Yes, but the best synth in the known universe (pianoteq)
only costs $200, and there are many excellent cheap or
free microtonal-capable softsynths around the way.

> All of this and you
> still have to connect it to a computer and set up your some
> tuning software and deal with that if you ever want to play
> it live.

It's a bit of a pain I admit but not one that warrants the
number of complaints I hear about it.

> Never mind the fact that if you want decent samples

Samples?? Blechk!

> possibly have to deal with latency issues

Pianoteq runs like a champ on my 4-year-old laptop and
sounds better than any other synth I've ever played (which
is a lot, since I used to review them for Keyboard magazine).
You can't beat that with a stick.

> I definitely like the
> Sims-Maneri notation for 72-tet as a starting point,

I strongly recommend decimal notation for 72.

> >> I think that rather than add random corollaries to common
> >> practice theory about what sounds good or bad, we should take
> >> the concept up to a higher level of abstraction and figure
> >> out WHY things sound good or bad
> >
> > Well you've come to the right place then!
>
> Yeah man! I think we just need to formalize all of these ideas.

They're more formalized than I can handle already. Please
give it some time before passing judgment.

-Carl

🔗Carl Lumma <carl@...>

6/8/2008 11:34:19 AM

Torsten!

> > the Ricercar from Bach's Musikalisches Oper.

The ricercar a3. Not quite the a6 but still one of the
deeper pieces of music ever written.

> > The ricercar is available online
> >
> > http://www.plainsoundmusic.org/videos/Ricercar.mov
> > http://www.plainsound.de/scores/ricercar.pdf
> > http://www.plainsound.de/research/ricercartext.pdf

Ahh! I've been to the plainsound site a dozen times
and never saw this. Do you know when it was posted?

> Perhaps I should mention that this is at least 7-limit
> adaptive JI, it also includes higher limits such as
> 17 and 19. I find downright crazy what they did
> here -- its actually a new piece.

What you need to do is mention everything you know about
this, right away. :)

Too slow but jeez, what an achievement.

To tie things together, Godel Escher Bach is how I first
learned of the Musical Offering, and also a primary
reason I went to Indiana University to pursue a Cognitive
Science degree.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

6/8/2008 11:42:26 AM

[ Attachment content not displayed ]

🔗Carl Lumma <carl@...>

6/8/2008 12:04:50 PM

Hi Chris,

> What is a "neutral triad"?

Usually this means 9:11:18, or to spell that
another way, 1/1 11/9 3/2.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

6/8/2008 12:07:37 PM

[ Attachment content not displayed ]

🔗Carl Lumma <carl@...>

6/8/2008 12:34:34 PM

> Hi Carl,
>
> I'm new to the microtonal terminology.
>
> 1/1 = root
> 3/2 = fifth
> 11/9 = no idea what that is

11/9 is a neutral third. These things are frequency ratios,
e.g. G = 300 Hz. and C = 200 Hz. is 3/2. You can convert
to cents by taking the base-2 logs and multiplying by 1200.
So 3/2 = 702 cents and 11/9 = 347 cents. 347 cents is right
in between 386 cents (5/4) and 316 cents (6/5), hence the
term "neutral". In fact it is the simplest ratio between
the major and minor 3rd, as can be established by the fact
that it is the *mediant* of 5/4 and 6/5.

http://en.wikipedia.org/wiki/Mediant_%28mathematics%29

Neutral thirds of one kind or another are prominent in
middle eastern scales.

I'm sorry I screwed up with the harmonic series subset
I gave. It's not 9:11:18, it's 18:22:27, as 22/18 = 11/9
and 27/18 = 3/2.

-Carl

🔗Carl Lumma <carl@...>

6/8/2008 12:48:43 PM

--- In tuning@yahoogroups.com, Torsten Anders <torstenanders@...> wrote:
>
> On Jun 8, 2008, at 11:32 AM, Torsten Anders wrote:
> > the Ricercar from Bach's Musikalisches Oper.
> > The ricercar is available online
> >
> > http://www.plainsoundmusic.org/videos/Ricercar.mov
> > http://www.plainsound.de/scores/ricercar.pdf
> > http://www.plainsound.de/research/ricercartext.pdf
>
> Perhaps I should mention that this is at least 7-limit
> adaptive JI, it also includes higher limits such as
> 17 and 19. I find downright crazy what they did here --
> its actually a new piece.

I actually had the text pdf on my hard drive already,
but not the video or the score. It sounds like this
ends on the same pitch it begins on!
The text basically says that they used artistic
judgment to do the intonation. They do say they
allowed the intonation of the theme to vary throughout
as necessary. They also say they were driven to
higher limits after trying 5-limit schismatic and
not liking the results.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

6/8/2008 12:56:27 PM

[ Attachment content not displayed ]

🔗Carl Lumma <carl@...>

6/8/2008 1:18:14 PM

> Would this "neutral third" be related to the "blues third"?

Not especially. I think that's more like 7/6. -C.

🔗Torsten Anders <torstenanders@...>

6/8/2008 1:30:25 PM

> It sounds like this ends on the same pitch it begins on!

Although they they introduce a large set of pitches for their adaptive tuning (67 pitches if I counted right their harmonic lattice on http://www.plainsound.de/scores/ricercar.pdf), it appears they never adapt the tonic (C) nor the dominant (G). Actually, the harmonic lattice does list adapted version like C\ (C flat a syntonic comma). However, I never noticed that while listening -- 1/1 always rules :)

Best
Torsten

On Jun 8, 2008, at 8:48 PM, Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Torsten Anders <torstenanders@...> > wrote:
> >
> > On Jun 8, 2008, at 11:32 AM, Torsten Anders wrote:
> > > the Ricercar from Bach's Musikalisches Oper.
> > > The ricercar is available online
> > >
> > > http://www.plainsoundmusic.org/videos/Ricercar.mov
> > > http://www.plainsound.de/scores/ricercar.pdf
> > > http://www.plainsound.de/research/ricercartext.pdf
> >
> > Perhaps I should mention that this is at least 7-limit
> > adaptive JI, it also includes higher limits such as
> > 17 and 19. I find downright crazy what they did here --
> > its actually a new piece.
>
> I actually had the text pdf on my hard drive already,
> but not the video or the score. It sounds like this
> ends on the same pitch it begins on!
> The text basically says that they used artistic
> judgment to do the intonation. They do say they
> allowed the intonation of the theme to vary throughout
> as necessary. They also say they were driven to
> higher limits after trying 5-limit schismatic and
> not liking the results.
>
> -Carl
>
>
>
--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

🔗Mike Battaglia <battaglia01@...>

6/8/2008 1:54:46 PM

On Sun, Jun 8, 2008 at 3:56 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> Would this "neutral third" be related to the "blues third"?

You will hear some disagreement here in regards to that, but I do hear
the neutral third used often over the blues, as well as the interval
between a perfect 4th and a perfect 5th, which is pretty close to
11/4.

-Mike

🔗Mark Rankin <markrankin95511@...>

6/8/2008 4:02:38 PM

Carl,

Have you or anyone you know ever tried to download Ricecar.mov?

I have tried repearedly. At the fifth bar the download stalls.

Mark

--- On Sun, 6/8/08, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Music Theory
To: tuning@yahoogroups.com
Date: Sunday, June 8, 2008, 11:34 AM

Torsten!

> > the Ricercar from Bach's Musikalisches Oper.

The ricercar a3. Not quite the a6 but still one of the
deeper pieces of music ever written.

> > The ricercar is available online
> >
> > http://www.plainsou ndmusic.org/ videos/Ricercar. mov
> > http://www.plainsou nd.de/scores/ ricercar. pdf
> > http://www.plainsou nd.de/research/ ricercartext. pdf

Ahh! I've been to the plainsound site a dozen times
and never saw this. Do you know when it was posted?

> Perhaps I should mention that this is at least 7-limit
> adaptive JI, it also includes higher limits such as
> 17 and 19. I find downright crazy what they did
> here -- its actually a new piece.

What you need to do is mention everything you know about
this, right away. :)

Too slow but jeez, what an achievement.

To tie things together, Godel Escher Bach is how I first
learned of the Musical Offering, and also a primary
reason I went to Indiana University to pursue a Cognitive
Science degree.

-Carl

🔗Kraig Grady <kraiggrady@...>

6/8/2008 8:12:04 PM

Historically the list has been rather contradictory about the blues third bouncing between the two at one moment changing to the other in different context. Some how i think the blues needs them both.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> On Sun, Jun 8, 2008 at 3:56 PM, Chris Vaisvil <chrisvaisvil@... > <mailto:chrisvaisvil%40gmail.com>> wrote:
> > Would this "neutral third" be related to the "blues third"?
>
> You will hear some disagreement here in regards to that, but I do hear
> the neutral third used often over the blues, as well as the interval
> between a perfect 4th and a perfect 5th, which is pretty close to
> 11/4.
>
> -Mike
>
>

🔗Mike Battaglia <battaglia01@...>

6/8/2008 8:47:32 PM

On Sun, Jun 8, 2008 at 2:17 PM, Carl Lumma <carl@...> wrote:
> Mike wrote:
>
>> > Human psychology varies greatly by individual and by trial
>> > (what kind of day you're having), so it's difficult to
>> > formalize anything about it in a music theory.
>>
>> Difficult but necessary.
>
> Nah.

Wow. Don't complain to me any more about how I don't read your posts
before replying.

>> assuming that you're writing music for a certain audience,
>> you would first have in mind the mood of the audience as
>> they sat down.
>
> That's what DJing is all about. But see:
> http://lumma.org/microwave/#2005.09.21
>
> A related idea also features prominently in Indian classical
> music, but from a more religious angle.
>

I agree wholeheartedly. I would then say that Indian classical music
has a stronger basis in that regard than Western classical music.

>> Good composers do this all of the time.
>
> Yes. It's nothing specific to microtonality that I can see.

As far as I know, this forum isn't about topics that are completely
exclusive to microtonality, but rather that apply to microtonality :)
Are you saying this thread is "off-topic?" I'm not sure what you mean
here.

The entire paragraph was meant to shed light on these psychological
"gestalt-altering" techniques and look at how they apply to music.
Alternately, you can look at these musical techniques from a
psychological perspective. Music and psychology are already
interwoven. The entire paragraph was written to support the statement
that an elucidating and understanding of these psychological tools
would be useful in a "music theory," rather than the current system
which has "rules" as to what sounds good or bad and a vague notion
that "the rules can be broken." So basically it was meant to support
the first statement in my sentence, which you so eloquently dismissed
with a "Nah." :)

The fact that composers already do this means that it is already part
of their own internal "music theory." I am simply suggesting that we
work out the inconsistencies and formalize it, as common practice
theory is formalized.

>> If you think about it, common practice theory is already partially
>> tied in with psychology because of its attempts to label certain
>> things as sounding "good" or "bad." We're already into it.
>
> Nah. You can derive most of the common-practice rules
> from psychoacoustics.

Yes. Many of them. The "ban" on parallel fifths and octaves in 4 part
writing is a good example of how psychoacoustics comes into play. The
omitting of the fifth being allowed does as well. Psychoacoustics
doesn't often talk about what sounds "good" or "bad" because whether
or not someone LIKES something has nothing to do with psychoacoustics,
but rather the psychological composition of the listener. So I suggest
that we either stop teaching what sounds good and bad in music schools
(which partially defeats the purpose of a music school), or we dig in
deeper and get further into the psychology of things rather than what
sounded good to the average person in the 17th century.

>> I think my main point about psychology is that even as gestalt
>> psychology predicts certain things about how someone will
>> perceive a chord or phrase, there will be those whose gestalts
>> differ. Different expectations yield different gestalts. And
>> different expectations usually stem from different cultures.
>
> If you know a way to get falsifiable predictions out of
> gestalt psychology you should submit to Nature now.

That's sort of the line of research I'm proposing with this thread.
I'd be happy with a prediction rate of 75-85%. The predictions don't
necessarily have to be perfect. Just better than they are now. The
concept of the predictions never actually reaching perfection could be
a key point in the teaching of music.

>> So ethnomusicology should be brought into the fold as well.
>
> You could say that the regular mapping paradigm is the
> resulting of turning ethnomusicology on Western music.

Yeah, I've been reading it for a day now. It's really, really
interesting, and actually does adequately address a lot of the
problems I was talking about, as well as leave areas for further
research (sum and difference tones and such).

>> > Assuming that people do complain about this and that it is
>> > because of the smaller whole step, what you have is a
>> > tendency to hear *melodic* intervals in terms of other melodic
>> > intervals. This is very different from the whole
>> > 16:19 v. 6:5 thing. The theory of harmonic approximation is
>> > on solid footing at this point. Our understanding of a similar
>> > concept for melodic intervals is more formative.
>>
>> Ah yeah, that's interesting. Harmony is different. You are
>> right. Why the schism in harmony and melody here, I wonder...
>
> It's because the former doesn't require memory. Harmonies
> are processed directly by the virtual pitch detector in the
> auditory midbrain.

Interesting, does Rothenberg's model address people with absolute
pitch? I am blessed with the ability but I find little to no research
involving it in a microtonal sense... When I hear a melody, I don't
hear up/down/up, but rather A B A or something, so it isn't that I
hear music in terms of just intervals. I can see what Rothenberg's
talking about, but for me there is this virtual conflict -- let's say
you have a melody ascending in major whole tones and then descending
in minor whole tones. If the melody ends up a half step higher from
where it started, for example, I will be very very confused, as I'll
hear whole tones in either direction, but that will be in conflict
with the fact that the end note I'm hearing is much different from the
start note.

I definitely do see what you're talking about about the "skill" of
memorizing intervals though.

>> > Rothenberg's model actually makes predictions. For example,
>> > as you morph one scale to another (by sliding the pitches
>> > around), it predicts when you'll start to call it some tuning
>> > of the new scale instead of some tuning of the old. These
>> > predictions can be tested experimentally, but so far haven't
>> > been (to my knowledge).
>>
>> Do you have a link to his model? This is really interesting.
>
> Yes. I should warn you it's heavy going.
> http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf

Thanks, I'll check it out. 85 pages is gonna be fun to get through.
//

> Oh, it gets far worse that that! Know anything about
> "music set theory"?

I just gave it a look on Wikipedia. My main beef with it is that it's
one step away from JI, which is what really needs to be taught in
schools, IMO. Might be useful for something, I can't tell from the
first glance. The concept of an "interval vector" I found to be
laughable.

> The field of attraction of 7 is effectively much broader
> than the field of attraction of 21, because 21 runs into
> the nearby very strong field of 4/3.
> Or it could be that you want to hear 11 there. The point
> is that F doesn't fit into the harmonic series interp as
> well as the other notes, so it weakens the interp. If we
> had hexadic harmonic entropy, you could actually calculate
> that the harmonic entropy goes down as you go from C E
> to C E G to C E G Bb to C E G Bb D and then pops up when
> you add the F.

OK, let me give you a better example - something a little further from
the harmonic series. how about C Eb G Bb D F Ab? That Ab on the top to
my ears sounds pretty weak structurally, and if I ever hear that chord
voiced in jazz they usually put the Ab where I have the G and
vice-versa. Let's assume this to be 5 limit - the 5-limit JI chord
version of this displays this same property. This chord:

100:120:150:180:225:270:324

is the one I'm talking about. The first 6 notes sound good, but when
you add that 324, the whole chord is destabilized.

Jazz has this concept of "avoid notes" - over major, you're supposed
to avoid playing the 4th scale degree for too long over a major chord.
In Aeolian, you're supposed to avoid playing the b6 for too long. My
teacher was basically trying to teach me that concept in the context
of harmony.

I thought that it had something to do with mixing utonalities and
otonalities in the same chord... Then I realized that a dominant 7
chord with 16:9 as the 7 is 2 fourths, and that doesn't sound bad. Not
to mention a good ol minor chord.

> Yes. That's musical context and its study is really out of
> the scope of tuning theory. But if you want to post your
> findings here people will probably be receptive, especially
> if you use alternate tunings in your experiments. But if
> you just want to ask about it here it's probably not the
> right venue.

Alright, fair enough. Perhaps it would be a better question for the
MMM group. I was using that as another example to how gestalt
psychology ties into music theory as described in my first paragraph.
It demonstrates how the "gestalt" of the chord changes depending on
the circumstances, which is a concept that I think would have some
profound implications in other areas of tuning theory.

> No. When you check every dyad you don't care where they are
> in the chord (checking the harmonic series interp takes care
> of that). For intance, the dyads in C E G Bb approximate:
>
> 5/4
> 6/5
> 7/6
> 3/2
> 7/5
> 7/4
>
> All of those are 7-limit consonances. So assuming the
> approximations are any good, the chord will be consonant.

So how does C Eb G Bb D F Ab fit into that? That chord sounds
dissonant, but C F G Db does not. I suppose they both sound to some
extent "dissonant," and "unresolved," but the first one sounds less
stable, I suppose.

> There are two things: low harmonic entropy and low roughness.
> You can have one, the other, or both. Consonance is actually
> two different perceptions. But for harmonic timbres usually
> used in Western music, these two components of consonance
> usually move together. When you get into adaptive synthesis
> like Bill Sethares, you can make timbres that are beatless
> in 10-ET, but at the cost of increasing harmonic entropy
> somewhat. So you can begin to hear one without the other
> in that case.
>
> But probably the best way to hear one without the other is
> by playing extended utonalities -- try a subharmonic
> 4:5:6:7:9:11 chord. It's should be just as beatless as the
> harmonic version because all its dyads are the same. But
> the harmonic series interp skyrockets, which means the
> harmonic entropy does too. And the chord by most accounts
> sounds waay less consonant.

Ah, wow. That's a good way of explaining it.

So then I suppose an alternate question is, C E G Bb D F sounds pretty
weak, but C E G Bb D F# sounds quite strong to me. 11/4 is halfway
between the F and the F#. Why does that F# work so well? Is it just
that the F# is out of the way of the field of attraction of the 4/3,
and so that it can jump to the 11/4 more easily?

>> > You and me both. We could buy a bunch of AXiSes and refretted
>> > guitars and pitch a workshop to Berklee. I'd bet they'd go
>> > for it. Might even give us some money.
>>
>> Hey, why not :P You buy the AXiSes, I'll write Berklee...
>
> We could write a grant, or suggest to Berklee that they
> pay us for giving the workshop.

I'm down. I would find it to be personally fulfilling for me as the
culmination of my efforts in finding the easiest microtonal system for
my non-mathematical friends to adjust to. There are a -lot- of schools
that I know of that would be interested in such a program, the
University of Miami and USC.

It would be good to build some kind of "course" to facilitate the
learning of this - perhaps people could start with something simple
such as 19- or 17-tet. Hell, maybe even throw in 5-tet before that
just to get them quickly accustomed to the fact that not everything
besides 12-tet sounds "weird." From there it might be nice to jump up
to something like 31, so they can jump into 7-limit and 11-limit music
fairly quickly. I think that might be a nice time to start addressing
the theory behind it, getting into 5-limit and 7-limit JI and such.
Maybe at that point let them screw around with a non-meantone
temperament like 53-equal, which might be a good choice as the harmony
is almost pure and nearly indistinguishable from JI, and some of the
more compositional-minded students would probably enjoy the ability to
modulate to any key. Alternately, we could let them screw around with
the Axis' harmonic table in pure 5 or 7-limit just (if we can get a
decent 7-limit pattern going for it). The culmination of the whole
course would be to introduce 72-equal to them, at which point all of
the stuff they've learned ties in together almost perfectly with the
system they already know, and they "see the light" just like most
people who are exposed to 72-equal for the first time :P

Another approach that Graham suggested in this same thread is to
alternately start them off with some non-equal temperament like magic
or blackjack to get them started with higher-limit chords right away,
for those who complain about "too many notes per octave." It's an
interesting idea to be sure, although I personally have never found
higher-order equal temperaments to be that intimidating as long as
some regular pattern can be seen amongst the notes. 31-tet's note
naming system, for example, stems directly from the usual meantone
tradition, and I found it extremely easy to grasp right away. Stuff
like 53-equal is a little harder at first, but I think once people
realize that 31 isn't the end of the world, they're much more likely
to jump into that. And 72-equal is pretty easy to grasp for the same
reasons. I think the "too many notes" thing stems from a misconception
that you have to mentally deal with all of those notes at the same
time.

>> > The AXiS is competitively priced with halberstadt MIDI keyboards.
>> > I looked at several by Kawai and Yamaha that were as expensive
>> > just the other day. They were also total junk FWIW.
>>
>> Yeah, it's $1700. It's almost twice as expensive as a Fender Rhodes
>
> How you figure? Rhodeses are total money pits. You could buy
> several AXiSes for one in any kind of condition.

http://cgi.ebay.com/Fender-Rhodes-Mark-I-Stage-Piano-73-Key_W0QQitemZ320258129120QQihZ011QQcategoryZ1289QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$640, good condition Mk. 1 stage. A little over a third of the cost of the AXiS.

>> and 2 and slightly less expensive than an Access TI Polar,
>
> By the way, I believe the Access TI has built-in Hermode
> tuning. (www.hermode.com)

Damn. I really need to get one of those keyboards. I'm stuck between
that and the Nord Electro, which has no microtonal functionality
whatsoever, but awesome electroacoustic samples to boast. I am torn.

> Yes, but the best synth in the known universe (pianoteq)
> only costs $200, and there are many excellent cheap or
> free microtonal-capable softsynths around the way.

Hahaha, funny. I do like pianoteq quite a bit. I find it to be a lot
better than the Pianoid, which is the only other physical modelling
piano synth I know.

>> All of this and you
>> still have to connect it to a computer and set up your some
>> tuning software and deal with that if you ever want to play
>> it live.
>
> It's a bit of a pain I admit but not one that warrants the
> number of complaints I hear about it.

It simply limits its audience to those with software and laptops and
the knowhow to get it all going. While you and I are obviously
capable, horn players and guitarists and such are pretty much left out
of the fold here. I envision the day when an all-in-one microtonal
synth and controller (in short, an instrument) is made so people can
just buy it and get moving. I'm thinking of picketing outside Yamaha's
office to maybe push it along.

>> Never mind the fact that if you want decent samples
>
> Samples?? Blechk!

I'm telling you, VSL and EWQL have the most realistic orchestral
samples you will ever hear in your entire life. Though if you used to
review for Keyboard Mag, you'll likely have heard them already. But
just in case not:

Vienna Symphonic Library -
http://vsl.co.at/downloader.asp?file=/Sounds/MP3/VI_DEMOS/00_Symphonic_Cube/AT_Firebird_Danse_infernale.mp3
(The Firebird)
EastWest Symphonic Orchestra -
http://www.soundsonline.com/cd_mp3_demos/229630.mp3 (Venus, from the
Planets)

While neither of them are perfect (the strings in both of these
weren't done very well at spots), they're definitely miles above what
you're going to find elsewhere :P Using the two in tandem usually
makes it sound pretty good. Hollywood movies sometimes do their entire
scores in these programs.

Here's an EastWest string quartet in which the strings were done a bit
more realistically:
http://www.soundsonline.com/cd_mp3_demos/229788.mp3

More VSL samples - http://vsl.co.at/en/67/702/703/413.htm
More EastWest samples - http://www.majormusic.com.au/products/ew_so_pro_xp.php

I find that using EastWest to write in 72tet usually yields much
better results than using the GM sound set, hah.

>> possibly have to deal with latency issues
>
> Pianoteq runs like a champ on my 4-year-old laptop and
> sounds better than any other synth I've ever played (which
> is a lot, since I used to review them for Keyboard magazine).
> You can't beat that with a stick.

Nor can you beat it with a Pianoid, although attempting to use the
Pianoid box to physically beat something may be the only thing that
it's good for.

-Mike

🔗Carl Lumma <carl@...>

6/8/2008 11:44:06 PM

Mike wrote:

> The fact that composers already do this means that it is
> already part of their own internal "music theory." I am simply
> suggesting that we work out the inconsistencies and formalize
> it, as common practice theory is formalized.

I think you mean "I work out". You could start your own
mailing list. If other people join and become active, then
you could upgrade this statement to "we".

> So I suggest that we either stop teaching what sounds good
> and bad in music schools

Just who is this "we" you keep talking about?

> > If you know a way to get falsifiable predictions out of
> > gestalt psychology you should submit to Nature now.
>
> That's sort of the line of research I'm proposing with this
> thread. I'd be happy with a prediction rate of 75-85%.

You're easy to please then! But anyway I suggest you do
more researching and less proposing.

> does Rothenberg's model address people with absolute pitch?

Not that I can remember.

> I am blessed with the ability but I find little to no research
> involving it in a microtonal sense... When I hear a melody, I
> don't hear up/down/up, but rather A B A or something, so it
> isn't that I hear music in terms of just intervals. I can see
> what Rothenberg's talking about, but for me there is this
> virtual conflict -- let's say you have a melody ascending in
> major whole tones and then descending in minor whole tones. If
> the melody ends up a half step higher from where it started,
> for example, I will be very very confused, as I'll hear whole
> tones in either direction, but that will be in conflict with
> the fact that the end note I'm hearing is much different from
> the start note.

Sounds like you're still listening to intervals then. If you
can recognize themes transposed into the relative minor and
such, then you are doing what Rothenberg is concerned with,
which is assigning scale degrees to pitches. You recognize
the theme by the fact it still has the same pattern of scale
intervals (5th 3rd 2nd etc.) even though the pitches and even
the qualities of the intervals (major 3rd vs. minor 3rd) are
different.

> > Oh, it gets far worse that that! Know anything about
> > "music set theory"?
>
> I just gave it a look on Wikipedia. My main beef with it is
> that it's one step away from JI, which is what really needs
> to be taught in schools, IMO. Might be useful for something,
> I can't tell from the first glance. The concept of an
> "interval vector" I found to be laughable.

It's what serialism morphed into. They publish lots of papers
explaining the rules of common practice music based on these
arcane (and acoustically meaningless) pitch transformations.
Many of the celebrated results in the field don't work if you
try to apply them in, say, 31-ET instead of 12-ET. Even though
by all accounts lots of music sounds just fine (if not
better) in 31.

> OK, let me give you a better example - something a little
> E further from the harmonic series. how about C Eb G Bb D F Ab?
> That Ab on the top to my ears sounds pretty weak structurally,

Alright, I've demonstrated the techniques. What do you think?

> Jazz has this concept of "avoid notes" - over major, you're
> supposed to avoid playing the 4th scale degree for too long
> over a major chord. In Aeolian, you're supposed to avoid
> playing the b6 for too long. My teacher was basically trying
> to teach me that concept in the context of harmony.

It would be interesting to try and reverse engineer avoid
note rules. They may be just capture what early players
happened to do ("frozen accidents"), or they may capture a
something deeper. 'Omit the 3rd' may make sense in the
following manner:

* you can't have the 4:5 in the bass because it could get
muddy (due to critical band effects)
* if you put the 4:7 in the bass and the other identities
in the treble you're putting them in a different order than
they first appear in the harmonic series
* if you put the 4:6 in the bass and the 5:7 in the treble
you run the risk of evoking polytonality
* if you omit the 7 you don't have anything new
* that leaves 'omit the 4 (3rd)'

> > Yes. That's musical context and its study is really out of
> > the scope of tuning theory. But if you want to post your
> > findings here people will probably be receptive, especially
> > if you use alternate tunings in your experiments. But if
> > you just want to ask about it here it's probably not the
> > right venue.
>
> Alright, fair enough. Perhaps it would be a better question
> for the MMM group.

I guess there's only one way to find out...

> So then I suppose an alternate question is, C E G Bb D F sounds
> pretty weak, but C E G Bb D F# sounds quite strong to me.
> 11/4 is halfway between the F and the F#. Why does that
> F# work so well? Is it just that the F# is out of the way of
> the field of attraction of the 4/3, and so that it can jump
> to the 11/4 more easily?

Bingo. F is really close to 8/3, but 8/3 doesn't fit into the
chord because the root is a power of 2 to all the other notes.

> >> > You and me both. We could buy a bunch of AXiSes and
> >> > refretted guitars and pitch a workshop to Berklee. I'd
> >> > bet they'd go for it. Might even give us some money.
//
> > We could write a grant, or suggest to Berklee that they
> > pay us for giving the workshop.
>
> I'm down. //
> There are a -lot- of schools that I know of that would be
> interested in such a program, the University of Miami and USC.

Want to take it off-list and come up with a proposal together?

> It would be good to build some kind of "course" to facilitate
> the learning of this - perhaps people could start with something
> simple such as 19- or 17-tet.

I think 19 is ideal for guitars. 17 is too weird for a first
attempt at mass appeal, though Jacob Barton has hosted a series
of very successful events based around it (look up "17-tone
piano project" if you're not familiar). For keyboards I
think 31 is a nice choice. But to harmonize with the guitars
maybe everybody should do 19.

> Hell, maybe even throw in 5-tet before that just to get
> them quickly accustomed to the fact that not everything
> besides 12-tet sounds "weird." From there it might be nice
> to jump up to something like 31, so they can jump into
> 7-limit and 11-limit music fairly quickly.

I think doing improv in 5 and 7 first would be a good idea,
at least for the keyboards.

> Alternately, we could let them screw around with the Axis'
> harmonic table in pure 5 or 7-limit just

Yeah, that'd be good.

> (if we can get a decent 7-limit pattern going for it)

I don't think that'll be a problem. :)

> $640, good condition Mk. 1 stage.

Have you ever owned a Rhodes? You couldn't pay me $640 to
take it.

> > By the way, I believe the Access TI has built-in Hermode
> > tuning. (www.hermode.com)
>
> Damn. I really need to get one of those keyboards. I'm stuck
> between that and the Nord Electro, which has no microtonal
> functionality whatsoever, but awesome electroacoustic samples
> to boast. I am torn.

I came so close to buying an electro. Yup, the sounds are
good ( for a sampler :P ). But nord instruments are kind of
candy-assed in some way and definitely overpriced. You should
totally check out the hermode site in depth if you haven't. My
current object of desire is a Kurzweil PC3. Yum. But it costs
more than an AXiS.

> >> // and you still have to connect it to a computer and //
> >
> > It's a bit of a pain I admit but not one that warrants the
> > number of complaints I hear about it.
//
> horn players and guitarists and such are pretty much left out
> of the fold here.

What use have they for synths?

> >> Never mind the fact that if you want decent samples
> >
> > Samples?? Blechk!
>
> I'm telling you, VSL and EWQL have the most realistic
> orchestral samples you will ever hear in your entire life.

I've heard them a plenty. But my favorite way to synthesize
orchestras is Synful.

-Carl

🔗Mike Battaglia <battaglia01@...>

6/9/2008 12:19:41 AM

> Mike wrote:
> > Insert a paragraph or two here that was the result of three nights worth of
> > synthesizing concepts together from three fields, complete
> > with three or four pages of notebook paper filled solid of unintelligible half-sentences and doodles and
> > remnants of the emotional ups and downs I went through at various stages of the process, eventually arriving
> > at an intellectually orgasmic "eureka" moment where things finally made sense
> > as I saw a consistent paradigm develop
> > and an actual direction forward for mainstream music theory, music education, microtonal theory, etc
> > to go in.
> > the results of this brainstorming session then submitted,
> > here, for review and feedback from the community

Carl wrote:
> > Sentence 1 from the aforementioned paragraph
> You are wrong and naive. Alternately, you are right but this has been discovered so much already
> that it bores me.
> I have been here for far longer than you here and used to moderate.
> Also, in case you didn't notice here, you are new to this forum, and thus what most would term a "noob."
> I would like to take this time to tell you that I do not share your enthusiasm for your ideas. Please stop being excited.
> I would also like to remind you that this isn't your group. It isn't mine either, but I used to moderate, and I've been around for
> 11 years. The third and fourth sentences of the paragraph were off-topic and did not immediately and/or exclusively relate
> to microtonal music/tuning theory.

> Mike wrote:
> > random fragment taken out of yet another paragraph attempting to communicate
> > ideas that appear consistent to me and were born entirely out of the desire to understand
> > music as much as possible and certainly better than is taught in schools, yet that
> > I certainly lack the capacity to independently research on my own and at the current
> > time, at least until I come up with a clear plan to do so; desiring instead rather for
> > a discussion of such ideas

Carl wrote:
> Without addressing your statements directly, I would just like to remind you that you are new to the group
> and thus do not know enough people here to form your own yahoo tuning-related group.
> (and if you did, I probably wouldn't join anyway)

-Mike

🔗Mike Battaglia <battaglia01@...>

6/9/2008 1:33:02 AM

> Sounds like you're still listening to intervals then. If you
> can recognize themes transposed into the relative minor and
> such, then you are doing what Rothenberg is concerned with,
> which is assigning scale degrees to pitches. You recognize
> the theme by the fact it still has the same pattern of scale
> intervals (5th 3rd 2nd etc.) even though the pitches and even
> the qualities of the intervals (major 3rd vs. minor 3rd) are
> different.

Ah. How does this stuff apply outside of diatonic scale theory...? Or
does he propose rather that the whole thing be fit into diatonic scale
theory?

As in, the 12tet octatonic scale - C Db D# E F# G A Bb C can be viewed
as having two separate 2nd's or 9th's, a b9 and a #9...
Or the "altered scale," C Db Eb Fb Gb Ab Bb C - which is usually
viewed in jazz theory more as C Db D# E F#/Gb G#/Ab Bb C, as if it has
two types of 9ths and notes that serve dual functions for different
kinds of fifths and sixths..

The octatonic scale in particular having 8 notes but often being
viewed as having 7 with two possible 9ths. Is he saying that is
because jazz musicians often haven't acquired the "skill" of hearing
all 8 notes in relation to one another, so they just fit it into their
existing paradigm of being the alterations of the existing 7 notes
that they have? Same with the altered scale... that you need to learn
to hear C-Fb as a kind of FOURTH rather than fitting it into ones
concept as a major third?

If that's what he's saying, then that's the kind of stuff I'm
proposing be taught in jazz schools and such around the country.
That's basically a huge step forward in my mind as it relates to
improvements in music theory in education. And if that's not what he's
saying, then I'm taking credit for it and calling it the
"Battagliastic principle of intervallic mapping."

> It's what serialism morphed into. They publish lots of papers
> explaining the rules of common practice music based on these
> arcane (and acoustically meaningless) pitch transformations.
> Many of the celebrated results in the field don't work if you
> try to apply them in, say, 31-ET instead of 12-ET. Even though
> by all accounts lots of music sounds just fine (if not
> better) in 31.

Acoustically meaningless being the key term. I did some more research
into the field and found that I had actually encountered the concept
on a "music theory" test I had taken online a while ago just for
fun... I ran into this stuff on the third or fourth page and was
baffled. I figured it out pretty quickly as being scale steps, as many
of the examples corresponded to simple 12tet major or minor chords,
but it's stuff like that that's being taught as "high-level" music
theory gospel that only further cements people into the 12tet fold and
takes them further confused as to where it all comes from.

>> OK, let me give you a better example - something a little
>> E further from the harmonic series. how about C Eb G Bb D F Ab?
>> That Ab on the top to my ears sounds pretty weak structurally,
>
> Alright, I've demonstrated the techniques. What do you think?

I think it makes sense for the first chord, but I don't see how it
relates to the second one I posted above, as I deliberately picked one
that was further from the harmonic series just to see how the
techniques would apply there. I'm not sure how they carry over to
things like that. Intuitively I feel that that G-Ab is really what is
causing it, but maybe not, because if you take the G out, it still
sounds weird. Maybe psychoacoustically the G is implied...? I didn't
get enough information from your
first explanation to see immediately how it would tie over into a case
like this.

Plus the Eb differing immediately from the expected E in the harmonic
series would cause its own harmonic entropy increase, but THAT doesn't
destabilize the chord.

Is that b9 dissonance just too hard to take at times?

>> Jazz has this concept of "avoid notes" - over major, you're
>> supposed to avoid playing the 4th scale degree for too long
>> over a major chord. In Aeolian, you're supposed to avoid
>> playing the b6 for too long. My teacher was basically trying
>> to teach me that concept in the context of harmony.
>
> It would be interesting to try and reverse engineer avoid
> note rules. They may be just capture what early players
> happened to do ("frozen accidents"), or they may capture a
> something deeper.

Yeah, the avoid note rules are basically just the melodic versions of
the "no b9" rule as outlined above. If you look closely, all of the
avoid notes usually talked about are just places where a b9 exists
over some other note. Intuitively I feel that something deeper is
happening, and that it has something to do with the b9 rule, but that
there is some effect beyond that that has to do with
sum-and-difference tones or perhaps the harmonic entropy as you
outlined above, though I still can't see how to apply the techniques
to chords that don't resemble the harmonic series.

> 'Omit the 3rd' may make sense in the following manner:

Hm. Usually the fifth is being omitted, not the third... The third and
seventh are usually seen as "color" tones, and intuitively it does
seem to make sense. I think it has to do with the principle of
anchoring mentioned earlier... C G Bb doesn't imply major or minor and
so the amount of information/entropy is low. C E Bb does imply a major
and gives the kind of 7th chord that it is as well.

> * you can't have the 4:5 in the bass because it could get
> muddy (due to critical band effects)

Yis.

> * if you put the 4:7 in the bass and the other identities
> in the treble you're putting them in a different order than
> they first appear in the harmonic series

So you don't like chord voicings along the lines of C Bb E G D?
Usually I hear those chords played more often in jazz as the added
"crunch" from putting them in that sort of inversion implies the
tonality of the chord more, not less

> * if you put the 4:6 in the bass and the 5:7 in the treble
> you run the risk of evoking polytonality

Er, you mean like C G E Bb or something? How is that polytonal?

> * if you omit the 7 you don't have anything new
> * that leaves 'omit the 4 (3rd)'

Confused... do you mean omit the 5? Are your guidelines here for how
to voice tetrads in 4 parts?

>> > Yes. That's musical context and its study is really out of
>> > the scope of tuning theory. But if you want to post your
>> > findings here people will probably be receptive, especially
>> > if you use alternate tunings in your experiments. But if
>> > you just want to ask about it here it's probably not the
>> > right venue.
>>
>> Alright, fair enough. Perhaps it would be a better question
>> for the MMM group.
>
> I guess there's only one way to find out...

Wait for my approval for join request?

>> So then I suppose an alternate question is, C E G Bb D F sounds
>> pretty weak, but C E G Bb D F# sounds quite strong to me.
>> 11/4 is halfway between the F and the F#. Why does that
>> F# work so well? Is it just that the F# is out of the way of
>> the field of attraction of the 4/3, and so that it can jump
>> to the 11/4 more easily?
>
> Bingo. F is really close to 8/3, but 8/3 doesn't fit into the
> chord because the root is a power of 2 to all the other notes.

Right. So how about actual dominant seventh chords, like 36:45:54:64?
That Bb as a 16/9 fits in pretty nice to me, even if that chord is
used as a tonic. I find it has a different, much brighter feel than
4:5:6:7, and works itself as a tonic for a kind of "going places,
unresolved" feel.

So how come, over a major chord, the note that is two fourths down
fits in to make a "strong" chord, but the note that is one fourth down
does not? Would you say that I'm still hearing 16/9 as just a brighter
type of 7/4, or as 16/9 in its own right?

Actually, I was just thinking, that principle of learning melodic
intervals as a "skill" might be useful in harmony as well. If you're
accustomed to 16/9 for dominant chords your whole life, when you first
hear 4:5:6:7, you might think it IS a dominant chord that needs to
resolve, as many do. After you listen to the chord enough though, you
become accustomed to it being a consonance that is unresolved in its
own right, and you acquire the "skill" to map that consonance out.
When I first heard 21/8 used in a chord, as in 16:20:24:28:35:42...
(two major chords, the second built off of the 7/4 of the first) I
first thought it WAS 4/3, and intuitively I was like "aw, that sounds
weird..." But after listening to it for a bit longer, I ended up
realizing that it is in fact its own.

>> >> > You and me both. We could buy a bunch of AXiSes and
>> >> > refretted guitars and pitch a workshop to Berklee. I'd
>> >> > bet they'd go for it. Might even give us some money.
> //
>> > We could write a grant, or suggest to Berklee that they
>> > pay us for giving the workshop.
>>
>> I'm down. //
>> There are a -lot- of schools that I know of that would be
>> interested in such a program, the University of Miami and USC.
>
> Want to take it off-list and come up with a proposal together?

You'll be getting an email shortly.

>> $640, good condition Mk. 1 stage.
>
> Have you ever owned a Rhodes? You couldn't pay me $640 to
> take it.

Incidentally, if you have a Fender Rhodes you'd like to get rid of...

>> > By the way, I believe the Access TI has built-in Hermode
>> > tuning. (www.hermode.com)
>>
>> Damn. I really need to get one of those keyboards. I'm stuck
>> between that and the Nord Electro, which has no microtonal
>> functionality whatsoever, but awesome electroacoustic samples
>> to boast. I am torn.
>
> I came so close to buying an electro. Yup, the sounds are
> good ( for a sampler :P ). But nord instruments are kind of
> candy-assed in some way and definitely overpriced. You should
> totally check out the hermode site in depth if you haven't. My
> current object of desire is a Kurzweil PC3. Yum. But it costs
> more than an AXiS.

They're candy-assed in that they have no effects. The nord electro 2
has some effects, but lacks basic things like reverb and delay. I hate
them so much. I have a nord lead 2, which is sort of useful, though
I'd trade it and one of my limbs for an Access TI Polar anyway. The
Nord lead 2 has no effects at all, although I made a patch that sweeps
through the harmonic series with it when I move the mod wheel. It's
pretty fun to go up to the 7th overtone and just play in 12tet... You
can get some interesting sounds that way. Plus, by splitting the patch
so that the left half of the keyboard is a normal 12tet setup and the
right half is down a septimal comma, you can play subminor triads and
supermajor triads and stuff live and have a good ol' time.

As for the Kurzweil PC3, I haven't heard much of it. I just looked up
some videos on it and it sounds really good, although I'll have to
hear the clavinet sounds before I really make my decision.

>> >> // and you still have to connect it to a computer and //
>> >
>> > It's a bit of a pain I admit but not one that warrants the
>> > number of complaints I hear about it.
> //
>> horn players and guitarists and such are pretty much left out
>> of the fold here.
>
> What use have they for synths?

I just mean that those people have to be taken into account too, or
else in an ensemble situation you're going to have one microtonal
keyboard player and three people stuck in 12tet.

>> >> Never mind the fact that if you want decent samples
>> >
>> > Samples?? Blechk!
>>
>> I'm telling you, VSL and EWQL have the most realistic
>> orchestral samples you will ever hear in your entire life.
>
> I've heard them a plenty. But my favorite way to synthesize
> orchestras is Synful.

Never ever heard of it. I'll have to check that out.

-Mike

🔗Cameron Bobro <misterbobro@...>

6/9/2008 2:20:41 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I've heard them a plenty. But my favorite way to synthesize
> orchestras is Synful.

Does it import Scala files or have some kind of tuning tables?

🔗Torsten Anders <torstenanders@...>

6/9/2008 3:26:41 AM

On Jun 9, 2008, at 12:02 AM, Mark Rankin wrote:
> Carl,
>
> Have you or anyone you know ever tried to download Ricecar.mov?
>
I just tried it again and have no problem. You may try to explicitly save the file to the HD first.

Best
Torsten

> I have tried repearedly. At the fifth bar the download stalls.
>
>
> Mark
>
> --- On Sun, 6/8/08, Carl Lumma <carl@...> wrote:
>
> From: Carl Lumma <carl@...>
> Subject: [tuning] Music Theory
> To: tuning@yahoogroups.com
> Date: Sunday, June 8, 2008, 11:34 AM
>
> Torsten!
>
> > > the Ricercar from Bach's Musikalisches Oper.
>
> The ricercar a3. Not quite the a6 but still one of the
> deeper pieces of music ever written.
>
> > > The ricercar is available online
> > >
> > > http://www.plainsou ndmusic.org/ videos/Ricercar. mov
> > > http://www.plainsou nd.de/scores/ ricercar. pdf
> > > http://www.plainsou nd.de/research/ ricercartext. pdf
>
> Ahh! I've been to the plainsound site a dozen times
> and never saw this. Do you know when it was posted?
>
> > Perhaps I should mention that this is at least 7-limit
> > adaptive JI, it also includes higher limits such as
> > 17 and 19. I find downright crazy what they did
> > here -- its actually a new piece.
>
> What you need to do is mention everything you know about
> this, right away. :)
>
> Too slow but jeez, what an achievement.
>
> To tie things together, Godel Escher Bach is how I first
> learned of the Musical Offering, and also a primary
> reason I went to Indiana University to pursue a Cognitive
> Science degree.
>
> -Carl
>
>
>
>
>
--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

🔗Chris Vaisvil <chrisvaisvil@...>

6/9/2008 9:16:49 AM

[ Attachment content not displayed ]

🔗Carl Lumma <carl@...>

6/9/2008 10:10:11 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Sounds like you're still listening to intervals then. If you
> > can recognize themes transposed into the relative minor and
> > such, then you are doing what Rothenberg is concerned with,
> > which is assigning scale degrees to pitches. You recognize
> > the theme by the fact it still has the same pattern of scale
> > intervals (5th 3rd 2nd etc.) even though the pitches and even
> > the qualities of the intervals (major 3rd vs. minor 3rd) are
> > different.
>
> Ah. How does this stuff apply outside of diatonic scale
> theory...?

Depends what you mean by "diatonic". It can be applied to
any scale. The decimal miracle scale has 9ths and 10ths
for example.

> that you need to learn
> to hear C-Fb as a kind of FOURTH rather than fitting it into ones
> concept as a major third?

Yes, that's it.

> If that's what he's saying, then that's the kind of stuff I'm
> proposing be taught in jazz schools and such around the country.

I'd be all for it.

> >> OK, let me give you a better example - something a little
> >> E further from the harmonic series. how about C Eb G Bb D F Ab?
> >> That Ab on the top to my ears sounds pretty weak structurally,
> >
> > Alright, I've demonstrated the techniques. What do you think?
>
> I think it makes sense for the first chord, but I don't see how it
> relates to the second one I posted above, as I deliberately picked
> one that was further from the harmonic series just to see how the
> techniques would apply there. I'm not sure how they carry over to
> things like that. Intuitively I feel that that G-Ab is really what
> is causing it, but maybe not, because if you take the G out, it
> still sounds weird.

Why don't you find the possible harmonic series interps of the
chord, and the version without Ab. And also list all the dyads.
Then we can discuss it. I do have a day job you know.

> If you look closely, all of the
> avoid notes usually talked about are just places where a b9 exists
> over some other note.

Is that true? Can you demonstrate this?

> > 'Omit the 3rd' may make sense in the following manner:
>
> Hm. Usually the fifth is being omitted, not the third...

Yeahp, that's what I get for posting at that hour.

> So how come, over a major chord, the note that is two fourths down
> fits in to make a "strong" chord, but the note that is one fourth
> down does not?

You mean up? I think the answer is that 16/9 approximates 7/4.

> Would you say that I'm still hearing 16/9 as just a brighter
> type of 7/4, or as 16/9 in its own right?

The former.

> > I came so close to buying an electro. Yup, the sounds are
> > good ( for a sampler :P ). But nord instruments are kind of
> > candy-assed in some way and definitely overpriced. You should
> > totally check out the hermode site in depth if you haven't. My
> > current object of desire is a Kurzweil PC3. Yum. But it costs
> > more than an AXiS.
>
> They're candy-assed in that they have no effects.

I kinda meant in the 'cheap red plastic' sense.

> As for the Kurzweil PC3, I haven't heard much of it.

It should start shipping next week or something.

> >> horn players and guitarists and such are pretty much left out
> >> of the fold here.
> >
> > What use have they for synths?
>
> I just mean that those people have to be taken into account too, or
> else in an ensemble situation you're going to have one microtonal
> keyboard player and three people stuck in 12tet.

Heavens no, they're not stuck. They'll play right along
just fine with the keyboard to guide them.

-Carl

🔗hstraub64 <straub@...>

6/9/2008 1:23:39 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > It's what serialism morphed into. They publish lots of papers
> > explaining the rules of common practice music based on these
> > arcane (and acoustically meaningless) pitch transformations.
> > Many of the celebrated results in the field don't work if you
> > try to apply them in, say, 31-ET instead of 12-ET. Even though
> > by all accounts lots of music sounds just fine (if not
> > better) in 31.
>
> Acoustically meaningless being the key term.

I have to say I do not really like this term. What is "acoustically
meaningless"? Is the retrograde acoustically meaningless, because an
average listener cannot recognize it? Is the inversion acoustically
meaningless? Maybe, but both transformations are, in any case, not
"musically meaningless", definitely.
--
Hans Straub

🔗Carl Lumma <carl@...>

6/9/2008 1:49:47 PM

Hans wrote:

> > Acoustically meaningless being the key term.
>
> I have to say I do not really like this term. What is "acoustically
> meaningless"? Is the retrograde acoustically meaningless, because an
> average listener cannot recognize it? Is the inversion acoustically
> meaningless? Maybe, but both transformations are, in any case, not
> "musically meaningless", definitely.

Neither of those transformations are musically meaningless,
and indeed it'd be hard to come up with one that was. Even
so, there are probably many transformations less musically
useful than these two. I was referring to certain things
involving 12-modular arithmetic I have seen, which claim
explanatory power over music old and new. I won't be interested
in digging up citations, but would rather prefer to focus
on constructive work. -Carl

🔗Cameron Bobro <misterbobro@...>

6/10/2008 6:03:13 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:

> Rick has been talking recently about how maybe we're hearing 3
steps of
> 12tet as being an only slightly out-of-tune 19/16 ratio rather than
a really
> out-of-tune 6/5 ratio. 19/16, however, has an entirely different
> *character*than 6/5. Which begs the question: what ARE we hearing?
> What is the nature
> of this change in character, and what does this character mean?

The character of different intervals is something I've been focussing
on for quite a while. Obviously this is kind of a given in musical
performance, so more specifically, the character of intervals in the
context of the tuning.

Be forewarned that Carl has called my ideas "eye of newt" :-D but
here goes: every interval has a character and in a tuning that hangs
together, or in which all seems "of a kind" or "from the same
pallete", the intervals share certain color/feeling characteristics.
So I listen for "character families". An obvious one is like the
slightly upwardly detuned 5/4 you mentioned before- it's a little
brighter. If you take for example 34-equal, there are genuine
approximations of 6/5 and 5/4; at two cents away it would be kooky to
pretend that there isn't an obvious relation between the m3 and M3 of
34-equal, and those of the harmonic partials. They're the "same" on
one hand, but both are two cents higher and brighter in character on
the other. Throw in the even brighter 34-equal "3/2" and you've got
a very clear character family right there in the first six partials:
bright and brassy.

Looking at things this way, it's easy to imagine that a whole tuning
can have a certain character, or "red thread". I call it an
uebertimbre to irk Carl, but in seriousness it's a Gesamtklangfarbe.

When you have intervals, whether rational or "irrational", that
create coincident or near-concident partials with great regularity,
you tend to put weight in specific places in the spectra. If you plot
the partials of say a complete "7-limit" u- and o-tonality tuning, it
is not hard to imagine that the regions coinciding with seventh
partials tend to get reinforced in a piece of music. As you can
easily demonstrate with an additive synthesizer, putting more energy
into the seventh partial makes for a different tone color.

Obviously a tuning in and of itself isn't enough to really have a
Gesamtklangfarbe, it's really a potential Gesamtklangfarbe because
key and modality also write the overall timbre- for example, a
secondary key center or an insistent figure can create a kind of
"formant" in the overall spectral envelope of the piece.

(Really wide voicings and punctalism would probably throw the whole
thing to the dogs, but that is nothing new, these things have been
effective tools of "atonalists" for a long time.)

Another thing that is common in distinctive and attractive instrument
timbres is gaps-and-lumps in the partials, analize a violin sound for
example. In my experience, gaps-and-lumps in the overall field of
coincident partials that a tuning tends to reinforce is a good thing.
So after long poking around with my ears at tuning until it floats my
boat, I (always?) find upon examination that has characteristics like
"primes: 2,3,5,23" or "2,5,7,73" and so on.

Notice that "73" or any extremely high partial needs absolutely no
numerology or wild claims of human hearing ability to be "justified".
73/64 is four cents from 8/7 so we're hearing something which is
both a thing of its own, and a flavor of 8/7. Other high partials
are great for blurring other regions- 23/18 for example splits the
difference between 9/7 and 14/11, and a "23" tuning (o's and u's to
use Partch's charmingly ridiculous but effective terminology) can
both blur the seventh partial while at the same time perhaps be on
the edge of hearing as "Just". These tasty and functional "blurred"
regions I call "shadows"- 23/18 is an example, another kind would be
found at a 25/24 above 5/4, which works as a kind of bright 13/10 (<
2.8 cents high) and is obviously nicely linked to 5/4 for smooth
rides in and out of shadow and light.

I would think that this all sounds quite tame and maybe even common-
sensical. The other day I read about the "spectralists" here (BTW
thanks for the information and links, guys!), a school I wasn't aware
of. As far as I can make out a lot of what I do is about the same, at
heart, only backwards. No big deal.

But if you think about it, you will realize how easily this can come
into conflict with the regular temperament paradigm. (I am not
putting "regular temperament paradigm" in quotes because I think it's
a serious thing and the guys here involved in defining it should be
proud of,not embarrassed by, the expression.) Right off the bat, it
is clear that if there's any legitamcy to this approach, reckoning
"errors" in temperaments would be a very big pain in the ass, for a
greater "error" (deviation from Just) in an interval could very well
mean more, and not less, continuity in "flavor" or "hue" or whatever.
And "shadows", or zones of ambiguity, rely on NOT being good
approximations of intervals, but on being in the (right) wrong place
in the audible spectrum.

Add to this the probability that it's the gapped-and-lumped spectra
that make for the nicest
"Gesamtflangfarben", and we're looking at "good" temperaments that
might appear on paper to be pretty crappy. As you have certainly
noticed, 12-tET, all questions of taste aside, is might flexible, and
it fits the kind of description I gave above: "damn near perfect 2
and 3, and some 19" The 19 is not the "justification" of 12-tET,
though who knows if there's some far-away feeling of it or not-
doesn't matter. "19" just a rough description of the place the
"shadows" of 12-tET dwell. In the case of 12-tET, it's the size and
vagueness of the shadow zones that make it flexible, but when 12-tET
is taken literally they're just too damn big and blurry IMO.

Anyway gotta run soon, take care

>
> What is it that we hear when we hear a 12tet major chord? Often
this chord
> is cited as having a relatively in-tune 3/2 and a slightly out-of-
tune
> 5/4... But is there some other way that we are really hearing it?
>
> Do we psychologically "move" these ratios to the nearest JI one, or
the
> simplest one, or...? If I play a JI minor chord with the minor
third as
> 19/16 am I hearing THAT as an out of tune 6/5?
>
> I think the context of it might matter. There is definitely some
difference
> between 11-tet and 12-tet, for example. 12-tet offers better
"matches" to
> intervals in the harmonic series. So to SOME extent, imposing some
kind of
> JI-related structure on equal temperaments offers useful results.
>
> Take the following 2 chords:
>
> 1:2:3:4:5:6
>
> and
>
> 100:200:300:400:504:600
>
> You will still most likely hear the resemblence to the overtone
series and
> hear that context superimposed over the second chord. The sharpened
"5" will
> cause some beating that you may or may not like, depending on the
context. I
> hear the second one as "vibrant," "exciting," etc. You might also
view it as
> "dissonant" and an "out-of-tune" version of 1:2:3:4:5:6. However,
you might
> ALSO view that second chord as an "inversion" of a completely
different JI
> chord, which would presumably act in a different way if you take
into
> account the "traditional" ways that chord inversions and such are
viewed -
> and these ways were groundbreaking in their own time and evolved
out of
> their own realizations.
>
> I.E.: the two approaches give differing results, and thus something
in the
> overall theory is inconsistent. All known musical truths will never
be
> accessible through any axiomatic system - but it might be useful to
at least
> make the current one consistent. As I see it (and I feel this is a
fairly
> common perspective), the way many of us have been taught music
theory in
> school fails to explain microtonal theory (see above for the b9
example),
> and the way many of us currently see microtonal theory fails to
explain good
> ol' fashioned 12tet music theory from school (the areas in which it
DOES
> work). If these two could be reconciled, I think it would be good.
>
>
> So to restate the question:
>
> Why do we sometimes hear intervals "guided" to their nearest match
in a
> harmonic series, and why do we sometimes hear them as new entities
in their
> own right with different feelings and characters to them?
>
> Or, in a more general sense, what causes someone to hear a certain
interval
> as a mistuned form of another interval?
>
> OR, in its *broadest* sense, what causes someone, when experiencing
a
> phenomenon, to view that phenomenon as an altered version of another
> phenomenon?
>
> Sometimes we get into "well the brain does this" or "the brain does
that,"
> and I think those answers often fall short of the truth.
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

6/10/2008 3:12:59 PM

> The character of different intervals is something I've been focussing
> on for quite a while. Obviously this is kind of a given in musical
> performance, so more specifically, the character of intervals in the
> context of the tuning.
> Be forewarned that Carl has called my ideas "eye of newt" :-D

He does tend to do that, doesn't he?

> but here goes: every interval has a character and in a tuning that hangs
> together, or in which all seems "of a kind" or "from the same
> pallete", the intervals share certain color/feeling characteristics.
> So I listen for "character families". An obvious one is like the
> slightly upwardly detuned 5/4 you mentioned before- it's a little
> brighter. If you take for example 34-equal, there are genuine
> approximations of 6/5 and 5/4; at two cents away it would be kooky to
> pretend that there isn't an obvious relation between the m3 and M3 of
> 34-equal, and those of the harmonic partials. They're the "same" on
> one hand, but both are two cents higher and brighter in character on
> the other. Throw in the even brighter 34-equal "3/2" and you've got
> a very clear character family right there in the first six partials:
> bright and brassy.

Yeah! That's always what attracted me to 17-tet, the wider fifths. I
think it usually sounds good because widening them slightly
accentuates the intervals that we're already used to. I also
hypothesize that it might be because of some resemblance to the
stretched harmonic series that we often hear in nature (although it
could just be my own bias). This is why I always liked 12-tet more
than 19-tet - the third and fifth (and harmonic 7th) are all flat in
19-tet, so everything sounds compressed and less accentuated. It
sounds like my brain is getting compressed. Although, the more I
listen to 19-tet, the more I like it, so it may just be my own bias
towards wider intervals that is being expressed here.

I suppose some cross-culture listening tests would have to be
performed in order to determine whether that theory is due to a
cultural bias for wider intervals (e.g. the 12tet major third) or
whether it has some acoustic basis. Honestly I think that the apparent
duality here can be resolved by noting that while there is likely SOME
acoustic basis on what you initially hear, the matter of whether you
LIKE what your brain shows you after all of this acoustic and
psychoacoustic stuff goes down is a different mental process entirely.
And then what you like or prefer makes up part of your overall
perception, or Gestalt.

> Looking at things this way, it's easy to imagine that a whole tuning
> can have a certain character, or "red thread". I call it an
> uebertimbre to irk Carl, but in seriousness it's a Gesamtklangfarbe.

Hahaha what? Gezundheit

> When you have intervals, whether rational or "irrational", that
> create coincident or near-concident partials with great regularity,
> you tend to put weight in specific places in the spectra. If you plot
> the partials of say a complete "7-limit" u- and o-tonality tuning, it
> is not hard to imagine that the regions coinciding with seventh
> partials tend to get reinforced in a piece of music. As you can
> easily demonstrate with an additive synthesizer, putting more energy
> into the seventh partial makes for a different tone color.

I remember hearing an example on the web of a JI major chord as
compared to the 12tet major chord. The website claimed that the equal
tempered one sounded better, and for their example, it did. Then they
had a JI major chord in which the notes were phase shifted so that I
think the 5th harmonic of the fundamental cancelled out with the 4th
harmonic of the major third, and it sounded much better, though I'm
not sure why that particular overtone was so offensive.

> Obviously a tuning in and of itself isn't enough to really have a
> Gesamtklangfarbe, it's really a potential Gesamtklangfarbe because
> key and modality also write the overall timbre- for example, a
> secondary key center or an insistent figure can create a kind of
> "formant" in the overall spectral envelope of the piece.

Interesting ideas. I'd like to hear some musical examples that utilize
this for some interesting effect. Apparently gesamtklangfarbe
translates to "total tone quality," which is a term I've never heard
before.

> (Really wide voicings and punctalism would probably throw the whole
> thing to the dogs, but that is nothing new, these things have been
> effective tools of "atonalists" for a long time.)

It would be awesome if there was some software that let you screw
around with JI chords and inharmonicity as such. Would most likely be
interesting in the end.

> Another thing that is common in distinctive and attractive instrument
> timbres is gaps-and-lumps in the partials, analize a violin sound for
> example. In my experience, gaps-and-lumps in the overall field of
> coincident partials that a tuning tends to reinforce is a good thing.
> So after long poking around with my ears at tuning until it floats my
> boat, I (always?) find upon examination that has characteristics like
> "primes: 2,3,5,23" or "2,5,7,73" and so on.

Interesting. Probably due to resonant effects of the body or something.

> Notice that "73" or any extremely high partial needs absolutely no
> numerology or wild claims of human hearing ability to be "justified".
> 73/64 is four cents from 8/7 so we're hearing something which is
> both a thing of its own, and a flavor of 8/7.

Yeah. That's the key. That's why I had second thoughts about the
assertions made above that a dominant 7 chord where the 7 is 16/9 will
be interpreted "by the brain" as being an out of tune 7/4. It's just
that 7/4 and 16/9 are fairly close in the pitch continuum, so
naturally they'll sound similar. The whole thing seems to ignore the
fact that these intervals have characters of their own as well; they
are not merely mistuned versions of other simpler intervals, although
you might hear them that way at first. You might also hear the simpler
intervals as mistunings of the more complicated ones, which is why
when people used to 12-tet hear music in just intonation for the first
time sometimes think it "sounds wrong," even if there is no commatic
drift or the like.

I think these fields of attraction are merely a way to describe the
phenomenon of how and under what circumstances we hear a resemblance
to the harmonic series in tempered or non-harmonic (or upper JI
harmonic) intervals.

It's like this image: http://en.wikipedia.org/wiki/Image:Invariance.jpg

"A" is the original object, and "D" is a distorted version of the same
object. The concept of a field of attraction is merely I think is an
attempt to explain how much of that distortion we can take before we
stop seeing it as the same object. However, saying that the images in
D are ONLY good at being "slightly erroneous" versions of the objects
in picture A is taking it too far. After all, no axiomatic theory is
complete (hint, hint).

I think a more accurate approach is that a person might interpret 16/9
as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
to hearing 16/9. They might then become used to 16/9 as a separate
interval in its own right later. This is why I am wary of labeling one
particular person's response to an interval or chord as though it were
something the "brain" does. One person's brain might exhibit a certain
behavior as the neurological correlate of a psychological
interpretation, but then attempting to generalize that behavior to
-all- people falls prey to the same fallacy that is currently ruining
how music theory is being taught in America.

Here's a simple example to demonstrate that concept... Play a 12 bar
blues, where the chords are 4:5:6:7. Let's say it's in the key of C.
Right before the C goes to F, change the 7th of the C chord to be
16/9, as in change it from an otonal tetrad to a pythagorean
"dominant" 7, that resolves as a V-I to the next chord. see if you
feel a difference!

Another way to say all of this is that you perhaps DEVELOP your fields
of attraction to intervals over time, depending on when you hear them.

> Other high partials
> are great for blurring other regions- 23/18 for example splits the
> difference between 9/7 and 14/11, and a "23" tuning (o's and u's to
> use Partch's charmingly ridiculous but effective terminology)

I never really understood the otonality and utonality thing... It
makes sense at first but breaks down the further you get into it. A
minor chord is both a utonality and an otonality, depending on how you
look at it. So is a major chord.

> can both blur the seventh partial while at the same time perhaps be on
> the edge of hearing as "Just". These tasty and functional "blurred"
> regions I call "shadows"- 23/18 is an example, another kind would be
> found at a 25/24 above 5/4, which works as a kind of bright 13/10 (<
> 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
> rides in and out of shadow and light.

Yeah, this is sort of related to the original question I was asking...
Is it that the 12tet major third approximates 5/4 but is really sharp,
or is it that it approximates a higher-prime interval, or is it that
the higher-prime interval itself approximates the lower-prime
interval? Perhaps moving 5/4 up slightly by some irrational number and
ignoring JI altogether would work as well.

Another example of what you're talking about here I think is the good
ol' neutral triad... I have a multistable perception of neutral triad
as an out of tune major and an out of tune minor simultaneously. I
suspect that the more I listen to it the more I will get used to it as
a stable chord in its own right, and then that interval will develop
its own "field of attraction" apart from the major and the minor one.

I suspect that fields of attraction are not drawn around actual
harmonic intervals, but around the MEMORIES we have of intervals. It
has to do with a tendency

> I would think that this all sounds quite tame and maybe even common-
> sensical. The other day I read about the "spectralists" here (BTW
> thanks for the information and links, guys!), a school I wasn't aware
> of. As far as I can make out a lot of what I do is about the same, at
> heart, only backwards. No big deal.

A teacher at my school was talking about the spectralists. I still
haven't heard any really good examples though. I searched for "Scelsi"
on Youtube and didn't find much,

> But if you think about it, you will realize how easily this can come
> into conflict with the regular temperament paradigm. (I am not
> putting "regular temperament paradigm" in quotes because I think it's
> a serious thing and the guys here involved in defining it should be
> proud of,not embarrassed by, the expression.)

I have been reading the regular temperament paradigm and find it very
interesting. There are cases where it seems brilliantly insightful and
others where it just seems like one particular way of looking at
certain aspects of harmony and temperament.

I am starting to become concerned with the "why"'s rather than the
"how"'s... I think one gestalt-related approach might be to state that
if we hear a 12-tet C C G C E G chord, we are likely to hear the
resemblance to the harmonic series and thus hear it that way. However,
people often hear that 12-tet major third as having its own sound,
sticking out and being much brighter than a just 5/4. Sometimes that
12-tet major third sticks out and implies a harmony and tonality of
its own completely separate from the major third.

The paradigm where everything is completely heard in terms of being
out of tune simple integer just intonation relationships I think is a
good rough start, but ultimately incomplete and inconsistent. It's an
attempt to describe the resemblance we hear between various tempered
intervals and other intervals in the harmonic series. This resemblance
is often used in equal tempered music to -imply- the existence of a
faux-harmonic series for musical purposes. Different just-intonated
intervals can also be used to imply the harmonic series as well, in
that sense. However, dismissing these intervals as serving -only- that
functionality is a non-sequitur.

In other words, this view goes wrong when it ignores the -difference-
between the harmonic series versions and the tempered versions.
Usually this difference is dismissed as being an "error," the
implication being that it is undesirable. Yet, as we've seen with
12-tet and 34-tet, this difference is often musical in character and
not at all "erroneous."

Not only for atonal music, which often draws from a disregarding of
harmony entirely, but for tonal music as well. The most obvious place
where the system breaks down that I've seen in recent memory is the
Wikipedia entry for "41 equal temperament."

Take this sentence near the bottom:

"41-ET also has 6 distinct intervals between a perfect fourth and
perfect fifth, whereas 31-ET has only four; the two additional
intervals are poor matches to the ratios 15:11 and 22:15."

It seems to be a common trend among these circles to hear one interval
as a "poor match" to another one. Seems like a matter of not being
used enough to that interval to hear it for what it is. 10 cent
differences in pitch can make quite a difference; we aren't talking
about a 3 cent distinction here.

It's like taking the triangle from letter A in this image
(http://en.wikipedia.org/wiki/Image:Reification.jpg) and saying it's a
"poor" match to a triangle because the sides are incomplete.

> Right off the bat, it is clear that if there's any legitamcy to this approach, reckoning
> "errors" in temperaments would be a very big pain in the ass, for a
> greater "error" (deviation from Just) in an interval could very well
> mean more, and not less, continuity in "flavor" or "hue" or whatever.
> And "shadows", or zones of ambiguity, rely on NOT being good
> approximations of intervals, but on being in the (right) wrong place
> in the audible spectrum.

Agreed. No newts found here.

> Add to this the probability that it's the gapped-and-lumped spectra
> that make for the nicest
> "Gesamtflangfarben", and we're looking at "good" temperaments that
> might appear on paper to be pretty crappy. As you have certainly
> noticed, 12-tET, all questions of taste aside, is might flexible, and
> it fits the kind of description I gave above: "damn near perfect 2
> and 3, and some 19" The 19 is not the "justification" of 12-tET,
> though who knows if there's some far-away feeling of it or not-
> doesn't matter. "19" just a rough description of the place the
> "shadows" of 12-tET dwell. In the case of 12-tET, it's the size and
> vagueness of the shadow zones that make it flexible, but when 12-tET
> is taken literally they're just too damn big and blurry IMO.

Don't understand this paragraph.. What do you mean, the 19th harmonic?
What do you mean by justification? Could you elaborate?

17 is also pretty good fwiw.

-Mike

🔗Carl Lumma <carl@...>

6/10/2008 3:56:32 PM

Cameron wrote:

> > I call it an
> > uebertimbre to irk Carl, but in seriousness it's a
> > Gesamtklangfarbe.

That doesn't irk me at all. I've long proposed that the
mistuning fingerprint of ETs (at least < 50) might add up
to a gestalt sound. In 1998 I suggested that's what
Ivor Darreg's "moods" were.

-Carl

🔗Mike Battaglia <battaglia01@...>

6/10/2008 4:06:54 PM

> That doesn't irk me at all. I've long proposed that the
> mistuning fingerprint of ETs (at least < 50) might add up
> to a gestalt sound. In 1998 I suggested that's what
> Ivor Darreg's "moods" were.

So then perhaps in that case, there's no point considering it a
"mistuning." Perhaps an "offset." Calling it an error or a mistuning
is quite misleading, imo.

-Mike

🔗Carl Lumma <carl@...>

6/10/2008 4:41:53 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > That doesn't irk me at all. I've long proposed that the
> > mistuning fingerprint of ETs (at least < 50) might add up
> > to a gestalt sound. In 1998 I suggested that's what
> > Ivor Darreg's "moods" were.
>
> So then perhaps in that case, there's no point considering it a
> "mistuning." Perhaps an "offset." Calling it an error or a
> mistuning is quite misleading, imo.
>
> -Mike

"Words should be your servants, not your masters."
--Marvin Minksy

🔗Dave Keenan <d.keenan@...>

6/10/2008 8:31:06 PM

I think that many intervals that people interpret as having something
to do with high-prime partials (say 17 or greater) have more to do
with _avoiding_ Just intervals than approximating them.

A dominant seventh whose job it is to provide tension that can then be
blessedly resolved, is likely to work better if it maximally avoids
4:7, 5:9 _and_ 9:16 in such a way that the attraction of all of these
intervals is balanced, i.e. so it has no net attraction to _any_ just
interval at all. 4:7 and 9:16 will be pulling it one way (although
9:16 has very little pull anyway) and 5:9 will be pulling it the other
way.

Notice that the sequence 7/4, 9/5, 16/9 can be continued in a
fibonacci-like manner by adding the two preceding denominators to get
the next denominator, likewise the numerator.

7/4, 9/5, 16/9, 25/14, 41/23, ...

This converges to a limit which is an irrational number involving the
golden mean, called a noble number. But the tuning of noble intervals
is far less critical than the tuning of just intervals so it is
tempting to just stick to rationals and call it 14:25 or 23:41 since
neither of them are audibly just (except possibly in some otonal
harmonic context having very many notes).

I think that's how many of these supposed high-prime intervals come to
prominence. They are really noble intervals, not just intervals.

Nobility is the shadow of justness.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> > Notice that "73" or any extremely high partial needs absolutely no
> > numerology or wild claims of human hearing ability to be "justified".
> > 73/64 is four cents from 8/7 so we're hearing something which is
> > both a thing of its own, and a flavor of 8/7.
>
> Yeah. That's the key. That's why I had second thoughts about the
> assertions made above that a dominant 7 chord where the 7 is 16/9 will
> be interpreted "by the brain" as being an out of tune 7/4. It's just
> that 7/4 and 16/9 are fairly close in the pitch continuum, so
> naturally they'll sound similar. The whole thing seems to ignore the
> fact that these intervals have characters of their own as well; they
> are not merely mistuned versions of other simpler intervals, although
> you might hear them that way at first. You might also hear the simpler
> intervals as mistunings of the more complicated ones, which is why
> when people used to 12-tet hear music in just intonation for the first
> time sometimes think it "sounds wrong," even if there is no commatic
> drift or the like.
>
> I think these fields of attraction are merely a way to describe the
> phenomenon of how and under what circumstances we hear a resemblance
> to the harmonic series in tempered or non-harmonic (or upper JI
> harmonic) intervals.

🔗Kraig Grady <kraiggrady@...>

6/10/2008 10:57:17 PM

i think 23 is used in cadences allot. 17 Helmholtz pointed out.
As maybe the person who works the most with sequences that lead to noble numbers i can say a few words about them. I have found that the tuning is even more critical than just as you want your difference tones to land on pitches in your scale. Otherwise the sound and reinforcement falls apart. I have tried both tuning to the converged noble number and to numerical sequences leading up to it. I have found that i actually prefer these series before they converge too much but also away from the simplest seed where one is not even sure where it is heading.
Possibly you are right to associate it with noble more than just and to distinguish the two. Personally i am not into introducing new terms and think it does more good to associate it with just, for the very reason in that it extends just as opposed to putting an end to it. Like 'performance art', sooner or later it all gets incorporated into 'theater' and does more good there than some isolated term that came and then goes away. So it is a matter of taste i guess

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> I think that many intervals that people interpret as having something
> to do with high-prime partials (say 17 or greater) have more to do
> with _avoiding_ Just intervals than approximating them.
>
> A dominant seventh whose job it is to provide tension that can then be
> blessedly resolved, is likely to work better if it maximally avoids
> 4:7, 5:9 _and_ 9:16 in such a way that the attraction of all of these
> intervals is balanced, i.e. so it has no net attraction to _any_ just
> interval at all. 4:7 and 9:16 will be pulling it one way (although
> 9:16 has very little pull anyway) and 5:9 will be pulling it the other
> way.
>
> Notice that the sequence 7/4, 9/5, 16/9 can be continued in a
> fibonacci-like manner by adding the two preceding denominators to get
> the next denominator, likewise the numerator.
>
> 7/4, 9/5, 16/9, 25/14, 41/23, ...
>
> This converges to a limit which is an irrational number involving the
> golden mean, called a noble number. But the tuning of noble intervals
> is far less critical than the tuning of just intervals so it is
> tempting to just stick to rationals and call it 14:25 or 23:41 since
> neither of them are audibly just (except possibly in some otonal
> harmonic context having very many notes).
>
> I think that's how many of these supposed high-prime intervals come to
> prominence. They are really noble intervals, not just intervals.
>
> Nobility is the shadow of justness.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...> wrote:
> > > Notice that "73" or any extremely high partial needs absolutely no
> > > numerology or wild claims of human hearing ability to be "justified".
> > > 73/64 is four cents from 8/7 so we're hearing something which is
> > > both a thing of its own, and a flavor of 8/7.
> >
> > Yeah. That's the key. That's why I had second thoughts about the
> > assertions made above that a dominant 7 chord where the 7 is 16/9 will
> > be interpreted "by the brain" as being an out of tune 7/4. It's just
> > that 7/4 and 16/9 are fairly close in the pitch continuum, so
> > naturally they'll sound similar. The whole thing seems to ignore the
> > fact that these intervals have characters of their own as well; they
> > are not merely mistuned versions of other simpler intervals, although
> > you might hear them that way at first. You might also hear the simpler
> > intervals as mistunings of the more complicated ones, which is why
> > when people used to 12-tet hear music in just intonation for the first
> > time sometimes think it "sounds wrong," even if there is no commatic
> > drift or the like.
> >
> > I think these fields of attraction are merely a way to describe the
> > phenomenon of how and under what circumstances we hear a resemblance
> > to the harmonic series in tempered or non-harmonic (or upper JI
> > harmonic) intervals.
>
>

🔗Kraig Grady <kraiggrady@...>

6/10/2008 11:09:07 PM

Thanks for explaining this as it made clearer to me exactly how you have been working. I would call it an empirical method over a rational one. Something that has occupied my thoughts quite a bit lately. I guess the next question is how one uses them, only for certain things or combinations? Kinda an if /then structure i could see working itself into it as opposed to some rational configuration, such as hexanies made of these etc. While you might it seems like your process of choosing might find such things as the result as opposed to the means. I am fishing which i hope you don't mind.

anyway it was what i like of Wilson tunings in Xen. 3 where one will have different configurations on different places on the keyboard or overall tuning. Pythagorean then 5 limit then 7. He is deliberately conservative in his approach but would never object to what you are doing here.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...>
> wrote:
>
> > Rick has been talking recently about how maybe we're hearing 3
> steps of
> > 12tet as being an only slightly out-of-tune 19/16 ratio rather than
> a really
> > out-of-tune 6/5 ratio. 19/16, however, has an entirely different
> > *character*than 6/5. Which begs the question: what ARE we hearing?
> > What is the nature
> > of this change in character, and what does this character mean?
>
> The character of different intervals is something I've been focussing
> on for quite a while. Obviously this is kind of a given in musical
> performance, so more specifically, the character of intervals in the
> context of the tuning.
>
> Be forewarned that Carl has called my ideas "eye of newt" :-D but
> here goes: every interval has a character and in a tuning that hangs
> together, or in which all seems "of a kind" or "from the same
> pallete", the intervals share certain color/feeling characteristics.
> So I listen for "character families". An obvious one is like the
> slightly upwardly detuned 5/4 you mentioned before- it's a little
> brighter. If you take for example 34-equal, there are genuine
> approximations of 6/5 and 5/4; at two cents away it would be kooky to
> pretend that there isn't an obvious relation between the m3 and M3 of
> 34-equal, and those of the harmonic partials. They're the "same" on
> one hand, but both are two cents higher and brighter in character on
> the other. Throw in the even brighter 34-equal "3/2" and you've got
> a very clear character family right there in the first six partials:
> bright and brassy.
>
> Looking at things this way, it's easy to imagine that a whole tuning
> can have a certain character, or "red thread". I call it an
> uebertimbre to irk Carl, but in seriousness it's a Gesamtklangfarbe.
>
> When you have intervals, whether rational or "irrational", that
> create coincident or near-concident partials with great regularity,
> you tend to put weight in specific places in the spectra. If you plot
> the partials of say a complete "7-limit" u- and o-tonality tuning, it
> is not hard to imagine that the regions coinciding with seventh
> partials tend to get reinforced in a piece of music. As you can
> easily demonstrate with an additive synthesizer, putting more energy
> into the seventh partial makes for a different tone color.
>
> Obviously a tuning in and of itself isn't enough to really have a
> Gesamtklangfarbe, it's really a potential Gesamtklangfarbe because
> key and modality also write the overall timbre- for example, a
> secondary key center or an insistent figure can create a kind of
> "formant" in the overall spectral envelope of the piece.
>
> (Really wide voicings and punctalism would probably throw the whole
> thing to the dogs, but that is nothing new, these things have been
> effective tools of "atonalists" for a long time.)
>
> Another thing that is common in distinctive and attractive instrument
> timbres is gaps-and-lumps in the partials, analize a violin sound for
> example. In my experience, gaps-and-lumps in the overall field of
> coincident partials that a tuning tends to reinforce is a good thing.
> So after long poking around with my ears at tuning until it floats my
> boat, I (always?) find upon examination that has characteristics like
> "primes: 2,3,5,23" or "2,5,7,73" and so on.
>
> Notice that "73" or any extremely high partial needs absolutely no
> numerology or wild claims of human hearing ability to be "justified".
> 73/64 is four cents from 8/7 so we're hearing something which is
> both a thing of its own, and a flavor of 8/7. Other high partials
> are great for blurring other regions- 23/18 for example splits the
> difference between 9/7 and 14/11, and a "23" tuning (o's and u's to
> use Partch's charmingly ridiculous but effective terminology) can
> both blur the seventh partial while at the same time perhaps be on
> the edge of hearing as "Just". These tasty and functional "blurred"
> regions I call "shadows"- 23/18 is an example, another kind would be
> found at a 25/24 above 5/4, which works as a kind of bright 13/10 (<
> 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
> rides in and out of shadow and light.
>
> I would think that this all sounds quite tame and maybe even common-
> sensical. The other day I read about the "spectralists" here (BTW
> thanks for the information and links, guys!), a school I wasn't aware
> of. As far as I can make out a lot of what I do is about the same, at
> heart, only backwards. No big deal.
>
> But if you think about it, you will realize how easily this can come
> into conflict with the regular temperament paradigm. (I am not
> putting "regular temperament paradigm" in quotes because I think it's
> a serious thing and the guys here involved in defining it should be
> proud of,not embarrassed by, the expression.) Right off the bat, it
> is clear that if there's any legitamcy to this approach, reckoning
> "errors" in temperaments would be a very big pain in the ass, for a
> greater "error" (deviation from Just) in an interval could very well
> mean more, and not less, continuity in "flavor" or "hue" or whatever.
> And "shadows", or zones of ambiguity, rely on NOT being good
> approximations of intervals, but on being in the (right) wrong place
> in the audible spectrum.
>
> Add to this the probability that it's the gapped-and-lumped spectra
> that make for the nicest
> "Gesamtflangfarben", and we're looking at "good" temperaments that
> might appear on paper to be pretty crappy. As you have certainly
> noticed, 12-tET, all questions of taste aside, is might flexible, and
> it fits the kind of description I gave above: "damn near perfect 2
> and 3, and some 19" The 19 is not the "justification" of 12-tET,
> though who knows if there's some far-away feeling of it or not-
> doesn't matter. "19" just a rough description of the place the
> "shadows" of 12-tET dwell. In the case of 12-tET, it's the size and
> vagueness of the shadow zones that make it flexible, but when 12-tET
> is taken literally they're just too damn big and blurry IMO.
>
> Anyway gotta run soon, take care
>
> >
> > What is it that we hear when we hear a 12tet major chord? Often
> this chord
> > is cited as having a relatively in-tune 3/2 and a slightly out-of-
> tune
> > 5/4... But is there some other way that we are really hearing it?
> >
> > Do we psychologically "move" these ratios to the nearest JI one, or
> the
> > simplest one, or...? If I play a JI minor chord with the minor
> third as
> > 19/16 am I hearing THAT as an out of tune 6/5?
> >
> > I think the context of it might matter. There is definitely some
> difference
> > between 11-tet and 12-tet, for example. 12-tet offers better
> "matches" to
> > intervals in the harmonic series. So to SOME extent, imposing some
> kind of
> > JI-related structure on equal temperaments offers useful results.
> >
> > Take the following 2 chords:
> >
> > 1:2:3:4:5:6
> >
> > and
> >
> > 100:200:300:400:504:600
> >
> > You will still most likely hear the resemblence to the overtone
> series and
> > hear that context superimposed over the second chord. The sharpened
> "5" will
> > cause some beating that you may or may not like, depending on the
> context. I
> > hear the second one as "vibrant," "exciting," etc. You might also
> view it as
> > "dissonant" and an "out-of-tune" version of 1:2:3:4:5:6. However,
> you might
> > ALSO view that second chord as an "inversion" of a completely
> different JI
> > chord, which would presumably act in a different way if you take
> into
> > account the "traditional" ways that chord inversions and such are
> viewed -
> > and these ways were groundbreaking in their own time and evolved
> out of
> > their own realizations.
> >
> > I.E.: the two approaches give differing results, and thus something
> in the
> > overall theory is inconsistent. All known musical truths will never
> be
> > accessible through any axiomatic system - but it might be useful to
> at least
> > make the current one consistent. As I see it (and I feel this is a
> fairly
> > common perspective), the way many of us have been taught music
> theory in
> > school fails to explain microtonal theory (see above for the b9
> example),
> > and the way many of us currently see microtonal theory fails to
> explain good
> > ol' fashioned 12tet music theory from school (the areas in which it
> DOES
> > work). If these two could be reconciled, I think it would be good.
> >
> >
> > So to restate the question:
> >
> > Why do we sometimes hear intervals "guided" to their nearest match
> in a
> > harmonic series, and why do we sometimes hear them as new entities
> in their
> > own right with different feelings and characters to them?
> >
> > Or, in a more general sense, what causes someone to hear a certain
> interval
> > as a mistuned form of another interval?
> >
> > OR, in its *broadest* sense, what causes someone, when experiencing
> a
> > phenomenon, to view that phenomenon as an altered version of another
> > phenomenon?
> >
> > Sometimes we get into "well the brain does this" or "the brain does
> that,"
> > and I think those answers often fall short of the truth.
> >
> > -Mike
> >
>
>

🔗Graham Breed <gbreed@...>

6/11/2008 1:22:55 AM

Mike Battaglia wrote:

> Yeah! That's always what attracted me to 17-tet, the wider fifths. I
> think it usually sounds good because widening them slightly
> accentuates the intervals that we're already used to. I also
> hypothesize that it might be because of some resemblance to the
> stretched harmonic series that we often hear in nature (although it
> could just be my own bias). This is why I always liked 12-tet more
> than 19-tet - the third and fifth (and harmonic 7th) are all flat in
> 19-tet, so everything sounds compressed and less accentuated. It
> sounds like my brain is getting compressed. Although, the more I
> listen to 19-tet, the more I like it, so it may just be my own bias
> towards wider intervals that is being expressed here.

If you like wider intervals, why not stretch the scale, instead of choosing tunings that happen to make primes other than 2 sharp?

> I think a more accurate approach is that a person might interpret 16/9
> as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
> to hearing 16/9. They might then become used to 16/9 as a separate
> interval in its own right later. This is why I am wary of labeling one
> particular person's response to an interval or chord as though it were
> something the "brain" does. One person's brain might exhibit a certain
> behavior as the neurological correlate of a psychological
> interpretation, but then attempting to generalize that behavior to
> -all- people falls prey to the same fallacy that is currently ruining
> how music theory is being taught in America.

The psychoacoustic results that I'm aware of say that the traditional assignment of chord roots is correct -- that is, naive listeners will hear A as the root of an A minor chord (A-C-E). For that to work we must be interpreting A-C as an out of tune 4:5. Given that, it's entirely plausible that 16/9 is interpreted as 7/4. Of course, we're also quite capable of telling the difference between major and minor thirds.

Beyond that I don't think it's helpful or even meaningful to argue about what interval some other interval's heard in terms of. Generally, an interval is what it is and, as you say, it's only interpreted as a different interval if that other interval happens to be one the listener's already familiar with. The exceptions may be octaves and fifths.

> I never really understood the otonality and utonality thing... It
> makes sense at first but breaks down the further you get into it. A
> minor chord is both a utonality and an otonality, depending on how you
> look at it. So is a major chord.

A minor chord as 10:12:15 is a 5-limit utonality or a 15-limit otonality. In a 5-limit context there's only one interpretation.

>> can both blur the seventh partial while at the same time perhaps be on
>> the edge of hearing as "Just". These tasty and functional "blurred"
>> regions I call "shadows"- 23/18 is an example, another kind would be
>> found at a 25/24 above 5/4, which works as a kind of bright 13/10 (<
>> 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
>> rides in and out of shadow and light.
> > Yeah, this is sort of related to the original question I was asking...
> Is it that the 12tet major third approximates 5/4 but is really sharp,
> or is it that it approximates a higher-prime interval, or is it that
> the higher-prime interval itself approximates the lower-prime
> interval? Perhaps moving 5/4 up slightly by some irrational number and
> ignoring JI altogether would work as well.

And this is the point where I say it doesn't matter at all.

> Another example of what you're talking about here I think is the good
> ol' neutral triad... I have a multistable perception of neutral triad
> as an out of tune major and an out of tune minor simultaneously. I
> suspect that the more I listen to it the more I will get used to it as
> a stable chord in its own right, and then that interval will develop
> its own "field of attraction" apart from the major and the minor one.

Discordance graphs tend to show a kind of plateau between major and minor thirds. So any third will do. Whether that's because 6:5 and 5:4 merge into each other or because they merge in with 11:9 and 16:13 doesn't matter at all.

> I suspect that fields of attraction are not drawn around actual
> harmonic intervals, but around the MEMORIES we have of intervals. It
> has to do with a tendency

A meaningful question is: do intervals like 11:9 represent minimum points of dissonance? This is the concept of "tunable intervals". If intervals sound more consonant the closer they get to some ideal, it's worth considering that ideal when you choose a tuning or notation.

> A teacher at my school was talking about the spectralists. I still
> haven't heard any really good examples though. I searched for "Scelsi"
> on Youtube and didn't find much,

There was a programme on the BBC a while back which I have on Mini Disc -- but not with me. I think I liked some Murail best. I downloaded a Grisey piece from Emusic after the recent discussion and it sounded like standard contemporary-classical fare.

Graham

🔗Torsten Anders <torstenanders@...>

6/11/2008 1:38:34 AM

On Jun 11, 2008, at 9:22 AM, Graham Breed wrote:

> Mike Battaglia wrote:
>
> > Yeah! That's always what attracted me to 17-tet, the wider fifths. I
> > think it usually sounds good because widening them slightly
> > accentuates the intervals that we're already used to. I also
> > hypothesize that it might be because of some resemblance to the
> > stretched harmonic series that we often hear in nature (although it
> > could just be my own bias). This is why I always liked 12-tet more
> > than 19-tet - the third and fifth (and harmonic 7th) are all flat in
> > 19-tet, so everything sounds compressed and less accentuated. It
> > sounds like my brain is getting compressed. Although, the more I
> > listen to 19-tet, the more I like it, so it may just be my own bias
> > towards wider intervals that is being expressed here.
>
> If you like wider intervals, why not stretch the scale,
> instead of choosing tunings that happen to make primes other
> than 2 sharp?
>
> > I think a more accurate approach is that a person might interpret > 16/9
> > as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
> > to hearing 16/9. They might then become used to 16/9 as a separate
> > interval in its own right later. This is why I am wary of > labeling one
> > particular person's response to an interval or chord as though it > were
> > something the "brain" does. One person's brain might exhibit a > certain
> > behavior as the neurological correlate of a psychological
> > interpretation, but then attempting to generalize that behavior to
> > -all- people falls prey to the same fallacy that is currently > ruining
> > how music theory is being taught in America.
>
> The psychoacoustic results that I'm aware of say that the
> traditional assignment of chord roots is correct -- that is,
> naive listeners will hear A as the root of an A minor chord
> (A-C-E). For that to work we must be interpreting A-C as an
> out of tune 4:5. Given that, it's entirely plausible that
> 16/9 is interpreted as 7/4. Of course, we're also quite
> capable of telling the difference between major and minor
> thirds.
>
> Beyond that I don't think it's helpful or even meaningful to
> argue about what interval some other interval's heard in
> terms of. Generally, an interval is what it is and, as you
> say, it's only interpreted as a different interval if that
> other interval happens to be one the listener's already
> familiar with. The exceptions may be octaves and fifths.
>
> > I never really understood the otonality and utonality thing... It
> > makes sense at first but breaks down the further you get into it. A
> > minor chord is both a utonality and an otonality, depending on > how you
> > look at it. So is a major chord.
>
> A minor chord as 10:12:15 is a 5-limit utonality or a
> 15-limit otonality. In a 5-limit context there's only one
> interpretation.
>
> >> can both blur the seventh partial while at the same time perhaps > be on
> >> the edge of hearing as "Just". These tasty and functional "blurred"
> >> regions I call "shadows"- 23/18 is an example, another kind > would be
> >> found at a 25/24 above 5/4, which works as a kind of bright > 13/10 (<
> >> 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
> >> rides in and out of shadow and light.
> >
> > Yeah, this is sort of related to the original question I was > asking...
> > Is it that the 12tet major third approximates 5/4 but is really > sharp,
> > or is it that it approximates a higher-prime interval, or is it that
> > the higher-prime interval itself approximates the lower-prime
> > interval? Perhaps moving 5/4 up slightly by some irrational > number and
> > ignoring JI altogether would work as well.
>
> And this is the point where I say it doesn't matter at all.
>
> > Another example of what you're talking about here I think is the > good
> > ol' neutral triad... I have a multistable perception of neutral > triad
> > as an out of tune major and an out of tune minor simultaneously. I
> > suspect that the more I listen to it the more I will get used to > it as
> > a stable chord in its own right, and then that interval will develop
> > its own "field of attraction" apart from the major and the minor > one.
>
> Discordance graphs tend to show a kind of plateau between
> major and minor thirds. So any third will do. Whether
> that's because 6:5 and 5:4 merge into each other or because
> they merge in with 11:9 and 16:13 doesn't matter at all.
>
> > I suspect that fields of attraction are not drawn around actual
> > harmonic intervals, but around the MEMORIES we have of intervals. It
> > has to do with a tendency
>
> A meaningful question is: do intervals like 11:9 represent
> minimum points of dissonance? This is the concept of
> "tunable intervals". If intervals sound more consonant the
> closer they get to some ideal, it's worth considering that
> ideal when you choose a tuning or notation.
>
> > A teacher at my school was talking about the spectralists. I still
> > haven't heard any really good examples though. I searched for > "Scelsi"
> > on Youtube and didn't find much,
>
> There was a programme on the BBC a while back which I have
> on Mini Disc -- but not with me. I think I liked some
> Murail best. I downloaded a Grisey piece from Emusic after
> the recent discussion and it sounded like standard
> contemporary-classical fare.
>

Concerning "spectral music", I recently found the following list of listening recommendations

http://differentwaters.blogspot.com/2006/12/spectral-special-2-re-ups.html

Best
Torsten

>
>
> Graham
>
>
>
--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

🔗Cameron Bobro <misterbobro@...>

6/11/2008 5:01:46 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Thanks for explaining this as it made clearer to me exactly how you
>have
> been working. I would call it an empirical method over a rational
>one.
> Something that has occupied my thoughts quite a bit lately. I guess
>the
> next question is how one uses them, only for certain things or
> combinations?

Definitely empirical first and foremost. For example, when I went
listening for a most "thorth" or "foird" interval between 5/4 and
4/3, I just kept poking at it by singing and playing the Theremin
over a drone, and found that it was "a hair above 13/10." Then
because 13/10 is a superparticular interval (these are the smoothest
and easiest in the long term to jam along with, as far as I can tell)
above 5/4, (26/25), I figured what the hell why not try a 25/24 above
5/4, which is just the relation between 6/5 and 5/4 shifted up and
results in the "classical augmented third". With such a "natural"
step I can slide in and out of light and shadow both melodically and
harmonically.

The classic augmented third sounded damn near perfect- singing and
playing the Theremin it doesn't matter a bit, don't even have to
"know", but using synthesizers you have to tell them exactly what to
play.

Then much later I measured a "phi-th" of the distance between 5/4 and
4/3, that is, the golden proportion on the frequency level, and find
that the "noble" interval as propounded by Dave and Margot is less
than <.78 cents higher than my best-guess "foird" figure for tuning
tables.

Hmmm.... I'll put a record of the process into Scala...

0:........1/1............0.000.....unison, perfect prime
1:........5/4............386.314...major third
2:........13/10..........454.214...tridecimal semi-diminished fourth
3:........456.214 cents..456.214...zlati rez 5/4 + 4/3
4:........125/96.........456.986...classic augmented third
5:........4/3............498.045...perfect four

>Kinda an if /then structure i could see working
>itself
> into it as opposed to some rational configuration, such as hexanies
made
> of these etc. While you might it seems like your process of
>choosing
> might find such things as the result as opposed to the means. I am
> fishing which i hope you don't mind.

It seems that it's all interlocked pretty sweetly, like the "thirth"
being 25/24 from 5/4- there's a noble minor third damn near exactly
5/6 down from the square root of two, another golden cut interval
23/24 of 3/2 (aka 9/8 above 23/18), etc. etc.

>
> anyway it was what i like of Wilson tunings in Xen. 3 where one
>will
> have different configurations on different places on the keyboard
>or
> overall tuning. Pythagorean then 5 limit then 7. He is deliberately
> conservative in his approach but would never object to what you are
> doing here.

I bet there are very regular chains involved, for everything I've
found so far can be found within two cents by wandering with simple
rational steps through different paths, taking different turns. For
example, whether you drop a 7/8 then a 10/13 from 7/4, or drop a
noble high "foird" (which in turn can be divided into 5/4 and 25/24)
from the golden cut of 7/5 and 7/4, you wind up either way at the
noble minor third, the discrepancy is less than one cent iirc.

It could very well be that it's simply a matter of using certain
points, where different kinds of harmonic series converge, as portals
between different series. And I don't think it's just the phi
intervals that do this, or at least, there are other ways to define
the shadowy points: the harmonic entropy charts I've seen have some
of them, or extremely close, and I've found some of the same (within
1 cent cent) intervals with bonehead simple divisions of Pi; 3/2Pi
also leads to the noble minor third Dave and Margot wrote about, and
that's the one I was using before I found out about their work in
this area.

Sorry to go on, kinda thinking out loud and finding excuses not to be
making drum beats by a deadline.

Just one more thing- after toiling for so long by ear to have found
some half dozen specific shadow regions just a couple of cents wide,
and then discovering that they can be described so exactly in such
simple ways, I will simply chortle at any accusations of numerology.
Not that there is anything wrong with numerology.

-Cameron Bobro

PS. In the unlikely event that any harmonic entropy fans have read
this far, about that 656 cent HE point: there's a shadow at 628 cents
(turns out to be a noble interval) and one about 670 cents (no
explanation for this one other than it's a 5/4 above the noble minor
third, so it may be a shadow of a shadow, as Jacques Brel would say)
but the 656 cent HE thing is a thing of its own, and a good one at
that, to my ears. It's very close to a 5/4 on 7/6. I would like to
know a more finely described figure for that particular HE point,
because if you drop it just half a cent or so (not to 5/4 above 7/6
which is sour), it's a winner.

🔗Cameron Bobro <misterbobro@...>

6/11/2008 5:56:59 AM

Say Mike have you read Terhardt? He has kind of a "gestalt" take that
seems to me to be right in principle at least- a combination of
nature and nurture. The idea that it's either one or the other, black
and white, seems to always come from someone who is trying to sell
you a particular nurture as "nature".

For example, a friend of mine who should know better was telling me
about a Just Intonation lecture.

"Cool!" I said. (The first JI lecture I ever heard was by Lou
Harrison at Laney Community College in California, 20 years ago.)

Then my friend went on to enthuse about the lecture, which turned out
to be a demonstration that the music of the spheres is diatonic
5-limit yet at the same time twelve tones to the octave comes from
nature, LOL.

Same crap different package can be found in textbooks and academic
studies, like one in the university library. It's relatively new, and
unlike most texts of the sets-n-symmetries variety (George Perle is
worth reading btw.), it has a bit about the harmonic series at the
beginning. Which concludes with what amounts to "noone can hear these
things anyway, there are twelve tones and that's it and f-k you",
hahaha!

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> > The character of different intervals is something I've been
focussing
> > on for quite a while. Obviously this is kind of a given in musical
> > performance, so more specifically, the character of intervals in
the
> > context of the tuning.
> > Be forewarned that Carl has called my ideas "eye of newt" :-D
>
> He does tend to do that, doesn't he?
>
> > but here goes: every interval has a character and in a tuning
that hangs
> > together, or in which all seems "of a kind" or "from the same
> > pallete", the intervals share certain color/feeling
characteristics.
> > So I listen for "character families". An obvious one is like the
> > slightly upwardly detuned 5/4 you mentioned before- it's a little
> > brighter. If you take for example 34-equal, there are genuine
> > approximations of 6/5 and 5/4; at two cents away it would be
kooky to
> > pretend that there isn't an obvious relation between the m3 and
M3 of
> > 34-equal, and those of the harmonic partials. They're the "same"
on
> > one hand, but both are two cents higher and brighter in character
on
> > the other. Throw in the even brighter 34-equal "3/2" and you've
got
> > a very clear character family right there in the first six
partials:
> > bright and brassy.
>
> Yeah! That's always what attracted me to 17-tet, the wider fifths. I
> think it usually sounds good because widening them slightly
> accentuates the intervals that we're already used to. I also
> hypothesize that it might be because of some resemblance to the
> stretched harmonic series that we often hear in nature (although it
> could just be my own bias). This is why I always liked 12-tet more
> than 19-tet - the third and fifth (and harmonic 7th) are all flat in
> 19-tet, so everything sounds compressed and less accentuated. It
> sounds like my brain is getting compressed. Although, the more I
> listen to 19-tet, the more I like it, so it may just be my own bias
> towards wider intervals that is being expressed here.

17 is a subset of 34 of course. 34 and 68 are the closest things to
alternating light and shadow, in my view, of any of the equal
divisions, and they're what I use for notation.
>
> I suppose some cross-culture listening tests would have to be
> performed in order to determine whether that theory is due to a
> cultural bias for wider intervals (e.g. the 12tet major third) or
> whether it has some acoustic basis. Honestly I think that the
apparent
> duality here can be resolved by noting that while there is likely
SOME
> acoustic basis on what you initially hear, the matter of whether you
> LIKE what your brain shows you after all of this acoustic and
> psychoacoustic stuff goes down is a different mental process
entirely.
> And then what you like or prefer makes up part of your overall
> perception, or Gestalt.
>
> > Looking at things this way, it's easy to imagine that a whole
tuning
> > can have a certain character, or "red thread". I call it an
> > uebertimbre to irk Carl, but in seriousness it's a
Gesamtklangfarbe.
>
> Hahaha what? Gezundheit
>
> > When you have intervals, whether rational or "irrational", that
> > create coincident or near-concident partials with great
regularity,
> > you tend to put weight in specific places in the spectra. If you
plot
> > the partials of say a complete "7-limit" u- and o-tonality
tuning, it
> > is not hard to imagine that the regions coinciding with seventh
> > partials tend to get reinforced in a piece of music. As you can
> > easily demonstrate with an additive synthesizer, putting more
energy
> > into the seventh partial makes for a different tone color.
>
> I remember hearing an example on the web of a JI major chord as
> compared to the 12tet major chord. The website claimed that the
equal
> tempered one sounded better, and for their example, it did. Then
they
> had a JI major chord in which the notes were phase shifted so that I
> think the 5th harmonic of the fundamental cancelled out with the 4th
> harmonic of the major third, and it sounded much better, though I'm
> not sure why that particular overtone was so offensive.
>
> > Obviously a tuning in and of itself isn't enough to really have a
> > Gesamtklangfarbe, it's really a potential Gesamtklangfarbe because
> > key and modality also write the overall timbre- for example, a
> > secondary key center or an insistent figure can create a kind of
> > "formant" in the overall spectral envelope of the piece.
>
> Interesting ideas. I'd like to hear some musical examples that
>utilize
> this for some interesting effect. Apparently gesamtklangfarbe
> translates to "total tone quality," which is a term I've never heard
> before.

Probably you'll find it most in music criticism or descriptions of
music, but I think it's the best word in this context. Not as funny
as "uebertimbre" though.
>
> > (Really wide voicings and punctalism would probably throw the
>whole
> > thing to the dogs, but that is nothing new, these things have been
> > effective tools of "atonalists" for a long time.)
>
> It would be awesome if there was some software that let you screw
> around with JI chords and inharmonicity as such. Would most likely
>be
> interesting in the end.

Csound, man!

>
> > Another thing that is common in distinctive and attractive
instrument
> > timbres is gaps-and-lumps in the partials, analize a violin sound
for
> > example. In my experience, gaps-and-lumps in the overall field of
> > coincident partials that a tuning tends to reinforce is a good
thing.
> > So after long poking around with my ears at tuning until it
floats my
> > boat, I (always?) find upon examination that has characteristics
like
> > "primes: 2,3,5,23" or "2,5,7,73" and so on.
>
> Interesting. Probably due to resonant effects of the body or
>something.

Those are responsible for formants as well. There are other things-
ever notice that a clarinet is an octave lower than it looks like?
Same thing that makes it so makes for the every-other nature of the
partials. (somebody is going to cringe at that but you have to admit
it's basically true and a decent poetic reference to the differences
between open/closed tapered/straight bores)

>
> > Notice that "73" or any extremely high partial needs absolutely no
> > numerology or wild claims of human hearing ability to be
"justified".
> > 73/64 is four cents from 8/7 so we're hearing something which is
> > both a thing of its own, and a flavor of 8/7.
>
> Yeah. That's the key. That's why I had second thoughts about the
> assertions made above that a dominant 7 chord where the 7 is 16/9
will
> be interpreted "by the brain" as being an out of tune 7/4. It's just
> that 7/4 and 16/9 are fairly close in the pitch continuum, so
> naturally they'll sound similar. The whole thing seems to ignore the
> fact that these intervals have characters of their own as well; they
> are not merely mistuned versions of other simpler intervals,
although
> you might hear them that way at first. You might also hear the
simpler
> intervals as mistunings of the more complicated ones, which is why
> when people used to 12-tet hear music in just intonation for the
first
> time sometimes think it "sounds wrong," even if there is no commatic
> drift or the like.

In music that has conjunct tetrachords as structual elements it's the
16/9 that's likely going to be "more Just", not the 7/4.
>
> I think these fields of attraction are merely a way to describe the
> phenomenon of how and under what circumstances we hear a resemblance
> to the harmonic series in tempered or non-harmonic (or upper JI
> harmonic) intervals.
>
> It's like this image: http://en.wikipedia.org/wiki/
Image:Invariance.jpg
>
> "A" is the original object, and "D" is a distorted version of the
same
> object. The concept of a field of attraction is merely I think is an
> attempt to explain how much of that distortion we can take before we
> stop seeing it as the same object. However, saying that the images
in
> D are ONLY good at being "slightly erroneous" versions of the
objects
> in picture A is taking it too far. After all, no axiomatic theory is
> complete (hint, hint).
>
> I think a more accurate approach is that a person might interpret
16/9
> as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
> to hearing 16/9. They might then become used to 16/9 as a separate
> interval in its own right later. This is why I am wary of labeling
one
> particular person's response to an interval or chord as though it
were
> something the "brain" does. One person's brain might exhibit a
certain
> behavior as the neurological correlate of a psychological
> interpretation, but then attempting to generalize that behavior to
> -all- people falls prey to the same fallacy that is currently
ruining
> how music theory is being taught in America.
>
> Here's a simple example to demonstrate that concept... Play a 12 bar
> blues, where the chords are 4:5:6:7. Let's say it's in the key of C.
> Right before the C goes to F, change the 7th of the C chord to be
> 16/9, as in change it from an otonal tetrad to a pythagorean
> "dominant" 7, that resolves as a V-I to the next chord. see if you
> feel a difference!
>
> Another way to say all of this is that you perhaps DEVELOP your
fields
> of attraction to intervals over time, depending on when you hear
them.
>
> > Other high partials
> > are great for blurring other regions- 23/18 for example splits the
> > difference between 9/7 and 14/11, and a "23" tuning (o's and u's
to
> > use Partch's charmingly ridiculous but effective terminology)
>
> I never really understood the otonality and utonality thing... It
> makes sense at first but breaks down the further you get into it. A
> minor chord is both a utonality and an otonality, depending on how
you
> look at it. So is a major chord.
>
> > can both blur the seventh partial while at the same time perhaps
be on
> > the edge of hearing as "Just". These tasty and functional
"blurred"
> > regions I call "shadows"- 23/18 is an example, another kind would
be
> > found at a 25/24 above 5/4, which works as a kind of bright 13/10
(<
> > 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
> > rides in and out of shadow and light.
>
> Yeah, this is sort of related to the original question I was
asking...
> Is it that the 12tet major third approximates 5/4 but is really
sharp,
> or is it that it approximates a higher-prime interval, or is it that
> the higher-prime interval itself approximates the lower-prime
> interval? Perhaps moving 5/4 up slightly by some irrational number
and
> ignoring JI altogether would work as well.
>
> Another example of what you're talking about here I think is the
good
> ol' neutral triad... I have a multistable perception of neutral
triad
> as an out of tune major and an out of tune minor simultaneously. I
> suspect that the more I listen to it the more I will get used to it
as
> a stable chord in its own right, and then that interval will develop
> its own "field of attraction" apart from the major and the minor
one.
>
> I suspect that fields of attraction are not drawn around actual
> harmonic intervals, but around the MEMORIES we have of intervals. It
> has to do with a tendency

I think that Terhardt is right in viewing things as a whole- what is
exerting gravity (hehe) changes in context.
>
> > I would think that this all sounds quite tame and maybe even
common-
> > sensical. The other day I read about the "spectralists" here (BTW
> > thanks for the information and links, guys!), a school I wasn't
aware
> > of. As far as I can make out a lot of what I do is about the
same, at
> > heart, only backwards. No big deal.
>
> A teacher at my school was talking about the spectralists. I still
> haven't heard any really good examples though. I searched for
"Scelsi"
> on Youtube and didn't find much,
>
> > But if you think about it, you will realize how easily this can
come
> > into conflict with the regular temperament paradigm. (I am not
> > putting "regular temperament paradigm" in quotes because I think
it's
> > a serious thing and the guys here involved in defining it should
be
> > proud of,not embarrassed by, the expression.)
>
> I have been reading the regular temperament paradigm and find it
very
> interesting. There are cases where it seems brilliantly insightful
and
> others where it just seems like one particular way of looking at
> certain aspects of harmony and temperament.
>
> I am starting to become concerned with the "why"'s rather than the
> "how"'s... I think one gestalt-related approach might be to state
that
> if we hear a 12-tet C C G C E G chord, we are likely to hear the
> resemblance to the harmonic series and thus hear it that way.
However,
> people often hear that 12-tet major third as having its own sound,
> sticking out and being much brighter than a just 5/4. Sometimes that
> 12-tet major third sticks out and implies a harmony and tonality of
> its own completely separate from the major third.
>
> The paradigm where everything is completely heard in terms of being
> out of tune simple integer just intonation relationships I think is
>a
> good rough start, but ultimately incomplete and inconsistent.

>It's
>an
> attempt to describe the resemblance we hear between various tempered
> intervals and other intervals in the harmonic series. This
resemblance
> is often used in equal tempered music to -imply- the existence of a
> faux-harmonic series for musical purposes. Different just-intonated
> intervals can also be used to imply the harmonic series as well, in
> that sense. However, dismissing these intervals as serving -only-
>that
> functionality is a non-sequitur.
>
> In other words, this view goes wrong when it ignores the -
difference-
> between the harmonic series versions and the tempered versions.
> Usually this difference is dismissed as being an "error," the
> implication being that it is undesirable. Yet, as we've seen with
> 12-tet and 34-tet, this difference is often musical in character and
> not at all "erroneous."
>
> Not only for atonal music, which often draws from a disregarding of
> harmony entirely, but for tonal music as well. The most obvious
place
> where the system breaks down that I've seen in recent memory is the
> Wikipedia entry for "41 equal temperament."
>
> Take this sentence near the bottom:
>
> "41-ET also has 6 distinct intervals between a perfect fourth and
> perfect fifth, whereas 31-ET has only four; the two additional
> intervals are poor matches to the ratios 15:11 and 22:15."
>
> It seems to be a common trend among these circles to hear one
interval
> as a "poor match" to another one. Seems like a matter of not being
> used enough to that interval to hear it for what it is. 10 cent
> differences in pitch can make quite a difference; we aren't talking
> about a 3 cent distinction here.
>
> It's like taking the triangle from letter A in this image
> (http://en.wikipedia.org/wiki/Image:Reification.jpg) and saying
it's a
> "poor" match to a triangle because the sides are incomplete.
>
> > Right off the bat, it is clear that if there's any legitamcy to
this approach, reckoning
> > "errors" in temperaments would be a very big pain in the ass, for
a
> > greater "error" (deviation from Just) in an interval could very
well
> > mean more, and not less, continuity in "flavor" or "hue" or
whatever.
> > And "shadows", or zones of ambiguity, rely on NOT being good
> > approximations of intervals, but on being in the (right) wrong
place
> > in the audible spectrum.
>
> Agreed. No newts found here.
>
> > Add to this the probability that it's the gapped-and-lumped
spectra
> > that make for the nicest
> > "Gesamtflangfarben", and we're looking at "good" temperaments that
> > might appear on paper to be pretty crappy. As you have certainly
> > noticed, 12-tET, all questions of taste aside, is might flexible,
and
> > it fits the kind of description I gave above: "damn near perfect 2
> > and 3, and some 19" The 19 is not the "justification" of 12-tET,
> > though who knows if there's some far-away feeling of it or not-
> > doesn't matter. "19" just a rough description of the place the
> > "shadows" of 12-tET dwell. In the case of 12-tET, it's the size
and
> > vagueness of the shadow zones that make it flexible, but when 12-
tET
> > is taken literally they're just too damn big and blurry IMO.
>
> Don't understand this paragraph.. What do you mean, the 19th
harmonic?

> What do you mean by justification? Could you elaborate?
-Mike
>

By justification, I mean you could say that the m3 and M3 of 12-tET
are approximating 19/16 and 19/15, which they approximate better on
paper than they do 6/5 and 5/4. Maybe that's audible or not, doesn't
really matter- what they do do is nicely fail to approximate all
kinds of intervals, remaining vague enough to be interpreted as all
kinds of things in practice. Autotune, by enforcing 12-tET, is going
to kill it dead because it robs 12-tET of this, its one true power
aside from the exactness of the first coupla perfect intervals. The
19 approximations are just rough descriptions of where the "fuzz"
lies. If they do impart some lessening of dissonance, so much the
better, whatever, but we're dealing with "fuzzies", not
"approximations" in 12-tET, as far as thirds and sixths.

🔗Cameron Bobro <misterbobro@...>

6/11/2008 6:32:10 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i think 23 is used in cadences allot. 17 Helmholtz pointed out.
> As maybe the person who works the most with sequences that lead
>to
> noble numbers i can say a few words about them. I have found that
>the
> tuning is even more critical than just as you want your difference
>tones
> to land on pitches in your scale.

That's an interesting point I hadn't thought of.

>Otherwise the sound and
>reinforcement
> falls apart. I have tried both tuning to the converged noble
number and
> to numerical sequences leading up to it. I have found that i
actually
> prefer these series before they converge too much but also away
from the
> simplest seed where one is not even sure where it is heading.
> Possibly you are right to associate it with noble more than
>just
> and to distinguish the two. Personally i am not into introducing
>new
> terms and think it does more good to associate it with just, for
>the
> very reason in that it extends just as opposed to putting an end to
>it.

Yeah I must agree with that because it all does link together and am
sticking to "shadows"- you've got the harmonic series and these
shadows. Also I feel quite strongly that there are either more kinds
of shadows or more ways to get at them than we know. In the end it
must all relate to the harmonic series, or whatever the partials of
your instruments are, in some elegant ways, otherwise it sounds
"approximate". There's enough approximate in the world without my
having to add to it intentionally.

-Cameron Bobro

🔗Cameron Bobro <misterbobro@...>

6/11/2008 7:10:24 AM

But it's not just mistuning of Just, which can also be viewed as Just
Intonation performed on an "inharmonic" spectrum. It's also the lumps
and gaps (regions of lesser or no energy and regions of stronger
energy) in the spectrum that give a timbre color.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Cameron wrote:
>
> > > I call it an
> > > uebertimbre to irk Carl, but in seriousness it's a
> > > Gesamtklangfarbe.
>
> That doesn't irk me at all. I've long proposed that the
> mistuning fingerprint of ETs (at least < 50) might add up
> to a gestalt sound. In 1998 I suggested that's what
> Ivor Darreg's "moods" were.
>
> -Carl
>

🔗Kraig Grady <kraiggrady@...>

6/11/2008 7:15:35 AM

I would assume the music of the Spheres thing was someone talking about Kepler. Who i am sure if he was alive today would draw different conclusions

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> Say Mike have you read Terhardt? He has kind of a "gestalt" take that
> seems to me to be right in principle at least- a combination of
> nature and nurture. The idea that it's either one or the other, black
> and white, seems to always come from someone who is trying to sell
> you a particular nurture as "nature".
>
> For example, a friend of mine who should know better was telling me
> about a Just Intonation lecture.
>
> "Cool!" I said. (The first JI lecture I ever heard was by Lou
> Harrison at Laney Community College in California, 20 years ago.)
>
> Then my friend went on to enthuse about the lecture, which turned out
> to be a demonstration that the music of the spheres is diatonic
> 5-limit yet at the same time twelve tones to the octave comes from
> nature, LOL.
>
> Same crap different package can be found in textbooks and academic
> studies, like one in the university library. It's relatively new, and
> unlike most texts of the sets-n-symmetries variety (George Perle is
> worth reading btw.), it has a bit about the harmonic series at the
> beginning. Which concludes with what amounts to "noone can hear these
> things anyway, there are twelve tones and that's it and f-k you",
> hahaha!
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...>
> wrote:
> >
> > > The character of different intervals is something I've been
> focussing
> > > on for quite a while. Obviously this is kind of a given in musical
> > > performance, so more specifically, the character of intervals in
> the
> > > context of the tuning.
> > > Be forewarned that Carl has called my ideas "eye of newt" :-D
> >
> > He does tend to do that, doesn't he?
> >
> > > but here goes: every interval has a character and in a tuning
> that hangs
> > > together, or in which all seems "of a kind" or "from the same
> > > pallete", the intervals share certain color/feeling
> characteristics.
> > > So I listen for "character families". An obvious one is like the
> > > slightly upwardly detuned 5/4 you mentioned before- it's a little
> > > brighter. If you take for example 34-equal, there are genuine
> > > approximations of 6/5 and 5/4; at two cents away it would be
> kooky to
> > > pretend that there isn't an obvious relation between the m3 and
> M3 of
> > > 34-equal, and those of the harmonic partials. They're the "same"
> on
> > > one hand, but both are two cents higher and brighter in character
> on
> > > the other. Throw in the even brighter 34-equal "3/2" and you've
> got
> > > a very clear character family right there in the first six
> partials:
> > > bright and brassy.
> >
> > Yeah! That's always what attracted me to 17-tet, the wider fifths. I
> > think it usually sounds good because widening them slightly
> > accentuates the intervals that we're already used to. I also
> > hypothesize that it might be because of some resemblance to the
> > stretched harmonic series that we often hear in nature (although it
> > could just be my own bias). This is why I always liked 12-tet more
> > than 19-tet - the third and fifth (and harmonic 7th) are all flat in
> > 19-tet, so everything sounds compressed and less accentuated. It
> > sounds like my brain is getting compressed. Although, the more I
> > listen to 19-tet, the more I like it, so it may just be my own bias
> > towards wider intervals that is being expressed here.
>
> 17 is a subset of 34 of course. 34 and 68 are the closest things to
> alternating light and shadow, in my view, of any of the equal
> divisions, and they're what I use for notation.
> >
> > I suppose some cross-culture listening tests would have to be
> > performed in order to determine whether that theory is due to a
> > cultural bias for wider intervals (e.g. the 12tet major third) or
> > whether it has some acoustic basis. Honestly I think that the
> apparent
> > duality here can be resolved by noting that while there is likely
> SOME
> > acoustic basis on what you initially hear, the matter of whether you
> > LIKE what your brain shows you after all of this acoustic and
> > psychoacoustic stuff goes down is a different mental process
> entirely.
> > And then what you like or prefer makes up part of your overall
> > perception, or Gestalt.
> >
> > > Looking at things this way, it's easy to imagine that a whole
> tuning
> > > can have a certain character, or "red thread". I call it an
> > > uebertimbre to irk Carl, but in seriousness it's a
> Gesamtklangfarbe.
> >
> > Hahaha what? Gezundheit
> >
> > > When you have intervals, whether rational or "irrational", that
> > > create coincident or near-concident partials with great
> regularity,
> > > you tend to put weight in specific places in the spectra. If you
> plot
> > > the partials of say a complete "7-limit" u- and o-tonality
> tuning, it
> > > is not hard to imagine that the regions coinciding with seventh
> > > partials tend to get reinforced in a piece of music. As you can
> > > easily demonstrate with an additive synthesizer, putting more
> energy
> > > into the seventh partial makes for a different tone color.
> >
> > I remember hearing an example on the web of a JI major chord as
> > compared to the 12tet major chord. The website claimed that the
> equal
> > tempered one sounded better, and for their example, it did. Then
> they
> > had a JI major chord in which the notes were phase shifted so that I
> > think the 5th harmonic of the fundamental cancelled out with the 4th
> > harmonic of the major third, and it sounded much better, though I'm
> > not sure why that particular overtone was so offensive.
> >
> > > Obviously a tuning in and of itself isn't enough to really have a
> > > Gesamtklangfarbe, it's really a potential Gesamtklangfarbe because
> > > key and modality also write the overall timbre- for example, a
> > > secondary key center or an insistent figure can create a kind of
> > > "formant" in the overall spectral envelope of the piece.
> >
> > Interesting ideas. I'd like to hear some musical examples that
> >utilize
> > this for some interesting effect. Apparently gesamtklangfarbe
> > translates to "total tone quality," which is a term I've never heard
> > before.
>
> Probably you'll find it most in music criticism or descriptions of
> music, but I think it's the best word in this context. Not as funny
> as "uebertimbre" though.
> >
> > > (Really wide voicings and punctalism would probably throw the
> >whole
> > > thing to the dogs, but that is nothing new, these things have been
> > > effective tools of "atonalists" for a long time.)
> >
> > It would be awesome if there was some software that let you screw
> > around with JI chords and inharmonicity as such. Would most likely
> >be
> > interesting in the end.
>
> Csound, man!
>
> >
> > > Another thing that is common in distinctive and attractive
> instrument
> > > timbres is gaps-and-lumps in the partials, analize a violin sound
> for
> > > example. In my experience, gaps-and-lumps in the overall field of
> > > coincident partials that a tuning tends to reinforce is a good
> thing.
> > > So after long poking around with my ears at tuning until it
> floats my
> > > boat, I (always?) find upon examination that has characteristics
> like
> > > "primes: 2,3,5,23" or "2,5,7,73" and so on.
> >
> > Interesting. Probably due to resonant effects of the body or
> >something.
>
> Those are responsible for formants as well. There are other things-
> ever notice that a clarinet is an octave lower than it looks like?
> Same thing that makes it so makes for the every-other nature of the
> partials. (somebody is going to cringe at that but you have to admit
> it's basically true and a decent poetic reference to the differences
> between open/closed tapered/straight bores)
>
> >
> > > Notice that "73" or any extremely high partial needs absolutely no
> > > numerology or wild claims of human hearing ability to be
> "justified".
> > > 73/64 is four cents from 8/7 so we're hearing something which is
> > > both a thing of its own, and a flavor of 8/7.
> >
> > Yeah. That's the key. That's why I had second thoughts about the
> > assertions made above that a dominant 7 chord where the 7 is 16/9
> will
> > be interpreted "by the brain" as being an out of tune 7/4. It's just
> > that 7/4 and 16/9 are fairly close in the pitch continuum, so
> > naturally they'll sound similar. The whole thing seems to ignore the
> > fact that these intervals have characters of their own as well; they
> > are not merely mistuned versions of other simpler intervals,
> although
> > you might hear them that way at first. You might also hear the
> simpler
> > intervals as mistunings of the more complicated ones, which is why
> > when people used to 12-tet hear music in just intonation for the
> first
> > time sometimes think it "sounds wrong," even if there is no commatic
> > drift or the like.
>
> In music that has conjunct tetrachords as structual elements it's the
> 16/9 that's likely going to be "more Just", not the 7/4.
> >
> > I think these fields of attraction are merely a way to describe the
> > phenomenon of how and under what circumstances we hear a resemblance
> > to the harmonic series in tempered or non-harmonic (or upper JI
> > harmonic) intervals.
> >
> > It's like this image: http://en.wikipedia.org/wiki/ > <http://en.wikipedia.org/wiki/>
> Image:Invariance.jpg
> >
> > "A" is the original object, and "D" is a distorted version of the
> same
> > object. The concept of a field of attraction is merely I think is an
> > attempt to explain how much of that distortion we can take before we
> > stop seeing it as the same object. However, saying that the images
> in
> > D are ONLY good at being "slightly erroneous" versions of the
> objects
> > in picture A is taking it too far. After all, no axiomatic theory is
> > complete (hint, hint).
> >
> > I think a more accurate approach is that a person might interpret
> 16/9
> > as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
> > to hearing 16/9. They might then become used to 16/9 as a separate
> > interval in its own right later. This is why I am wary of labeling
> one
> > particular person's response to an interval or chord as though it
> were
> > something the "brain" does. One person's brain might exhibit a
> certain
> > behavior as the neurological correlate of a psychological
> > interpretation, but then attempting to generalize that behavior to
> > -all- people falls prey to the same fallacy that is currently
> ruining
> > how music theory is being taught in America.
> >
> > Here's a simple example to demonstrate that concept... Play a 12 bar
> > blues, where the chords are 4:5:6:7. Let's say it's in the key of C.
> > Right before the C goes to F, change the 7th of the C chord to be
> > 16/9, as in change it from an otonal tetrad to a pythagorean
> > "dominant" 7, that resolves as a V-I to the next chord. see if you
> > feel a difference!
> >
> > Another way to say all of this is that you perhaps DEVELOP your
> fields
> > of attraction to intervals over time, depending on when you hear
> them.
> >
> > > Other high partials
> > > are great for blurring other regions- 23/18 for example splits the
> > > difference between 9/7 and 14/11, and a "23" tuning (o's and u's
> to
> > > use Partch's charmingly ridiculous but effective terminology)
> >
> > I never really understood the otonality and utonality thing... It
> > makes sense at first but breaks down the further you get into it. A
> > minor chord is both a utonality and an otonality, depending on how
> you
> > look at it. So is a major chord.
> >
> > > can both blur the seventh partial while at the same time perhaps
> be on
> > > the edge of hearing as "Just". These tasty and functional
> "blurred"
> > > regions I call "shadows"- 23/18 is an example, another kind would
> be
> > > found at a 25/24 above 5/4, which works as a kind of bright 13/10
> (<
> > > 2.8 cents high) and is obviously nicely linked to 5/4 for smooth
> > > rides in and out of shadow and light.
> >
> > Yeah, this is sort of related to the original question I was
> asking...
> > Is it that the 12tet major third approximates 5/4 but is really
> sharp,
> > or is it that it approximates a higher-prime interval, or is it that
> > the higher-prime interval itself approximates the lower-prime
> > interval? Perhaps moving 5/4 up slightly by some irrational number
> and
> > ignoring JI altogether would work as well.
> >
> > Another example of what you're talking about here I think is the
> good
> > ol' neutral triad... I have a multistable perception of neutral
> triad
> > as an out of tune major and an out of tune minor simultaneously. I
> > suspect that the more I listen to it the more I will get used to it
> as
> > a stable chord in its own right, and then that interval will develop
> > its own "field of attraction" apart from the major and the minor
> one.
> >
> > I suspect that fields of attraction are not drawn around actual
> > harmonic intervals, but around the MEMORIES we have of intervals. It
> > has to do with a tendency
>
> I think that Terhardt is right in viewing things as a whole- what is
> exerting gravity (hehe) changes in context.
> >
> > > I would think that this all sounds quite tame and maybe even
> common-
> > > sensical. The other day I read about the "spectralists" here (BTW
> > > thanks for the information and links, guys!), a school I wasn't
> aware
> > > of. As far as I can make out a lot of what I do is about the
> same, at
> > > heart, only backwards. No big deal.
> >
> > A teacher at my school was talking about the spectralists. I still
> > haven't heard any really good examples though. I searched for
> "Scelsi"
> > on Youtube and didn't find much,
> >
> > > But if you think about it, you will realize how easily this can
> come
> > > into conflict with the regular temperament paradigm. (I am not
> > > putting "regular temperament paradigm" in quotes because I think
> it's
> > > a serious thing and the guys here involved in defining it should
> be
> > > proud of,not embarrassed by, the expression.)
> >
> > I have been reading the regular temperament paradigm and find it
> very
> > interesting. There are cases where it seems brilliantly insightful
> and
> > others where it just seems like one particular way of looking at
> > certain aspects of harmony and temperament.
> >
> > I am starting to become concerned with the "why"'s rather than the
> > "how"'s... I think one gestalt-related approach might be to state
> that
> > if we hear a 12-tet C C G C E G chord, we are likely to hear the
> > resemblance to the harmonic series and thus hear it that way.
> However,
> > people often hear that 12-tet major third as having its own sound,
> > sticking out and being much brighter than a just 5/4. Sometimes that
> > 12-tet major third sticks out and implies a harmony and tonality of
> > its own completely separate from the major third.
> >
> > The paradigm where everything is completely heard in terms of being
> > out of tune simple integer just intonation relationships I think is
> >a
> > good rough start, but ultimately incomplete and inconsistent.
>
> >It's
> >an
> > attempt to describe the resemblance we hear between various tempered
> > intervals and other intervals in the harmonic series. This
> resemblance
> > is often used in equal tempered music to -imply- the existence of a
> > faux-harmonic series for musical purposes. Different just-intonated
> > intervals can also be used to imply the harmonic series as well, in
> > that sense. However, dismissing these intervals as serving -only-
> >that
> > functionality is a non-sequitur.
> >
> > In other words, this view goes wrong when it ignores the -
> difference-
> > between the harmonic series versions and the tempered versions.
> > Usually this difference is dismissed as being an "error," the
> > implication being that it is undesirable. Yet, as we've seen with
> > 12-tet and 34-tet, this difference is often musical in character and
> > not at all "erroneous."
> >
> > Not only for atonal music, which often draws from a disregarding of
> > harmony entirely, but for tonal music as well. The most obvious
> place
> > where the system breaks down that I've seen in recent memory is the
> > Wikipedia entry for "41 equal temperament."
> >
> > Take this sentence near the bottom:
> >
> > "41-ET also has 6 distinct intervals between a perfect fourth and
> > perfect fifth, whereas 31-ET has only four; the two additional
> > intervals are poor matches to the ratios 15:11 and 22:15."
> >
> > It seems to be a common trend among these circles to hear one
> interval
> > as a "poor match" to another one. Seems like a matter of not being
> > used enough to that interval to hear it for what it is. 10 cent
> > differences in pitch can make quite a difference; we aren't talking
> > about a 3 cent distinction here.
> >
> > It's like taking the triangle from letter A in this image
> > (http://en.wikipedia.org/wiki/Image:Reification.jpg > <http://en.wikipedia.org/wiki/Image:Reification.jpg>) and saying
> it's a
> > "poor" match to a triangle because the sides are incomplete.
> >
> > > Right off the bat, it is clear that if there's any legitamcy to
> this approach, reckoning
> > > "errors" in temperaments would be a very big pain in the ass, for
> a
> > > greater "error" (deviation from Just) in an interval could very
> well
> > > mean more, and not less, continuity in "flavor" or "hue" or
> whatever.
> > > And "shadows", or zones of ambiguity, rely on NOT being good
> > > approximations of intervals, but on being in the (right) wrong
> place
> > > in the audible spectrum.
> >
> > Agreed. No newts found here.
> >
> > > Add to this the probability that it's the gapped-and-lumped
> spectra
> > > that make for the nicest
> > > "Gesamtflangfarben", and we're looking at "good" temperaments that
> > > might appear on paper to be pretty crappy. As you have certainly
> > > noticed, 12-tET, all questions of taste aside, is might flexible,
> and
> > > it fits the kind of description I gave above: "damn near perfect 2
> > > and 3, and some 19" The 19 is not the "justification" of 12-tET,
> > > though who knows if there's some far-away feeling of it or not-
> > > doesn't matter. "19" just a rough description of the place the
> > > "shadows" of 12-tET dwell. In the case of 12-tET, it's the size
> and
> > > vagueness of the shadow zones that make it flexible, but when 12-
> tET
> > > is taken literally they're just too damn big and blurry IMO.
> >
> > Don't understand this paragraph.. What do you mean, the 19th
> harmonic?
>
> > What do you mean by justification? Could you elaborate?
> -Mike
> >
>
> By justification, I mean you could say that the m3 and M3 of 12-tET
> are approximating 19/16 and 19/15, which they approximate better on
> paper than they do 6/5 and 5/4. Maybe that's audible or not, doesn't
> really matter- what they do do is nicely fail to approximate all
> kinds of intervals, remaining vague enough to be interpreted as all
> kinds of things in practice. Autotune, by enforcing 12-tET, is going
> to kill it dead because it robs 12-tET of this, its one true power
> aside from the exactness of the first coupla perfect intervals. The
> 19 approximations are just rough descriptions of where the "fuzz"
> lies. If they do impart some lessening of dissonance, so much the
> better, whatever, but we're dealing with "fuzzies", not
> "approximations" in 12-tET, as far as thirds and sixths.
>
>

🔗Kraig Grady <kraiggrady@...>

6/11/2008 7:21:58 AM

I wholly agree with this which is why i stay on this list:)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> Also I feel quite strongly that there are either more kinds
> of shadows or more ways to get at them than we know.
>
>
>

🔗George D. Secor <gdsecor@...>

6/11/2008 11:44:54 AM

Hi Mike,

I made a few comments in which you may be interested, regarding the
melodic properties of wide-fifth vs. narrow-fifth temperaments, in my
17-tone paper (most of which was written in 2001, before I joined the
tuning lists, but not published until 5 years later, in Xenharmonikon
18):
http://xenharmony.wikispaces.com/space/showimage/17puzzle.pdf
beginning with the section heading in the middle of the 3rd page
(numbered as p. 57).

In case you decide to read the entire paper (or to entice you to do
so), I also made a 17-tone jazz excerpt using the 9-tone scale
(subset of 17) that I described near the bottom of the 22nd page
(numbered as p. 76):
http://xenharmony.wikispaces.com/space/showimage/17WTjazz.mp3

While we're on the subject of the psychology of alternative tunings,
there's a 17-tone piece (by Aaron Krister Johnson) that you might be
interested in listening to, Adagio for Margo, at:
http://www.akjmusic.com/works.html
and then read about a particular observation I made:
/makemicromusic/topicId_15226.html#15247
and Aaron's reply:
/makemicromusic/topicId_15226.html#15249

--George

🔗Mike Battaglia <battaglia01@...>

6/11/2008 5:04:30 PM

>> Yeah! That's always what attracted me to 17-tet, the wider fifths. I
>> think it usually sounds good because widening them slightly
>> accentuates the intervals that we're already used to. I also
>> hypothesize that it might be because of some resemblance to the
>> stretched harmonic series that we often hear in nature (although it
>> could just be my own bias). This is why I always liked 12-tet more
>> than 19-tet - the third and fifth (and harmonic 7th) are all flat in
>> 19-tet, so everything sounds compressed and less accentuated. It
>> sounds like my brain is getting compressed. Although, the more I
>> listen to 19-tet, the more I like it, so it may just be my own bias
>> towards wider intervals that is being expressed here.
>
> If you like wider intervals, why not stretch the scale,
> instead of choosing tunings that happen to make primes other
> than 2 sharp?

Stretched 2's sound good imo as well. It's kind of a novel sound to
hear beating on an octave at first, but I think most people would like
the sound of it as well. I was more just trying to figure out why
34-et had the sound that it did.

>> I think a more accurate approach is that a person might interpret 16/9
>> as an out-of-tune 7/4 if they are used to hearing 7/4 and not at all
>> to hearing 16/9. They might then become used to 16/9 as a separate
>> interval in its own right later. This is why I am wary of labeling one
>> particular person's response to an interval or chord as though it were
>> something the "brain" does. One person's brain might exhibit a certain
>> behavior as the neurological correlate of a psychological
>> interpretation, but then attempting to generalize that behavior to
>> -all- people falls prey to the same fallacy that is currently ruining
>> how music theory is being taught in America.
>
> The psychoacoustic results that I'm aware of say that the
> traditional assignment of chord roots is correct -- that is,
> naive listeners will hear A as the root of an A minor chord
> (A-C-E). For that to work we must be interpreting A-C as an
> out of tune 4:5. Given that, it's entirely plausible that
> 16/9 is interpreted as 7/4. Of course, we're also quite
> capable of telling the difference between major and minor
> thirds.

What do you mean by this? You think that given the note "A" people
will fill in that it's the root of a minor chord due to them somehow
intuitively knowing its diatonic role in a C major scale...? Or do you
mean that, given the key of C major, we will perceive the note "A" in
a chord root as having a minor quality, due to priming effects?

Furthermore, are you suggesting that the feeling and perception of a
minor triad is due to its proximity to a major third, but its being
out of tune gives it the "sad" minor feel to it? The concept seems to
be at odds with the one that Carl was referring to above, i.e. that
both 5/4 and 6/5 will have their own fields of attraction.

What psychoacoustic results are you referring to in this case? I'd
really like to see them.

> Beyond that I don't think it's helpful or even meaningful to
> argue about what interval some other interval's heard in
> terms of. Generally, an interval is what it is and, as you
> say, it's only interpreted as a different interval if that
> other interval happens to be one the listener's already
> familiar with. The exceptions may be octaves and fifths.

I think I agree with you. It seemed to me like Carl was saying that
these intervals will be approximated in terms of other intervals
because of psychoacoustic effects that are done in the brain, and that
the listener has no input or affect on this whatsoever. What "mental
label" people assign to an interval, even unconsciously, would
obviously have something to do with what labels they have.

Even deeper, regardless of how people consciously assign verbal
meaning to intervals, everyone has an internal cognitive "schema" or
symbol for an interval that they may or may not be aware of. At first,
when you hear a new interval that is close to an interval you already
know, you might experience it as an altered form of a mental symbol
that you already have, but after being constantly exposed to that
interval and its symbolic meaning for you, you may learn to
differentiate between that symbol and the other one. You will most
likely operate on the new symbol and come up with new thoughts derived
from it, and build on that schema just as you did the other one. What
role, then, would the concept of a purely acoustic "field of
attraction" have in this process anymore? You could potentially start
to develop another field of attraction around a second interval as
there is one around the first one.

It's sort of the equivalent of if the only two colors you know are red
and orange. You then run into reddish-orange for the first time. Are
you going to view that as a shade of red, or as a shade of orange? You
might view it either way, or have a multistable perception of the
color that "flickers" back and forth between the two. Eventually,
though, you might develop your own internal "symbol" or feeling for it
in the same way that you have a symbol for red and green and such, and
then draw inferences from it, such as perhaps starting to see how the
color would be used in a visual context for artistic effect.
Ironically, men and women often display disparities in their abilities
in this area, with men often categorizing and seeing everything in
terms of being shades of colors they already know, and women seeing
the colors as colors in their own right.

Psychologically, I think it depends on whether you build your schema
of an experience based on the physical experience alone, or whether
you build it based on another schema, though that might be slightly
out of context here.

>> I never really understood the otonality and utonality thing... It
>> makes sense at first but breaks down the further you get into it. A
>> minor chord is both a utonality and an otonality, depending on how you
>> look at it. So is a major chord.
>
> A minor chord as 10:12:15 is a 5-limit utonality or a
> 15-limit otonality. In a 5-limit context there's only one
> interpretation.

Ah, gotcha. It makes sense in terms of the limit that the chord is.

>> Another example of what you're talking about here I think is the good
>> ol' neutral triad... I have a multistable perception of neutral triad
>> as an out of tune major and an out of tune minor simultaneously. I
>> suspect that the more I listen to it the more I will get used to it as
>> a stable chord in its own right, and then that interval will develop
>> its own "field of attraction" apart from the major and the minor one.
>
> Discordance graphs tend to show a kind of plateau between
> major and minor thirds. So any third will do. Whether
> that's because 6:5 and 5:4 merge into each other or because
> they merge in with 11:9 and 16:13 doesn't matter at all.
>
>> I suspect that fields of attraction are not drawn around actual
>> harmonic intervals, but around the MEMORIES we have of intervals. It
>> has to do with a tendency
>
> A meaningful question is: do intervals like 11:9 represent
> minimum points of dissonance? This is the concept of
> "tunable intervals". If intervals sound more consonant the
> closer they get to some ideal, it's worth considering that
> ideal when you choose a tuning or notation.

I just screwed around with this in scala for a bit, and I think that
at least I am interpreting 11/9 as a flat version of 17/14. I'm not
sure why or what about that interval would make it sound so consonant,
but I screwed around with the cents ratios and I found it to sound the
most like a "new chord" when the neutral third got up to like 333.67
cents, which is in the ball park of 17/14.

Actually, from looking at it further, 17/14 - 11/9 (if you subtract
the numerators and denominators) is 6/5, which if you subtract 11/9
from 6/5 gives you 5/4. So maybe I'm really just getting closer to
that "noble number" limit that was posted above...

> There was a programme on the BBC a while back which I have
> on Mini Disc -- but not with me. I think I liked some
> Murail best. I downloaded a Grisey piece from Emusic after
> the recent discussion and it sounded like standard
> contemporary-classical fare.

Interesting, I'll have to check that out.

🔗Carl Lumma <carl@...>

6/11/2008 5:12:25 PM

Mike wrote:
> It seemed to me like Carl was saying that
> these intervals will be approximated in terms of other intervals
> because of psychoacoustic effects that are done in the brain,
> and that the listener has no input or affect on this whatsoever.

Where'd you get that notion? Didn't I say multiple times that
musical context, listener training, and even how good a day you
were having played a role?

> >> I suspect that fields of attraction are not drawn around
> >> actual harmonic intervals, but around the MEMORIES we have
> >> of intervals.

I guess that depends on how you define memory, but the
psychoacoustic fields of attraction are part of a DSP-like
system in the brain that's built out somewhere between
the 3rd trimester and 2nd birthday. If you want to call
that memory you can.

-Carl

🔗Mike Battaglia <battaglia01@...>

6/11/2008 8:20:35 PM

On Wed, Jun 11, 2008 at 8:12 PM, Carl Lumma <carl@...> wrote:
> Mike wrote:
>> It seemed to me like Carl was saying that
>> these intervals will be approximated in terms of other intervals
>> because of psychoacoustic effects that are done in the brain,
>> and that the listener has no input or affect on this whatsoever.
>
> Where'd you get that notion? Didn't I say multiple times that
> musical context, listener training, and even how good a day you
> were having played a role?

I got that notion because the first time I brought up the notion that
gestalt psychology might be involved, and that the questions I was
having wouldn't really be answerable within psychoacoustics alone, you
gave me a fairly condescending and sarcastic response about how I keep
asking the same questions and am never happy with the answers you
give, which by your own words tend to be usually about "things the
brain does."

To be honest, I wasn't really sure what you were saying at all at some
points in this thread, as there were so many patronizing or sarcastic
remarks in your posts that I was left with the understanding that you
didn't think that individual differences really mattered in terms of
how chords were perceived, given your response that the theory of
harmonic approximation was on solid footing and occurred at the
psychoacoustic level where the effects were "largely
listener-invariant."

It then seemed to me that you were interpreting my comments regarding
"gestalt psychology" to have to do with the mood of the listener and
such, which isn't what I was talking about - I was more getting at
principles similar to the ones Rothenburg figured out, but as they
might apply to harmony. So I tried to clarify my question a few times,
with each successive time you responding with more and more
condescending remarks thrown in (that I usually ignored) until I
eventually gave up, both due to an understanding that you have already
spent a lot of time in this thread, and also that I don't really have
an interest in starting a flamewar about Gestalt psychology in a yahoo
group about tuning on the internet.

So I'm sorry if I'm a bit confused about what you're saying, as there
appear from my vantage point to be a few contradictions,
inconsistencies, or places in these theories that don't correlate with
my actual experience of the chords (which begs the question as to how
these theories were formed in the first place). My attempts to get a
better picture of the whole thing by asking you directly were usually
unfruitful, so I gave up.

> I guess that depends on how you define memory, but the
> psychoacoustic fields of attraction are part of a DSP-like
> system in the brain that's built out somewhere between
> the 3rd trimester and 2nd birthday. If you want to call
> that memory you can.

Well, that seems like a good time for a budding human being to first
get accustomed to the 3rd and 5th and possibly 7th overtones, doesn't
it? Seems to be in line with my hypothesis that new fields of
attraction could be drawn as individuals then get accustomed to other,
more complex intervals later in life.

-Mike

🔗Dave Keenan <d.keenan@...>

6/11/2008 8:45:15 PM

Hi Cameron,

You have reminded us that the term "noble" applies to the numbers, not
the intervals, and we need a different term for these intervals that
have a special sound but are not close to ratios of small whole numbers.

So I realise that my statement that "Nobility is the shadow of
Justness", while perhaps poetically memorable, is not strictly true.
When referring to the numbers we could say "Nobility is the shadow of
Rationality", but we need something else to describe the _sound_, and
to contrast it against Justness.

Kraig prefers to consider these intervals just another kind of Just
interval. But I think historical usage is against you there, Kraig. I
don't think you'll find them included as "JI" in the writings of David
Doty or Kyle Gann. But even were it so, they would still need a
distinguishing term.

Cameron, you have called them "shadow" intervals below, which I like.
They could also be called "dark" intervals.

Margo (no "t") and I called their sound "metastable", for reasons we
explained in the paper.
http://dkeenan.com/Music/NobleMediant.txt
but maybe that sounds too much like physics, and not enough like
auditory perception.

I couldn't help thinking that Justice and Mercy are cardinal vitues
that are often considered together, and I couldn't help noticing how
similar the words "metastable" and "merciful" sound. I then googled:
"mercy justice", and could hardly believe it when the first article I
read had the words "golden mean" in the second paragraph! It all fits
so well. See
http://atheism.about.com/library/FAQs/phil/blphil_eth_mercyjustice.htm

So what do you think? Merciful intonation, mercifully intoned
intervals, merciful intervals, MI?

In the same way that
only _some_ Rational numbers correspond to Just intervals,
only _some_ Noble numbers correspond to Merciful intervals.
In both cases it is the simpler numbers of the appropriate class.

But there are clearly some merciful intervals that do not correspond
to simple noble numbers at all. I earlier said that harmonic entropy
(HE) maxima may be a better predictor of these merciful intervals than
are simple noble numbers, however there is a problem in the fact that
the positions of the HE maxima are very sensitive to the choice of
Paul Erlich's accuracy parameter "s". They move around quite a bit,
particularly those near the unison, octave and fifth. See the various
graphs here:
/tuning/files/dyadic/

And neither the noble mediants of Just-interval ratios, nor the maxima
of harmonic entropy, take timbre into account. They both seem to
assume some kind of "typical" harmonic timbre.

Do some merciful intervals move more than others when the timbre is
changed, say from sine waves to sawtooths? What timbre were you using
when you found the 628, 656 and 670 cent intervals?

The simplest nobles in that vicinity are
(3+ 7phi)/(2+5phi) ~= 607 cents
(3+10phi)/(2+7phi) ~= 630 cents
(3+13phi)/(2+9phi) ~= 645 cents
after 13/9 we certainly couldn't claim to be taking the noble mediant
of two Just intervals, so we're into "eye of newt" territory. e.g.
(3+16phi)/(2+11phi) ~= 654 cents

And the 670 cent Merciful certainly can't be "explained" by noble
numbers, since they get very complex and only 3 or 4 cents apart, by
the time you get to that region.

It might be "explained" by HE if only that maximum didn't move around
so much as "s" is changed.

Do we even know if different people find these 656 and 670 cent
merciful intervals to be in the same place, given the same physical setup?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
> It could very well be that it's simply a matter of using certain
> points, where different kinds of harmonic series converge, as portals
> between different series. And I don't think it's just the phi
> intervals that do this, or at least, there are other ways to define
> the shadowy points: the harmonic entropy charts I've seen have some
> of them, or extremely close, and I've found some of the same (within
> 1 cent cent) intervals with bonehead simple divisions of Pi; 3/2Pi
> also leads to the noble minor third Dave and Margot wrote about, and
> that's the one I was using before I found out about their work in
> this area.
>
> Sorry to go on, kinda thinking out loud and finding excuses not to be
> making drum beats by a deadline.
>
> Just one more thing- after toiling for so long by ear to have found
> some half dozen specific shadow regions just a couple of cents wide,
> and then discovering that they can be described so exactly in such
> simple ways, I will simply chortle at any accusations of numerology.
> Not that there is anything wrong with numerology.
>
> -Cameron Bobro
>
> PS. In the unlikely event that any harmonic entropy fans have read
> this far, about that 656 cent HE point: there's a shadow at 628 cents
> (turns out to be a noble interval) and one about 670 cents (no
> explanation for this one other than it's a 5/4 above the noble minor
> third, so it may be a shadow of a shadow, as Jacques Brel would say)
> but the 656 cent HE thing is a thing of its own, and a good one at
> that, to my ears. It's very close to a 5/4 on 7/6. I would like to
> know a more finely described figure for that particular HE point,
> because if you drop it just half a cent or so (not to 5/4 above 7/6
> which is sour), it's a winner.
>

🔗Kraig Grady <kraiggrady@...>

6/11/2008 9:33:31 PM

I think Kyle would also not object to me calling it JI and La Monte Young does use higher harmonics as Just intonation. As i expressed my inclination is to progress the term and field, not to hold to historical use which as we have seen cause problems even with Partch using the term since it went past 5 limit. I can also say that i am apart of the history as i think you would be hard pressed to find many or even a few that have used recurrent sequences. Much less at the extent i have

Yet if another term were to be added Medient would be better than merciful cause that imply all types of things and does not say what it is in a concise way (at least for me). But this would be better implied to Ancient greek music. Recurrent sequence JI is what i state and then people have some idea of what something means.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
>
> Kraig prefers to consider these intervals just another kind of Just
> interval. But I think historical usage is against you there, Kraig. I
> don't think you'll find them included as "JI" in the writings of David
> Doty or Kyle Gann. But even were it so, they would still need a
> distinguishing term.
>
>
>
> >
>
>

🔗Dave Keenan <d.keenan@...>

6/11/2008 9:40:06 PM

Here's another reason to consider calling them Merciful Intervals.

In the second-last page of http://anaphoria.com/tres.PDF
Erv Wilson writes:
----------------------------------------------------------------------
Phi is uncanny if you ask me there's no doubt about it. It is the most
"unjust" interval Lorne Temes can think of, although he neglects to
prove it his point is well taken in that it satisfies the condition of
"maximal harmonic mismatch" between 2 harmonic series, it is the
worstest of the worst -- and yet somehow with divinity imbued, Lord
have mercy!
----------------------------------------------------------------------

Yes! When the Lord created musical intervals he had both justice _and_
mercy. It has just taken us a long time to realise this. ;-)

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/11/2008 10:04:31 PM

Mike wrote:
> To be honest, I wasn't really sure what you were saying at all
> at some points in this thread,

I know. The solution is to ask questions.

> as there were so many patronizing or sarcastic remarks in
> your posts

I admit I was condescending and shouldn't have been, but it
was all I could do to keep the conversation out of the
tratosphere. I don't remember making excessively sarcastic
or rude remarks. I do remember conversing at length and
providing lots of information. I was being sincere about
you starting your own list for your 'psychology of music'
pursuit and about you trying a post on MMM by the way

> that I was left with the understanding that you didn't think
> that individual differences really mattered in terms of how
> chords were perceived,

I thought I said individual differences (and trial-specific
ones) make the higher-order stuff hard to model, not that
it didn't matter. I linked to the anchoring effect.

-Carl

🔗Cameron Bobro <misterbobro@...>

6/11/2008 10:29:53 PM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Hi Cameron,
>
> You have reminded us that the term "noble" applies to the numbers,
>not
> the intervals, and we need a different term for these intervals that
> have a special sound but are not close to ratios of small whole
numbers.

Note that I'm using the golden proportion as a mean (golden mean is
traditionally a philosophical term I believe).

The goal has been to strike the point of real-life balance and I've
tried the usual means- of these the harmonic mean usually seems the
most poised-inbetween.

Of course the usual means sometimes coincide and often are very
similar in this context. For example, the 12-tET m3 and M3 can be
described as the arithmetic, geometric, and harmonic means of,
respectively, 6/5 and 13/11, and 5/4 and 14/11. The variations among
the means in these cases fall within zones less than .1 cents wide,
and the greatest differences between any of these means and the 12-
tET interval is less than 2.5 cents.

But using the golden ratio as a mean seems to coincide most
consistently with the floating areas. Obviously you can divide an
interval up or down so to speak, favoring one interval or the other,
the cut being asymmetrical- I do it both ways and judge by ear. In a
big interval like the octave they'll both float, but in other
intervals one will and one won't, to my ears.
>
> So I realise that my statement that "Nobility is the shadow of
> Justness", while perhaps poetically memorable, is not strictly true.
> When referring to the numbers we could say "Nobility is the shadow
of
> Rationality", but we need something else to describe the _sound_,
and
> to contrast it against Justness.
>
> Kraig prefers to consider these intervals just another kind of Just
> interval. But I think historical usage is against you there, Kraig.
I
> don't think you'll find them included as "JI" in the writings of
David
> Doty or Kyle Gann. But even were it so, they would still need a
> distinguishing term.
>
> Cameron, you have called them "shadow" intervals below, which I
>like.
> They could also be called "dark" intervals.

I'm sticking to "shadows". I called the google page where I host
files ab umbris lumen, and one of the songs on my CD is "the shadows
were shining softly", it's a theme of long standing for me.
>
> Margo (no "t")

Whoops, sorry! How embarassing. Say, I can blame it on Unicode. I DO
get some serious &&&&--˘°K kinds of things, really. :-D

>and I called their sound "metastable", for reasons we
> explained in the paper.
> http://dkeenan.com/Music/NobleMediant.txt
> but maybe that sounds too much like physics, and not enough like
> auditory perception.

Metastable is really good, except that I want to say MeTAStable,
which sounds like an alchemists tool.
>
> I couldn't help thinking that Justice and Mercy are cardinal vitues
> that are often considered together, and I couldn't help noticing how
> similar the words "metastable" and "merciful" sound. I then googled:
> "mercy justice", and could hardly believe it when the first article
I
> read had the words "golden mean" in the second paragraph! It all
fits
> so well. See
> http://atheism.about.com/library/FAQs/phil/
blphil_eth_mercyjustice.htm
>
> So what do you think? Merciful intonation, mercifully intoned
> intervals, merciful intervals, MI?

Um, that's a little bit TOO good, LOL.
>
> In the same way that
> only _some_ Rational numbers correspond to Just intervals,
> only _some_ Noble numbers correspond to Merciful intervals.
> In both cases it is the simpler numbers of the appropriate class.
>
> But there are clearly some merciful intervals that do not correspond
> to simple noble numbers at all. I earlier said that harmonic entropy
> (HE) maxima may be a better predictor of these merciful intervals
than
> are simple noble numbers, however there is a problem in the fact
>that
> the positions of the HE maxima are very sensitive to the choice of
> Paul Erlich's accuracy parameter "s". They move around quite a bit,
> particularly those near the unison, octave and fifth. See the
various
> graphs here:
> /tuning/files/dyadic/
>
> And neither the noble mediants of Just-interval ratios, nor the
>maxima
> of harmonic entropy, take timbre into account. They both seem to
> assume some kind of "typical" harmonic timbre.
>
> Do some merciful intervals move more than others when the timbre is
> changed, say from sine waves to sawtooths? What timbre were you
>using
> when you found the 628, 656 and 670 cent intervals?

I'm using some... hmmm.... good dozen, different timbres. Make that
two dozen, just remembered my set of Csound sounds. Haven't noticed a
wonky episode yet.
>
> The simplest nobles in that vicinity are
> (3+ 7phi)/(2+5phi) ~= 607 cents
> (3+10phi)/(2+7phi) ~= 630 cents
> (3+13phi)/(2+9phi) ~= 645 cents

Of these I've only found 630 Hz, more like 629, which is at a golden
ratio between 4/3 and 3/2. I'll buy 607 and anything in the region of
about +/- 5 cents or so around the square root of two. 645 cents I
haven't heard as a shadow, maybe in some context, we'll see.

> after 13/9 we certainly couldn't claim to be taking the noble
>mediant
> of two Just intervals, so we're into "eye of newt" territory. e.g.
> (3+16phi)/(2+11phi) ~= 654 cents

I hear 654 as something else. It's groovy but it doesn't fit as far
as I can hear.
>
> And the 670 cent Merciful certainly can't be "explained" by noble
> numbers, since they get very complex and only 3 or 4 cents apart, by
> the time you get to that region.

Well it's 5/4 above the noble dark minor third (the square root of
two being 6/5 above). I think that's it, and that's how I use it a
lot. This makes for a very "far-away" kind of diminished triad, try
it.

>
> It might be "explained" by HE if only that maximum didn't move
>around
> so much as "s" is changed.
>
> Do we even know if different people find these 656 and 670 cent
> merciful intervals to be in the same place, given the same physical
setup?

Now that we don't know at all. At this point I suspect that only
33/28 and 23/18, and the phi-th of the octave "sixth", speaking with
a slop of a cent or so plus/minus, have been more or less
"independently observed" or used in enough different ways to qualify
as "definites" as in "there's definitely SOMETHING going on there".

-Cameron Bobro

🔗Dave Keenan <d.keenan@...>

6/11/2008 10:36:17 PM

Hi Kraig,

In La Monte Young's case they really are higher harmonics,
electronically phase-locked, so it really is JI.

But maybe we're talking about two different things here. You are
talking about the _field_ of JI, as in the field of performance art or
theatre. I am talking about the audible quality of certain intervals.

There is no problem with still calling music JI when it contains
noble/shadow/merciful intervals as well as just ones. JI music has
always made use of non-just intervals as well as just.

You certainly are part of the history. But I can't remember ever
before reading where anyone, and certainly not you or Kyle Gann, have
described a noble-numbered interval as Just. Consonant perhaps, but
not just. I'd be pleased if you could show me otherwise.

You have been adamant over the years, that for you, Just means
rational-numbered, despite the fact that this means it is impossible
to determine whether or not _any_ interval is Just, since no amount of
listening or measurement can distinguish a rational interval from an
irrational one. Noble numbers are of course irrational, in fact, in
one sense they are the _most_ irrational real numbers.

So I have to assume that you are really only concerned about the name
of the field, as mentioned above, with which I have no quarrel.

"Mediant" is good for describing the numbers, but not the sound of
these intervals. And some of these "dark" intervals do not appear to
have anything to do with mediants, e.g. those in the range of about 30
to 70 cents either side of the unison, fifth and octave.

"Recurrent sequence JI" is meaningful when you are using the rational
mediants in the sequence. But when you have no particulatr interest in
using the mediant intervals, but just want to jump straight to the
noble-number limit of the sequence, it is not so meaningful.

Regards,
-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I think Kyle would also not object to me calling it JI and La Monte
> Young does use higher harmonics as Just intonation. As i expressed my
> inclination is to progress the term and field, not to hold to
> historical use which as we have seen cause problems even with Partch
> using the term since it went past 5 limit. I can also say that i am
> apart of the history as i think you would be hard pressed to find many
> or even a few that have used recurrent sequences. Much less at the
> extent i have
>
> Yet if another term were to be added Medient would be better than
> merciful cause that imply all types of things and does not say what it
> is in a concise way (at least for me). But this would be better
implied
> to Ancient greek music. Recurrent sequence JI is what i state and then
> people have some idea of what something means.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Dave Keenan wrote:
> >
> >
> >
> > Kraig prefers to consider these intervals just another kind of Just
> > interval. But I think historical usage is against you there, Kraig. I
> > don't think you'll find them included as "JI" in the writings of David
> > Doty or Kyle Gann. But even were it so, they would still need a
> > distinguishing term.
> >
> >
> >
> > >
> >
> >
>

🔗Kraig Grady <kraiggrady@...>

6/11/2008 11:18:22 PM

yes i knows Erv's thinking on this, but we don't always agree.
Temes failed to find the most dissonant which in turn also undermines the idea also of harmonic entropy as likewise being meaningless
And i fully understand your viewpoint but i am afaid you have missed mine, and my application of recurrent sequences
I don't like the term Merciful at all. Why not Meru Scales
I don't see neither mercy nor justice anywhere in the world or the next.
Especially on the tuning list.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Here's another reason to consider calling them Merciful Intervals.
>
> In the second-last page of http://anaphoria.com/tres.PDF > <http://anaphoria.com/tres.PDF>
> Erv Wilson writes:
> ----------------------------------------------------------
> Phi is uncanny if you ask me there's no doubt about it. It is the most
> "unjust" interval Lorne Temes can think of, although he neglects to
> prove it his point is well taken in that it satisfies the condition of
> "maximal harmonic mismatch" between 2 harmonic series, it is the
> worstest of the worst -- and yet somehow with divinity imbued, Lord
> have mercy!
> ----------------------------------------------------------
>
> Yes! When the Lord created musical intervals he had both justice _and_
> mercy. It has just taken us a long time to realise this. ;-)
>
> -- Dave Keenan
>
>

🔗Kraig Grady <kraiggrady@...>

6/11/2008 11:31:42 PM

but i am using rational numbers, as i said i do not like the pure converged noble number as much as the series before it converges too much. The difference is subtle in sound except that i find i fine the pure form less interesting, in that i tire of it monotony rather quickly. At times i will use it and as noted are getting there from JI practice and thinking.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Kraig,
>
> In La Monte Young's case they really are higher harmonics,
> electronically phase-locked, so it really is JI.
>
> But maybe we're talking about two different things here. You are
> talking about the _field_ of JI, as in the field of performance art or
> theatre. I am talking about the audible quality of certain intervals.
>
> There is no problem with still calling music JI when it contains
> noble/shadow/merciful intervals as well as just ones. JI music has
> always made use of non-just intervals as well as just.
>
> You certainly are part of the history. But I can't remember ever
> before reading where anyone, and certainly not you or Kyle Gann, have
> described a noble-numbered interval as Just. Consonant perhaps, but
> not just. I'd be pleased if you could show me otherwise.
>
> You have been adamant over the years, that for you, Just means
> rational-numbered, despite the fact that this means it is impossible
> to determine whether or not _any_ interval is Just, since no amount of
> listening or measurement can distinguish a rational interval from an
> irrational one. Noble numbers are of course irrational, in fact, in
> one sense they are the _most_ irrational real numbers.
>
> So I have to assume that you are really only concerned about the name
> of the field, as mentioned above, with which I have no quarrel.
>
> "Mediant" is good for describing the numbers, but not the sound of
> these intervals. And some of these "dark" intervals do not appear to
> have anything to do with mediants, e.g. those in the range of about 30
> to 70 cents either side of the unison, fifth and octave.
>
> "Recurrent sequence JI" is meaningful when you are using the rational
> mediants in the sequence. But when you have no particulatr interest in
> using the mediant intervals, but just want to jump straight to the
> noble-number limit of the sequence, it is not so meaningful.
>
> Regards,
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > I think Kyle would also not object to me calling it JI and La Monte
> > Young does use higher harmonics as Just intonation. As i expressed my
> > inclination is to progress the term and field, not to hold to
> > historical use which as we have seen cause problems even with Partch
> > using the term since it went past 5 limit. I can also say that i am
> > apart of the history as i think you would be hard pressed to find many
> > or even a few that have used recurrent sequences. Much less at the
> > extent i have
> >
> > Yet if another term were to be added Medient would be better than
> > merciful cause that imply all types of things and does not say what it
> > is in a concise way (at least for me). But this would be better
> implied
> > to Ancient greek music. Recurrent sequence JI is what i state and then
> > people have some idea of what something means.
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Dave Keenan wrote:
> > >
> > >
> > >
> > > Kraig prefers to consider these intervals just another kind of Just
> > > interval. But I think historical usage is against you there, Kraig. I
> > > don't think you'll find them included as "JI" in the writings of David
> > > Doty or Kyle Gann. But even were it so, they would still need a
> > > distinguishing term.
> > >
> > >
> > >
> > > >
> > >
> > >
> >
>
>

🔗Dave Keenan <d.keenan@...>

6/11/2008 11:55:49 PM

Hi Kraig,

Forget "merciful". How about calling them "cruel intervals" instead?
Only joking. ;-)

Cameron's term "shadow intervals" works for me. Or simply "shadows"
when it's clear from the context that we're talking about intervals.

I don't understand what Mt Meru scales have to do with these
intervals. Erv's Mt Meru scales have generators which are noble
fractions of an octave in the logarithmic sense, not noble frequency
ratios.

For example the golden scale generator is 1200/phi cents = 741.6 cents
(or equivalently 1200-741.6 = 458.4 cents). But the golden frequency
ratio (the "shadow" sixth) is log2(phi)*1200 cents = 833.1 cents.

I'm sorry I've failed to understand your viewpoint. I really want to.
I'm trying my hardest.

You should know that I don't actually believe in a "Lord" dispensing
justice or mercy either, hence the winky-face.

Sorry if I've upset you.

Hugs,
-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> yes i knows Erv's thinking on this, but we don't always agree.
> Temes failed to find the most dissonant which in turn also undermines
> the idea also of harmonic entropy as likewise being meaningless
> And i fully understand your viewpoint but i am afaid you have missed
> mine, and my application of recurrent sequences
> I don't like the term Merciful at all. Why not Meru Scales
> I don't see neither mercy nor justice anywhere in the world or the next.
> Especially on the tuning list.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Dave Keenan wrote:
> >
> > Here's another reason to consider calling them Merciful Intervals.
> >
> > In the second-last page of http://anaphoria.com/tres.PDF
> > <http://anaphoria.com/tres.PDF>
> > Erv Wilson writes:
> > ----------------------------------------------------------
> > Phi is uncanny if you ask me there's no doubt about it. It is the most
> > "unjust" interval Lorne Temes can think of, although he neglects to
> > prove it his point is well taken in that it satisfies the condition of
> > "maximal harmonic mismatch" between 2 harmonic series, it is the
> > worstest of the worst -- and yet somehow with divinity imbued, Lord
> > have mercy!
> > ----------------------------------------------------------
> >
> > Yes! When the Lord created musical intervals he had both justice _and_
> > mercy. It has just taken us a long time to realise this. ;-)
> >
> > -- Dave Keenan
> >
> >
>

🔗Kraig Grady <kraiggrady@...>

6/12/2008 12:28:41 AM

I think Cameron use is specific to how he is using them. I think of it as a 'poetic' statement on his part, tied to how he is thinking.
I understand the two ways of approaching Phi but i understand the scale of Mt. Meru as being generated by a recurrent sequence of harmonics not a division of the octave. which if you look at http://anaphoria.com/meruthree.pdf
page 2 you will see it is clear. that phi comes out 833.090 cents. The idea of doing it the other way is an interesting problem

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Kraig,
>
> Forget "merciful". How about calling them "cruel intervals" instead?
> Only joking. ;-)
>
> Cameron's term "shadow intervals" works for me. Or simply "shadows"
> when it's clear from the context that we're talking about intervals.
>
> I don't understand what Mt Meru scales have to do with these
> intervals. Erv's Mt Meru scales have generators which are noble
> fractions of an octave in the logarithmic sense, not noble frequency
> ratios.
>
> For example the golden scale generator is 1200/phi cents = 741.6 cents
> (or equivalently 1200-741.6 = 458.4 cents). But the golden frequency
> ratio (the "shadow" sixth) is log2(phi)*1200 cents = 833.1 cents.
>
> I'm sorry I've failed to understand your viewpoint. I really want to.
> I'm trying my hardest.
>
> You should know that I don't actually believe in a "Lord" dispensing
> justice or mercy either, hence the winky-face.
>
> Sorry if I've upset you.
>
> Hugs,
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > yes i knows Erv's thinking on this, but we don't always agree.
> > Temes failed to find the most dissonant which in turn also undermines
> > the idea also of harmonic entropy as likewise being meaningless
> > And i fully understand your viewpoint but i am afaid you have missed
> > mine, and my application of recurrent sequences
> > I don't like the term Merciful at all. Why not Meru Scales
> > I don't see neither mercy nor justice anywhere in the world or the next.
> > Especially on the tuning list.
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Dave Keenan wrote:
> > >
> > > Here's another reason to consider calling them Merciful Intervals.
> > >
> > > In the second-last page of http://anaphoria.com/tres.PDF > <http://anaphoria.com/tres.PDF>
> > > <http://anaphoria.com/tres.PDF <http://anaphoria.com/tres.PDF>>
> > > Erv Wilson writes:
> > > ----------------------------------------------------------
> > > Phi is uncanny if you ask me there's no doubt about it. It is the most
> > > "unjust" interval Lorne Temes can think of, although he neglects to
> > > prove it his point is well taken in that it satisfies the condition of
> > > "maximal harmonic mismatch" between 2 harmonic series, it is the
> > > worstest of the worst -- and yet somehow with divinity imbued, Lord
> > > have mercy!
> > > ----------------------------------------------------------
> > >
> > > Yes! When the Lord created musical intervals he had both justice _and_
> > > mercy. It has just taken us a long time to realise this. ;-)
> > >
> > > -- Dave Keenan
> > >
> > >
> >
>
>

🔗Graham Breed <gbreed@...>

6/12/2008 12:55:31 AM

Mike Battaglia wrote:

>> The psychoacoustic results that I'm aware of say that the
>> traditional assignment of chord roots is correct -- that is,
>> naive listeners will hear A as the root of an A minor chord
>> (A-C-E). For that to work we must be interpreting A-C as an
>> out of tune 4:5. Given that, it's entirely plausible that
>> 16/9 is interpreted as 7/4. Of course, we're also quite
>> capable of telling the difference between major and minor
>> thirds.
> > What do you mean by this? You think that given the note "A" people
> will fill in that it's the root of a minor chord due to them somehow
> intuitively knowing its diatonic role in a C major scale...? Or do you
> mean that, given the key of C major, we will perceive the note "A" in
> a chord root as having a minor quality, due to priming effects?

I think that given the chord A-C-E people will associate A as being the root. And that association is natural and connected with the virtual pitch mechanism.

> Furthermore, are you suggesting that the feeling and perception of a
> minor triad is due to its proximity to a major third, but its being
> out of tune gives it the "sad" minor feel to it? The concept seems to
> be at odds with the one that Carl was referring to above, i.e. that
> both 5/4 and 6/5 will have their own fields of attraction.

The feeling and perception of a minor triad follows from it being a minor triad, and being tuned a specific way and played with specific timbres. I don't know I how should expect it to feel if it was or wasn't attracted to 4:5:6, 10:12:15, 16:19:24, or anything else.

> What psychoacoustic results are you referring to in this case? I'd
> really like to see them.

http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/basse.html

These links are new to me:

http://home.austin.rr.com/jmjensen/VirtualPitch.html
http://www.springerlink.com/content/d137684108735m25/

Incidentally, this may relate to your problem of a b9 being bad in a chord without the root. The reason being that the b9 is easily confused with the root if you don't reinforce the latter.

> Even deeper, regardless of how people consciously assign verbal
> meaning to intervals, everyone has an internal cognitive "schema" or
> symbol for an interval that they may or may not be aware of. At first,
> when you hear a new interval that is close to an interval you already
> know, you might experience it as an altered form of a mental symbol
> that you already have, but after being constantly exposed to that
> interval and its symbolic meaning for you, you may learn to
> differentiate between that symbol and the other one. You will most
> likely operate on the new symbol and come up with new thoughts derived
> from it, and build on that schema just as you did the other one. What
> role, then, would the concept of a purely acoustic "field of
> attraction" have in this process anymore? You could potentially start
> to develop another field of attraction around a second interval as
> there is one around the first one.

If you care about your listeners, the lesson to take from this is that they won't be as familiar with the intervals you're working with as you are. So they'll naturally hear them relative to some other intervals. You can either help them to hear things the way you do or play with their confusion.

>>> Another example of what you're talking about here I think is the good
>>> ol' neutral triad... I have a multistable perception of neutral triad
>>> as an out of tune major and an out of tune minor simultaneously. I
>>> suspect that the more I listen to it the more I will get used to it as
>>> a stable chord in its own right, and then that interval will develop
>>> its own "field of attraction" apart from the major and the minor one.
>> Discordance graphs tend to show a kind of plateau between
>> major and minor thirds. So any third will do. Whether
>> that's because 6:5 and 5:4 merge into each other or because
>> they merge in with 11:9 and 16:13 doesn't matter at all.
>>
>>> I suspect that fields of attraction are not drawn around actual
>>> harmonic intervals, but around the MEMORIES we have of intervals. It
>>> has to do with a tendency
>> A meaningful question is: do intervals like 11:9 represent
>> minimum points of dissonance? This is the concept of
>> "tunable intervals". If intervals sound more consonant the
>> closer they get to some ideal, it's worth considering that
>> ideal when you choose a tuning or notation.
> > I just screwed around with this in scala for a bit, and I think that
> at least I am interpreting 11/9 as a flat version of 17/14. I'm not
> sure why or what about that interval would make it sound so consonant,
> but I screwed around with the cents ratios and I found it to sound the
> most like a "new chord" when the neutral third got up to like 333.67
> cents, which is in the ball park of 17/14.
> > Actually, from looking at it further, 17/14 - 11/9 (if you subtract
> the numerators and denominators) is 6/5, which if you subtract 11/9
> from 6/5 gives you 5/4. So maybe I'm really just getting closer to
> that "noble number" limit that was posted above...

A nearby noble number interval is (5+6*phi)/(4+5*phi) at 339 cents. Simplifies as (1+5*phi)/(1+4*phi).

Graham

🔗Mike Battaglia <battaglia01@...>

6/12/2008 1:02:33 AM

On Thu, Jun 12, 2008 at 1:04 AM, Carl Lumma <carl@...> wrote:
> Mike wrote:
>> To be honest, I wasn't really sure what you were saying at all
>> at some points in this thread,
>
> I know. The solution is to ask questions.

Note:
> It then seemed to me that you were interpreting my comments regarding
> "gestalt psychology" to have to do with the mood of the listener and
> such, which isn't what I was talking about - I was more getting at
> principles similar to the ones Rothenburg figured out, but as they
> might apply to harmony. So I tried to clarify my question a few times,
> with each successive time you responding with more and more
> condescending remarks thrown in (that I usually ignored) until I
> eventually gave up, both due to an understanding that you have already
> spent a lot of time in this thread, and also that I don't really have
> an interest in starting a flamewar about Gestalt psychology in a yahoo
> group about tuning on the internet.

> I admit I was condescending and shouldn't have been, but it
> was all I could do to keep the conversation out of the
> tratosphere.

Here is the pattern that persisted throughout the whole thread:

1) I post some idea that I came up with by applying psychological
concepts to my conscious experience of microtonal music
2) you give me a theory that is well-known and established but, on the
surface, seems to contradict my experience. I feel that we are on
different pages and that you misunderstand what I am saying.
3) I attempt to explain the psychological principle behind my idea so
that we are on the same page
4) you accuse me of being off-topic
5) I give up as I am aware there is no point bickering about what is
on or off topic, as you used to moderate and likely get to determine
these things. i never get to really explain my idea, give up and am
frustrated

Most of what you would label the "stratosphere" I would wager are
places where I was either first trying to explain a general concept
before specifically applying it to music theory or places where I was
applying the general concept to music theory before I applied it to
tuning theory. Take my remarks about

> I don't remember making excessively sarcastic
> or rude remarks.

Are you serious?

So far you've given me rude comments about my "transcribing my math
for liberal arts majors textbooks" (I spent a good hour crafting that
post to express the concept as clearly as possible), dismissing me
offhand by claiming that I "think I'm an expert," about how my
approach is "good enough to get by in some universities but won't cut
the mustard here," dismissing entire paragraphs of ideas by quoting
the first sentence and responding with a swift "Nah," and perhaps my
favorite of all of these:

> If it doesn't, then I can let you know that your question is
> still an open problem and maybe WE can pursue afresh.

and then

> I think you mean "I work out". You could start your own
> mailing list. If other people join and become active, then
> you could upgrade this statement to "we".

To be honest I ended up feeling like I just couldn't win, so I gave up.

> I do remember conversing at length and
> providing lots of information. I was being sincere about
> you starting your own list for your 'psychology of music'
> pursuit and about you trying a post on MMM by the way

And I do appreciate the information that you've given me. I will
eventually make a post on MMM. As for starting an entirely new list on
how psychology affects music (of which alternate tunings are certainly
related), I may eventually do that as well, but I wanted to get some
feedback on my ideas here first.

-Mike

🔗Dave Keenan <d.keenan@...>

6/12/2008 1:50:34 AM

Hi Kraig,

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I think Cameron use is specific to how he is using them. I think of it
> as a 'poetic' statement on his part, tied to how he is thinking.

Undoubtedly so. But the funny thing is that I wasn't aware he used the
term "shadow" for them when I described them as "the shadow of
justness". I actually thought he'd adopted that usage from me, but I
see now that his usage of it goes way back.

> I understand the two ways of approaching Phi but i understand the scale
> of Mt. Meru as being generated by a recurrent sequence of harmonics not
> a division of the octave. which if you look at
> http://anaphoria.com/meruthree.pdf

That link didn't work, but I eventually found
http://www.anaphoria.com/meruthree.PDF
(uppercase "PDF")

> page 2 you will see it is clear. that phi comes out 833.090 cents. The
> idea of doing it the other way is an interesting problem

I'm afraid I don't see any 833.090 cents there, or on any of the other
Meru or Meta- PDFs (5 in total). I see that he takes the base-2 log of
phi. There's no reason to do that if you're using it as a frequency
ratio, but every reason to do it if you're using it as a logarithmic
fraction of an octave. Everything I read there confirms what I said.
What am I missing?

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/12/2008 1:59:49 AM

Maybe i missing something cause when i multiply his log 2 of phi
.694219113631 by 1200 i get 833 cents

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
>
> I'm afraid I don't see any 833.090 cents there, or on any of the other
> Meru or Meta- PDFs (5 in total). I see that he takes the base-2 log of
> phi. There's no reason to do that if you're using it as a frequency
> ratio, but every reason to do it if you're using it as a logarithmic
> fraction of an octave. Everything I read there confirms what I said.
> What am I missing?
>
> -- Dave Keenan
>
>

🔗Dave Keenan <d.keenan@...>

6/12/2008 2:21:27 AM

You're not missing anything. It's me.

You're quite right.

I had it exactly backwards. In fact there's no reason to take the log
if you're using it as a logarithmic fraction of an octave (since 1200
cents is already logarithmic) but every reason to do it if you're
using it as a frequency ratio and you want to describe it in cents.

So it's clear to me now, that he intended them to be used in both ways.

However I don't see 833 cents used as a scale generator in any of
these pages. When you say "scales of Mt Meru" I think of things like
Meta-meantone, Meta-mavila and various other "Meta-"s, which all
appear to me to use noble logarithmic fractions of the octave, and
therefore lead to a neverending series of self-similar MOS scales.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
>
> Maybe i missing something cause when i multiply his log 2 of phi
> .694219113631 by 1200 i get 833 cents
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Dave Keenan wrote:
> >
> >
> >
> > I'm afraid I don't see any 833.090 cents there, or on any of the other
> > Meru or Meta- PDFs (5 in total). I see that he takes the base-2 log of
> > phi. There's no reason to do that if you're using it as a frequency
> > ratio, but every reason to do it if you're using it as a logarithmic
> > fraction of an octave. Everything I read there confirms what I said.
> > What am I missing?
> >
> > -- Dave Keenan
> >
> >
>

🔗Cameron Bobro <misterbobro@...>

6/12/2008 4:05:26 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I think Cameron use is specific to how he is using them.

I'm also using ratios because of the linking with Just I described
before. It would work out the same within some tiny zones of
variance, if you used an irrational shadow as a key and built Just
intervals off of that.

Your use is maybe kind of like putting a prism on white light,
because the shadows are also like white light, with the duality of
no color/all colors. Or like never using pure black, which also has
the percieved duality of all colors/no color.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

>
> However I don't see 833 cents used as a scale generator in any of
> these pages. When you say "scales of Mt Meru" I think of things like
> Meta-meantone, Meta-mavila and various other "Meta-"s, which all
> appear to me to use noble logarithmic fractions of the octave, and
> therefore lead to a neverending series of self-similar MOS scales.
>
> -- Dave Keenan

Have to print out the Wilson .pdfs because they're that kind of
thing- I get a shoulder cramp and frustrated trying to read them at
the computer. But I'm dead certain that he's using the noble
intervals, a lot.

I just made a simple demonstration tuning, going for a simple 12-like
thing:

0: 1/1 0.000 unison, perfect prime
1: 21/20 84.467 minor semitone
2: 9/8 203.910 major whole tone
3: 33/28 284.447 undecimal minor third
4: 99/80 368.914
5: 297/224 488.357
6: 99/70 600.088 2nd quasi-equal tritone
7: 165/112 670.761
8: 11/7 782.492 undecimal augmented fifth
9: 33/20 866.959
10: 99/56 986.402
11: 66/35 1098.133
12: 2/1 1200.000 octave

for copy and paste on the off chance anyone would try it:
!
Shadowy 12
12
!
21/20
9/8
33/28
99/80
297/224
99/70
165/112
11/7
33/20
99/56
66/35
2/1

It is very close to a "triaphonic 12" in the Scala archives, whoever
made that? (sounds like a Wilson name), particularly in sound.

The entire thing is made of superparticular and simple Just moves
wandering from the noble dark m3 at 33/28. The maximum "error" is
something like 1.8 cents even in this "ll-limit" interpretation. This
is just scratching the surface- for instance I didn't go the route of
noble m3 + 6/5 + noble mid3, which puts you .2 cents away from 7/4,
maybe exactly there if you start from a more accurate noble m3.

Notice that noble m3 + 6/5 - 8/7 puts you at the inverse of 1/phi,
a noble middle third. 11/7 is also a 36/35 down from 1/phi (and is
very close to Pi/2 as well as being a 4/3 above the noble dark m3
which is indistinguishable from 3/2Pi, etc.) I don't understand the
Pi connection but it seems intuitively inevitable as phi is also
2cos(Pi/5).

Also notice that the whole thing could be done with microscope
differences by starting at 2cos(Pi/4), which is 600 cents exactly,
and wandering about by superparticular and Just steps from there.

This tuning probably has too much clear water and not enough red wine
to fit in with my usual work, but I think it's a good demonstration
of how smoothly the noble intervals link with Just, and it does quite
tall chords very smoothly as well.

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:06:27 AM

>>> The psychoacoustic results that I'm aware of say that the
>>> traditional assignment of chord roots is correct -- that is,
>>> naive listeners will hear A as the root of an A minor chord
>>> (A-C-E). For that to work we must be interpreting A-C as an
>>> out of tune 4:5. Given that, it's entirely plausible that
>>> 16/9 is interpreted as 7/4. Of course, we're also quite
>>> capable of telling the difference between major and minor
>>> thirds.
>>
>> What do you mean by this? You think that given the note "A" people
>> will fill in that it's the root of a minor chord due to them somehow
>> intuitively knowing its diatonic role in a C major scale...? Or do you
>> mean that, given the key of C major, we will perceive the note "A" in
>> a chord root as having a minor quality, due to priming effects?
>
> I think that given the chord A-C-E people will associate A
> as being the root. And that association is natural and
> connected with the virtual pitch mechanism.

Ah, wow. That's astounding. I have never thought of that before.
You're talking about how they hear the root as A as opposed to the
phantom fundamental of F, right? That makes perfect sense -- also why
major 7 chords have a sometimes melancholy tone to them.

Although, I was just thinking, at least for 12tet an A-C-E minor chord
actually HAS an A fundamental, because that A-C is pretty close to
16:19, so the fundamental will be 4 octaves below the A. I remember
playing A and C simultaneously on a vibraphone and hearing that low A,
wondering why it wasn't an F (I didn't realize the 16:19 relationship
before). Might that have something to do with it?

>> What psychoacoustic results are you referring to in this case? I'd
>> really like to see them.
>
> http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/basse.html

I checked this one out, I'm not sure how this relates to hearing 6/5
as a mistuning of 5/4.

> These links are new to me:
>
> http://home.austin.rr.com/jmjensen/VirtualPitch.html
> http://www.springerlink.com/content/d137684108735m25/

The virtual pitch one was interesting. For an equal tempered C E G,
the fundamental that it calculated was an F, likely due to the E being
as sharp as it is.

> Incidentally, this may relate to your problem of a b9 being
> bad in a chord without the root. The reason being that the
> b9 is easily confused with the root if you don't reinforce
> the latter.

Erm, the rule was that a b9 can be in a chord unless it is placed over
a note that isn't the root. So the following:

C E G Bb Db

is okay, but this chord:

C E G B D F

is not, because there is a b9 between E and F, and F isn't the root.

Carl's explanation (which I am growing to understand) is that the F on
top is right in the middle of a 4/3 ratio and so completely undermines
the structure and resonance of the chord (at least that's what I make
of it). It's like you have all of these tones in an otonal
relationship, and then that F on top screws it all up.

In jazz, leaving the root out of a chord is encouraged (likely because
they've figured out you're going to hear it anyway), and you often get
some weird situations where an E-G-B minor chord is played, but the
right hand can play melodies so that you hear the root as the C below
it, and the chord stops sounding minor (although it sounds precarious,
as though at any point it could slip back into minor). Weirdness, I
tell you.

I think this rule is probably a rough attempt at figuring out some
considerably more difficult harmonic principles, but it is sort of
accurate.

> If you care about your listeners, the lesson to take from
> this is that they won't be as familiar with the intervals
> you're working with as you are. So they'll naturally hear
> them relative to some other intervals. You can either help
> them to hear things the way you do or play with their confusion.

Precisely. From a musical standpoint, indeed. I would also like to
figure out precisely how this works, as I find it a fascinating
mechanism that would likely have a lot of useful results for tuning
theory. It seems to be based entirely off of cognitive/gestalt psych
(or both), although the assertion earlier that there are purely
psychoacoustic fields of attraction completely threw a wrench into the
works in terms of how I was figuring this all out. I can't tell if
they are simply not entirely psychoacoustic after all, and any theory
saying that they are is wrong, or if I'm missing something obvious.

> A nearby noble number interval is (5+6*phi)/(4+5*phi) at 339
> cents. Simplifies as (1+5*phi)/(1+4*phi).

Interesting. I actually posted the wrong number - I was looking at 366
cents, which doesn't have any noble anything near it. It had the
feeling of slightly major, but musically gray at the same time. I'm
not sure what that's about.

One thing I've noticed about the noble numbers is that two of them
exist between any interval. You have the one generated by going from
5/4, 6/5, etc... And the one from 6/5, 5/4, etc. You'll end up at
different places.

Either way I have enough information in this thread to publish a book.

-Mike

🔗Cameron Bobro <misterbobro@...>

6/12/2008 4:18:21 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:

> Interesting. I actually posted the wrong number - I was looking at
366
> cents, which doesn't have any noble anything near it. It had the
> feeling of slightly major, but musically gray at the same time. I'm
> not sure what that's about.

It's right there at the inversion of 1 phi-th of the octave.

>
> One thing I've noticed about the noble numbers is that two of them
> exist between any interval. You have the one generated by going from
> 5/4, 6/5, etc... And the one from 6/5, 5/4, etc. You'll end up at
> different places.

Didn't I mention this... anyway you have to point it at the less
dominant interval, or try or use both. The less dominate interval
can't be determined by n*d- for example with 5/4 and 4/3, the fuzzy
zone is more towards 4/3, maybe because 5/4 is the octaved version of
a low harmonic partial while 4/3 is the octaved version of a
relationship between harmonic partials, dunno.

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:19:08 AM

Just as a sidenote: I came up with this little sound clip a while ago
while screwing around:

http://www.box.net/shared/cz2uhrfcw8

The frequency ratio of each successive tone in this clip is the golden
mean times the tone before it. The harmonics are damped so it doesn't
kill you.

So transcendental numbers have their use in JI after all :P The tones
will never end up syncing up with anything in the harmonic series of
the fundamental ever.

Perhaps the "transcendental intervals?" Or why not just the "golden
intervals?" The "neutral intervals?" "grey intervals?" They're
definitely gray to me, though I propose that if we call them gray
intervals, we spell it "grey," for various aesthetic reasons.

-Mike

On Thu, Jun 12, 2008 at 7:05 AM, Cameron Bobro <misterbobro@...> wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>>
>> I think Cameron use is specific to how he is using them.
>
> I'm also using ratios because of the linking with Just I described
> before. It would work out the same within some tiny zones of
> variance, if you used an irrational shadow as a key and built Just
> intervals off of that.
>
> Your use is maybe kind of like putting a prism on white light,
> because the shadows are also like white light, with the duality of
> no color/all colors. Or like never using pure black, which also has
> the percieved duality of all colors/no color.
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
>>
>> However I don't see 833 cents used as a scale generator in any of
>> these pages. When you say "scales of Mt Meru" I think of things like
>> Meta-meantone, Meta-mavila and various other "Meta-"s, which all
>> appear to me to use noble logarithmic fractions of the octave, and
>> therefore lead to a neverending series of self-similar MOS scales.
>>
>> -- Dave Keenan
>
> Have to print out the Wilson .pdfs because they're that kind of
> thing- I get a shoulder cramp and frustrated trying to read them at
> the computer. But I'm dead certain that he's using the noble
> intervals, a lot.
>
> I just made a simple demonstration tuning, going for a simple 12-like
> thing:
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 21/20 84.467 minor semitone
> 2: 9/8 203.910 major whole tone
> 3: 33/28 284.447 undecimal minor third
> 4: 99/80 368.914
> 5: 297/224 488.357
> 6: 99/70 600.088 2nd quasi-equal tritone
> 7: 165/112 670.761
> 8: 11/7 782.492 undecimal augmented fifth
> 9: 33/20 866.959
> 10: 99/56 986.402
> 11: 66/35 1098.133
> 12: 2/1 1200.000 octave
>
> for copy and paste on the off chance anyone would try it:
> !
> Shadowy 12
> 12
> !
> 21/20
> 9/8
> 33/28
> 99/80
> 297/224
> 99/70
> 165/112
> 11/7
> 33/20
> 99/56
> 66/35
> 2/1
>
> It is very close to a "triaphonic 12" in the Scala archives, whoever
> made that? (sounds like a Wilson name), particularly in sound.
>
> The entire thing is made of superparticular and simple Just moves
> wandering from the noble dark m3 at 33/28. The maximum "error" is
> something like 1.8 cents even in this "ll-limit" interpretation. This
> is just scratching the surface- for instance I didn't go the route of
> noble m3 + 6/5 + noble mid3, which puts you .2 cents away from 7/4,
> maybe exactly there if you start from a more accurate noble m3.
>
> Notice that noble m3 + 6/5 - 8/7 puts you at the inverse of 1/phi,
> a noble middle third. 11/7 is also a 36/35 down from 1/phi (and is
> very close to Pi/2 as well as being a 4/3 above the noble dark m3
> which is indistinguishable from 3/2Pi, etc.) I don't understand the
> Pi connection but it seems intuitively inevitable as phi is also
> 2cos(Pi/5).
>
> Also notice that the whole thing could be done with microscope
> differences by starting at 2cos(Pi/4), which is 600 cents exactly,
> and wandering about by superparticular and Just steps from there.
>
> This tuning probably has too much clear water and not enough red wine
> to fit in with my usual work, but I think it's a good demonstration
> of how smoothly the noble intervals link with Just, and it does quite
> tall chords very smoothly as well.
>
> -Cameron Bobro
>
>

🔗Cameron Bobro <misterbobro@...>

6/12/2008 4:25:50 AM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@>
> wrote:
>
> > Interesting. I actually posted the wrong number - I was looking
at
> 366
> > cents, which doesn't have any noble anything near it. It had the
> > feeling of slightly major, but musically gray at the same time.
I'm
> > not sure what that's about.
>
> It's right there at the inversion of 1 phi-th of the octave.

And for the dippy hippy in us all (or maybe the wise man) I've
measured a field recording of a cuckoo bird (who sing with astounding
regularity of pitch) singing 368 cent thirds and I call it a "cuckoo
third" rather than a phi third.

The cuckoo I listened to each dawn over a good period of time sang
lower, always the same interval as far as I could tell, somewhere
between a 6/5 and an 11/9.

🔗Cameron Bobro <misterbobro@...>

6/12/2008 4:37:32 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> Just as a sidenote: I came up with this little sound clip a while
ago
> while screwing around:
>
> http://www.box.net/shared/cz2uhrfcw8
>
> The frequency ratio of each successive tone in this clip is the
golden
> mean times the tone before it. The harmonics are damped so it
doesn't
> kill you.
>
> So transcendental numbers have their use in JI after all :P The
tones
> will never end up syncing up with anything in the harmonic series of
> the fundamental ever.

They've been used for a good long time. There are some kind of built
in by accident into 34 equal, within 2 cents or so.
>
> Perhaps the "transcendental intervals?" Or why not just the "golden
> intervals?" The "neutral intervals?" "grey intervals?" They're
> definitely gray to me, though I propose that if we call them gray
> intervals, we spell it "grey," for various aesthetic reasons.

Erv Wilson has things like "golden Meantone". I'm sticking to shadow
intervals for reasons I've stated before.
>
> -Mike
>
> On Thu, Jun 12, 2008 at 7:05 AM, Cameron Bobro <misterbobro@...>
wrote:
> > --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> >>
> >> I think Cameron use is specific to how he is using them.
> >
> > I'm also using ratios because of the linking with Just I described
> > before. It would work out the same within some tiny zones of
> > variance, if you used an irrational shadow as a key and built Just
> > intervals off of that.
> >
> > Your use is maybe kind of like putting a prism on white light,
> > because the shadows are also like white light, with the duality of
> > no color/all colors. Or like never using pure black, which also
has
> > the percieved duality of all colors/no color.
> >
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> >>
> >> However I don't see 833 cents used as a scale generator in any of
> >> these pages. When you say "scales of Mt Meru" I think of things
like
> >> Meta-meantone, Meta-mavila and various other "Meta-"s, which all
> >> appear to me to use noble logarithmic fractions of the octave,
and
> >> therefore lead to a neverending series of self-similar MOS
scales.
> >>
> >> -- Dave Keenan
> >
> > Have to print out the Wilson .pdfs because they're that kind of
> > thing- I get a shoulder cramp and frustrated trying to read them
at
> > the computer. But I'm dead certain that he's using the noble
> > intervals, a lot.
> >
> > I just made a simple demonstration tuning, going for a simple 12-
like
> > thing:
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 21/20 84.467 minor semitone
> > 2: 9/8 203.910 major whole tone
> > 3: 33/28 284.447 undecimal minor third
> > 4: 99/80 368.914
> > 5: 297/224 488.357
> > 6: 99/70 600.088 2nd quasi-equal tritone
> > 7: 165/112 670.761
> > 8: 11/7 782.492 undecimal augmented fifth
> > 9: 33/20 866.959
> > 10: 99/56 986.402
> > 11: 66/35 1098.133
> > 12: 2/1 1200.000 octave
> >
> > for copy and paste on the off chance anyone would try it:
> > !
> > Shadowy 12
> > 12
> > !
> > 21/20
> > 9/8
> > 33/28
> > 99/80
> > 297/224
> > 99/70
> > 165/112
> > 11/7
> > 33/20
> > 99/56
> > 66/35
> > 2/1
> >
> > It is very close to a "triaphonic 12" in the Scala archives,
whoever
> > made that? (sounds like a Wilson name), particularly in sound.
> >
> > The entire thing is made of superparticular and simple Just moves
> > wandering from the noble dark m3 at 33/28. The maximum "error" is
> > something like 1.8 cents even in this "ll-limit" interpretation.
This
> > is just scratching the surface- for instance I didn't go the
route of
> > noble m3 + 6/5 + noble mid3, which puts you .2 cents away from 7/
4,
> > maybe exactly there if you start from a more accurate noble m3.
> >
> > Notice that noble m3 + 6/5 - 8/7 puts you at the inverse of 1/phi,
> > a noble middle third. 11/7 is also a 36/35 down from 1/phi (and is
> > very close to Pi/2 as well as being a 4/3 above the noble dark m3
> > which is indistinguishable from 3/2Pi, etc.) I don't understand
the
> > Pi connection but it seems intuitively inevitable as phi is also
> > 2cos(Pi/5).
> >
> > Also notice that the whole thing could be done with microscope
> > differences by starting at 2cos(Pi/4), which is 600 cents exactly,
> > and wandering about by superparticular and Just steps from there.
> >
> > This tuning probably has too much clear water and not enough red
wine
> > to fit in with my usual work, but I think it's a good
demonstration
> > of how smoothly the noble intervals link with Just, and it does
quite
> > tall chords very smoothly as well.
> >
> > -Cameron Bobro
> >
> >
>

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:41:32 AM

> And for the dippy hippy in us all (or maybe the wise man) I've
> measured a field recording of a cuckoo bird (who sing with astounding
> regularity of pitch) singing 368 cent thirds and I call it a "cuckoo
> third" rather than a phi third.

Huh. Wow. I've heard birds do interesting rhythmic things (like going
tweet, tweet tweet tweet, tweet tweet tweet, tweet tweet tweet), but
not interesting melodic things. Although now I hear a bird in the
distance singing some kind of flat major third, and it does seem to
sound like the 366 one I was saying that stuck out as a grey interval
in the other thread. Definitely sharp of 11/9 but flat of 5/4.

> The cuckoo I listened to each dawn over a good period of time sang
> lower, always the same interval as far as I could tell, somewhere
> between a 6/5 and an 11/9.

Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent third you meant?

-Mike

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:58:44 AM

>> The frequency ratio of each successive tone in this clip is the
> golden
>> mean times the tone before it. The harmonics are damped so it
> doesn't
>> kill you.
>>
>> So transcendental numbers have their use in JI after all :P The
> tones
>> will never end up syncing up with anything in the harmonic series of
>> the fundamental ever.
>
> They've been used for a good long time. There are some kind of built
> in by accident into 34 equal, within 2 cents or so.

Ah yes, that was another question I was going to ask -- what other
equal temperaments have these? 12-equal's minor 7 is pretty damn close
to the one between 7/4 and 9/5, I think.

The 356 cent one between 6/5 and 5/4 sounds AMAZING btw. I'm about to
use that in every composition that I write ever. That's as gray an
interval as they come.

> Erv Wilson has things like "golden Meantone". I'm sticking to shadow
> intervals for reasons I've stated before.

It's interesting, because the color that I get in my head when I hear
that shadow/gray/noble/whatever interval over C is this stony metallic
medium-light gray. It's like a grayscale chord. I can see why you
would call it a shadow as well. There is no chroma. I am in love with
the sound.

-Mike

🔗Cameron Bobro <misterbobro@...>

6/12/2008 5:06:06 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> > And for the dippy hippy in us all (or maybe the wise man) I've
> > measured a field recording of a cuckoo bird (who sing with
astounding
> > regularity of pitch) singing 368 cent thirds and I call it a
"cuckoo
> > third" rather than a phi third.
>
> Huh. Wow. I've heard birds do interesting rhythmic things (like
going
> tweet, tweet tweet tweet, tweet tweet tweet, tweet tweet tweet), but
> not interesting melodic things. Although now I hear a bird in the
> distance singing some kind of flat major third, and it does seem to
> sound like the 366 one I was saying that stuck out as a grey
interval
> in the other thread. Definitely sharp of 11/9 but flat of 5/4.
>
> > The cuckoo I listened to each dawn over a good period of time sang
> > lower, always the same interval as far as I could tell, somewhere
> > between a 6/5 and an 11/9.
>
> Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent third
you meant?
>
> -Mike
>

Two different cuckoos, one more major in a field recording,one more
minor and about 10 yards from my front door. There was another one
close by in the woods, but I never caught the interval, he had a big
hollow kind of sound.

🔗Kraig Grady <kraiggrady@...>

6/12/2008 5:17:56 AM

I got just one chord?

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> Just as a sidenote: I came up with this little sound clip a while ago
> while screwing around:
>
> http://www.box.net/shared/cz2uhrfcw8 > <http://www.box.net/shared/cz2uhrfcw8>
>
> The frequency ratio of each successive tone in this clip is the golden
> mean times the tone before it. The harmonics are damped so it doesn't
> kill you.
>
> So transcendental numbers have their use in JI after all :P The tones
> will never end up syncing up with anything in the harmonic series of
> the fundamental ever.
>
> Perhaps the "transcendental intervals?" Or why not just the "golden
> intervals?" The "neutral intervals?" "grey intervals?" They're
> definitely gray to me, though I propose that if we call them gray
> intervals, we spell it "grey," for various aesthetic reasons.
>
> -Mike
>
> On Thu, Jun 12, 2008 at 7:05 AM, Cameron Bobro <misterbobro@... > <mailto:misterbobro%40yahoo.com>> wrote:
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > Kraig Grady <kraiggrady@...> wrote:
> >>
> >> I think Cameron use is specific to how he is using them.
> >
> > I'm also using ratios because of the linking with Just I described
> > before. It would work out the same within some tiny zones of
> > variance, if you used an irrational shadow as a key and built Just
> > intervals off of that.
> >
> > Your use is maybe kind of like putting a prism on white light,
> > because the shadows are also like white light, with the duality of
> > no color/all colors. Or like never using pure black, which also has
> > the percieved duality of all colors/no color.
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "Dave Keenan" <d.keenan@...> wrote:
> >
> >>
> >> However I don't see 833 cents used as a scale generator in any of
> >> these pages. When you say "scales of Mt Meru" I think of things like
> >> Meta-meantone, Meta-mavila and various other "Meta-"s, which all
> >> appear to me to use noble logarithmic fractions of the octave, and
> >> therefore lead to a neverending series of self-similar MOS scales.
> >>
> >> -- Dave Keenan
> >
> > Have to print out the Wilson .pdfs because they're that kind of
> > thing- I get a shoulder cramp and frustrated trying to read them at
> > the computer. But I'm dead certain that he's using the noble
> > intervals, a lot.
> >
> > I just made a simple demonstration tuning, going for a simple 12-like
> > thing:
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 21/20 84.467 minor semitone
> > 2: 9/8 203.910 major whole tone
> > 3: 33/28 284.447 undecimal minor third
> > 4: 99/80 368.914
> > 5: 297/224 488.357
> > 6: 99/70 600.088 2nd quasi-equal tritone
> > 7: 165/112 670.761
> > 8: 11/7 782.492 undecimal augmented fifth
> > 9: 33/20 866.959
> > 10: 99/56 986.402
> > 11: 66/35 1098.133
> > 12: 2/1 1200.000 octave
> >
> > for copy and paste on the off chance anyone would try it:
> > !
> > Shadowy 12
> > 12
> > !
> > 21/20
> > 9/8
> > 33/28
> > 99/80
> > 297/224
> > 99/70
> > 165/112
> > 11/7
> > 33/20
> > 99/56
> > 66/35
> > 2/1
> >
> > It is very close to a "triaphonic 12" in the Scala archives, whoever
> > made that? (sounds like a Wilson name), particularly in sound.
> >
> > The entire thing is made of superparticular and simple Just moves
> > wandering from the noble dark m3 at 33/28. The maximum "error" is
> > something like 1.8 cents even in this "ll-limit" interpretation. This
> > is just scratching the surface- for instance I didn't go the route of
> > noble m3 + 6/5 + noble mid3, which puts you .2 cents away from 7/4,
> > maybe exactly there if you start from a more accurate noble m3.
> >
> > Notice that noble m3 + 6/5 - 8/7 puts you at the inverse of 1/phi,
> > a noble middle third. 11/7 is also a 36/35 down from 1/phi (and is
> > very close to Pi/2 as well as being a 4/3 above the noble dark m3
> > which is indistinguishable from 3/2Pi, etc.) I don't understand the
> > Pi connection but it seems intuitively inevitable as phi is also
> > 2cos(Pi/5).
> >
> > Also notice that the whole thing could be done with microscope
> > differences by starting at 2cos(Pi/4), which is 600 cents exactly,
> > and wandering about by superparticular and Just steps from there.
> >
> > This tuning probably has too much clear water and not enough red wine
> > to fit in with my usual work, but I think it's a good demonstration
> > of how smoothly the noble intervals link with Just, and it does quite
> > tall chords very smoothly as well.
> >
> > -Cameron Bobro
> >
> >
>
>

🔗Kraig Grady <kraiggrady@...>

6/12/2008 5:22:13 AM

on page two of Meru Three he list the first 197 diagonals and the formulas for them.
http://anaphoria.com/meruthree.PDF
The first one is for Phi

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
>
> However I don't see 833 cents used as a scale generator in any of
> these pages. When you say "scales of Mt Meru" I think of things like
> Meta-meantone, Meta-mavila and various other "Meta-"s, which all
> appear to me to use noble logarithmic fractions of the octave, and
> therefore lead to a neverending series of self-similar MOS scales.
>
> -- Dave Keenan
>
> -
>
>
> MARKETPLACE
> You rock! Blockbuster wants to give you a complimentary trial of > Blockbuster Total Access. > <http://us.ard.yahoo.com/SIG=13rjh89fq/M=624381.12730922.13032918.10835568/D=grplch/S=1705897753:MKP1/Y=YAHOO/EXP=1213269690/L=/B=zN.BBEJe5tg-/J=1213262490146746/A=5368226/R=0/SIG=14erof5si/*http://media.adrevolver.com/adrevolver/href?banner=189161&place=26143&url_=http://tc.deals.yahoo.com/tc/blockbuster/display.com?cid=bbi00028> >
> Yahoo! Groups > <http://groups.yahoo.com/;_ylc=X3oDMTJiMDE1b3BnBF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRzZWMDZnRyBHNsawNnZnAEc3RpbWUDMTIxMzI2MjQ5MA--> >
> Change settings via the Web > </tuning/join;_ylc=X3oDMTJkYWZrdmZrBF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRzZWMDZnRyBHNsawNzdG5ncwRzdGltZQMxMjEzMjYyNDkw> > (Yahoo! ID required)
> Change settings via email: Switch delivery to Daily Digest > <mailto:tuning-digest@yahoogroups.com?subject=Email%20Delivery:%20Digest> > | Switch format to Traditional > <mailto:tuning-traditional@yahoogroups.com?subject=Change%20Delivery%20Format:%20Traditional> >
> Visit Your Group > </tuning;_ylc=X3oDMTJiazljdnBqBF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRzZWMDZnRyBHNsawNocGYEc3RpbWUDMTIxMzI2MjQ5MA--> > | Yahoo! Groups Terms of Use <http://docs.yahoo.com/info/terms/> | > Unsubscribe <mailto:tuning-unsubscribe@yahoogroups.com?subject=>
> Recent Activity
>
> *
> 3
> New Members
> </tuning/members;_ylc=X3oDMTJkYTYxbjVkBF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRzZWMDdnRsBHNsawN2bWJycwRzdGltZQMxMjEzMjYyNDkw>
>
> Visit Your Group > </tuning;_ylc=X3oDMTJjOXIxMWJrBF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRzZWMDdnRsBHNsawN2Z2hwBHN0aW1lAzEyMTMyNjI0OTA-> >
> Wellness Spot
>
> Embrace Change > <http://us.ard.yahoo.com/SIG=13pnlo9ek/M=493064.12016299.12445691.11322765/D=grplch/S=1705897753:NC/Y=YAHOO/EXP=1213269690/L=/B=zd.BBEJe5tg-/J=1213262490146746/A=4990217/R=0/SIG=11d53kq3t/*http://advision.webevents.yahoo.com/curves/>
>
> Break the Yo-Yo
>
> weight loss cycle.
>
> Yahoo! Groups
>
> Special K Challenge > <http://us.ard.yahoo.com/SIG=13p2pnaps/M=493064.12016300.12445692.11323196/D=grplch/S=1705897753:NC/Y=YAHOO/EXP=1213269690/L=/B=zt.BBEJe5tg-/J=1213262490146746/A=5170418/R=0/SIG=11b5gu1oe/*http://new.groups.yahoo.com/specialKgroup>
>
> Join others who
>
> are losing pounds.
>
> Yahoo! Groups
>
> Find balance > <http://us.ard.yahoo.com/SIG=13o0eoghs/M=493064.12016238.12823558.8674578/D=grplch/S=1705897753:NC/Y=YAHOO/EXP=1213269690/L=/B=z9.BBEJe5tg-/J=1213262490146746/A=5286666/R=0/SIG=11in3uvr5/*http://new.groups.yahoo.com/planforabalancedlife>
>
> between nutrition,
>
> activity & well-being.
>
> .
>
>

🔗Kraig Grady <kraiggrady@...>

6/12/2008 5:23:33 AM

maybe it was the birds that impressed the interval on you in the first place:)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...>
> wrote:
> >
> > > And for the dippy hippy in us all (or maybe the wise man) I've
> > > measured a field recording of a cuckoo bird (who sing with
> astounding
> > > regularity of pitch) singing 368 cent thirds and I call it a
> "cuckoo
> > > third" rather than a phi third.
> >
> > Huh. Wow. I've heard birds do interesting rhythmic things (like
> going
> > tweet, tweet tweet tweet, tweet tweet tweet, tweet tweet tweet), but
> > not interesting melodic things. Although now I hear a bird in the
> > distance singing some kind of flat major third, and it does seem to
> > sound like the 366 one I was saying that stuck out as a grey
> interval
> > in the other thread. Definitely sharp of 11/9 but flat of 5/4.
> >
> > > The cuckoo I listened to each dawn over a good period of time sang
> > > lower, always the same interval as far as I could tell, somewhere
> > > between a 6/5 and an 11/9.
> >
> > Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent third
> you meant?
> >
> > -Mike
> >
>
> Two different cuckoos, one more major in a field recording,one more
> minor and about 10 yards from my front door. There was another one
> close by in the woods, but I never caught the interval, he had a big
> hollow kind of sound.
>
>

🔗Cameron Bobro <misterbobro@...>

6/12/2008 5:30:12 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> >> The frequency ratio of each successive tone in this clip is the
> > golden
> >> mean times the tone before it. The harmonics are damped so it
> > doesn't
> >> kill you.
> >>
> >> So transcendental numbers have their use in JI after all :P The
> > tones
> >> will never end up syncing up with anything in the harmonic
series of
> >> the fundamental ever.
> >
> > They've been used for a good long time. There are some kind of
built
> > in by accident into 34 equal, within 2 cents or so.
>
> Ah yes, that was another question I was going to ask -- what other
> equal temperaments have these? 12-equal's minor 7 is pretty damn
>close
> to the one between 7/4 and 9/5, I think.

Don't know. The guys here could very well be among the world's all-
time leading experts on the bazillion stats of equal temperaments and
ways to reckon whatever you'd like about them. Not exaggerating or
being snide or whatever, it's a simple statement of fact.

>
> The 356 cent one between 6/5 and 5/4 sounds AMAZING btw. I'm about
>to
> use that in every composition that I write ever. That's as gray an
> interval as they come.

I usually use 27/22 at 354.5 cents. I think it's really soft, and
apparently all kinds of people do, too. Nice!
>
> > Erv Wilson has things like "golden Meantone". I'm sticking to
shadow
> > intervals for reasons I've stated before.
>
> It's interesting, because the color that I get in my head when I
hear
> that shadow/gray/noble/whatever interval over C is this stony
>metallic
> medium-light gray. It's like a grayscale chord. I can see why you
> would call it a shadow as well. There is no chroma. I am in love
>with
> the sound.

I think the shadows are best used with strongly colored Just
intervals, and they're linked very simply as hopefully my previous
examples illustrated. You should check out everything at
anaphoria.org, Kraig has been using these kinds of things in a
different way for ages.

🔗Dave Keenan <d.keenan@...>

6/12/2008 5:31:46 AM

I only heard one tone.

> So transcendental numbers have their use in JI after all :P

Noble numbers are not transcendental as far as I know. Phi certainly
isn't since it is (sqrt(5)+1)/2, the solution of x^2 -x -1 = 0.

Pi is transcendental, but I see no evidence of its applicability in
this regard. There is no known mechanism for it to do so. Whereas the
phi-derived nobles guarantee tha we maximise what you say immediately
below.

> The tones
> will never end up syncing up with anything in the harmonic series of
> the fundamental ever.
>
> Perhaps the "transcendental intervals?" Or why not just the "golden
> intervals?"

"golden" is generally reserved only for the _most_ noble number, phi
(and its reciprocal). The name "noble" here comes from analogy with
the noble metals, of which gold is but one -- the most noble.

But the main objection to names such as these is that some of these
grey or shadow intervals do not correspond to noble numbers at all, at
least not simple ones.

> The "neutral intervals?"

Neutral intervals are those around midway between major and minor
intervals of the same diatonic degree. While some shadows are neutral,
some are not.

> "grey intervals?" They're
> definitely gray to me, though I propose that if we call them gray
> intervals, we spell it "grey," for various aesthetic reasons.

"Grey" is fine with me too. "Shadowy" and "grey" are of course quite
similar in meaning.

-- Dave Keenan

🔗Cameron Bobro <misterbobro@...>

6/12/2008 5:34:41 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> maybe it was the birds that impressed the interval on you in the
first
> place:)

Hmm, there were always a lot of vultures when I was growing up...
maybe you're right! Whales and gibbons sure as hell sing in really
concrete and defined ways.

Gibbons also do the accelerating Indian rhythm thing DJ Sheiman
mentioned.

>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://
anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Cameron Bobro wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
"Mike
> > Battaglia" <battaglia01@>
> > wrote:
> > >
> > > > And for the dippy hippy in us all (or maybe the wise man) I've
> > > > measured a field recording of a cuckoo bird (who sing with
> > astounding
> > > > regularity of pitch) singing 368 cent thirds and I call it a
> > "cuckoo
> > > > third" rather than a phi third.
> > >
> > > Huh. Wow. I've heard birds do interesting rhythmic things (like
> > going
> > > tweet, tweet tweet tweet, tweet tweet tweet, tweet tweet
tweet), but
> > > not interesting melodic things. Although now I hear a bird in
the
> > > distance singing some kind of flat major third, and it does
seem to
> > > sound like the 366 one I was saying that stuck out as a grey
> > interval
> > > in the other thread. Definitely sharp of 11/9 but flat of 5/4.
> > >
> > > > The cuckoo I listened to each dawn over a good period of time
sang
> > > > lower, always the same interval as far as I could tell,
somewhere
> > > > between a 6/5 and an 11/9.
> > >
> > > Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent
third
> > you meant?
> > >
> > > -Mike
> > >
> >
> > Two different cuckoos, one more major in a field recording,one
more
> > minor and about 10 yards from my front door. There was another one
> > close by in the woods, but I never caught the interval, he had a
big
> > hollow kind of sound.
> >
> >
>

🔗Kraig Grady <kraiggrady@...>

6/12/2008 5:42:13 AM

The birds in Australia are really something, i have yet to figure out what they all are!!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > maybe it was the birds that impressed the interval on you in the
> first
> > place:)
>
> Hmm, there were always a lot of vultures when I was growing up...
> maybe you're right! Whales and gibbons sure as hell sing in really
> concrete and defined ways.
>
> Gibbons also do the accelerating Indian rhythm thing DJ Sheiman
> mentioned.
>
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria <http://
> anaphoriasouth.blogspot.com/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Cameron Bobro wrote:
> > >
> > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> > <mailto:tuning%40yahoogroups.com>,
> "Mike
> > > Battaglia" <battaglia01@>
> > > wrote:
> > > >
> > > > > And for the dippy hippy in us all (or maybe the wise man) I've
> > > > > measured a field recording of a cuckoo bird (who sing with
> > > astounding
> > > > > regularity of pitch) singing 368 cent thirds and I call it a
> > > "cuckoo
> > > > > third" rather than a phi third.
> > > >
> > > > Huh. Wow. I've heard birds do interesting rhythmic things (like
> > > going
> > > > tweet, tweet tweet tweet, tweet tweet tweet, tweet tweet
> tweet), but
> > > > not interesting melodic things. Although now I hear a bird in
> the
> > > > distance singing some kind of flat major third, and it does
> seem to
> > > > sound like the 366 one I was saying that stuck out as a grey
> > > interval
> > > > in the other thread. Definitely sharp of 11/9 but flat of 5/4.
> > > >
> > > > > The cuckoo I listened to each dawn over a good period of time
> sang
> > > > > lower, always the same interval as far as I could tell,
> somewhere
> > > > > between a 6/5 and an 11/9.
> > > >
> > > > Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent
> third
> > > you meant?
> > > >
> > > > -Mike
> > > >
> > >
> > > Two different cuckoos, one more major in a field recording,one
> more
> > > minor and about 10 yards from my front door. There was another one
> > > close by in the woods, but I never caught the interval, he had a
> big
> > > hollow kind of sound.
> > >
> > >
> >
>
>

🔗Mike Battaglia <battaglia01@...>

6/12/2008 6:06:20 AM

>> Just as a sidenote: I came up with this little sound clip a while ago
>> while screwing around:
>>
>> http://www.box.net/shared/cz2uhrfcw8
>>
>> The frequency ratio of each successive tone in this clip is the golden
>> mean times the tone before it. The harmonics are damped so it doesn't
>> kill you.
>
> I only heard one tone.

That one tone you heard was a complex waveform generated by placing
sine waves on top of each other in the fashion described above. The
fact that you heard it as one bell-like tone demonstrates my point :P

The reason that you heard it as at one tone rather than as a chord is
because the harmonics are damped. Rather than generate a harmonic
series so that you'd hear a sawtooth wave, I simply took the
fundamental and multiplied it by phi. Then I multiplied the resultant
by phi, and so on and so on. But for each resultant, I decreased the
amplitude by 1/phi^n, where n is the number of tones into the sequence
we're at for any given tone.

>> So transcendental numbers have their use in JI after all :P
>
> Noble numbers are not transcendental as far as I know. Phi certainly
> isn't since it is (sqrt(5)+1)/2, the solution of x^2 -x -1 = 0.

Oh yeah. Whoops. I meant "irrational numbers that are not the root of
some rational number". E.g. phi, although having sqrt(5) in it, is not
going to give you a rational when you do phi^5. In fact, phi^anything
will never be a rational number.

> Pi is transcendental, but I see no evidence of its applicability in
> this regard. There is no known mechanism for it to do so. Whereas the
> phi-derived nobles guarantee tha we maximise what you say immediately
> below.

Ah I dunno what pi's about. Charles Lucy talks about it a lot. I
dunno. Something about how you have to beat the pi to get the
frequency... and spherical wavefronts and the beating and god knows
anymore. I'm sure he knows what he's talking about, but I sure as hell
don't.

>> The tones
>> will never end up syncing up with anything in the harmonic series of
>> the fundamental ever.
>>
>> Perhaps the "transcendental intervals?" Or why not just the "golden
>> intervals?"
>
> "golden" is generally reserved only for the _most_ noble number, phi
> (and its reciprocal). The name "noble" here comes from analogy with
> the noble metals, of which gold is but one -- the most noble.

oh phine (haha). however you want it.

> But the main objection to names such as these is that some of these
> grey or shadow intervals do not correspond to noble numbers at all, at
> least not simple ones.
>
>> The "neutral intervals?"
>
> Neutral intervals are those around midway between major and minor
> intervals of the same diatonic degree. While some shadows are neutral,
> some are not.

What gray/noble/shadow/mystic/double top secret intervals are out
there that aren't neutral? Like one between 5/4 and 4/3 or something?

>> "grey intervals?" They're
>> definitely gray to me, though I propose that if we call them gray
>> intervals, we spell it "grey," for various aesthetic reasons.
>
> "Grey" is fine with me too. "Shadowy" and "grey" are of course quite
> similar in meaning.

Yeah, but gray is a color, and they have blue notes, and I want my
gray notes, god damn it! That's all I'm saying. Chrominance-free
neutral gray notes.

Oddly enough, the more I see "grey" intervals, the more apt I am to
want to just call them "gray" with the normal spelling. Whatever.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/12/2008 6:17:14 AM

Hello George,

This is extremely ironic, but a lot of my statements made in the post
you referenced up there were actually ideas that I was sparked onto by
reading your paper about 6 months ago. At the time, I had just heard
for the first time Easley Blackwood's 17-tet "con moto" work from his
Twelve Microtonal Etudes album and found it extraordinarily beautiful
in its mood, and immediately set out about finding information as much
information on the tuning as I could.

The only other equal tuning I was familiar with at the time that
sounded even plausible for western music was 19-tet, which at the time
I found to be somewhat unsatisfactory, as the only compositions that
I'd heard in the tuning sounded at the time really "dirty" and with a
very "nervous" feel to them at the time. To put it bluntly, it sounded
"out of tune." Most of my friends who I was trying to get into
microtonal music felt the same way about it. Either way, we all
thought the 17-tet piece sounded amazing, particularly with regards to
the melody. If anything, it sounded MORE "in tune" than 12-tet, which
is more than I could say for 19-tet.

Actually, upon hearing this piece for the first time, I thought that
perhaps it WAS the much-heralded 19-tet that was so often cited as
being such an improvement on 12-equal. After I saw that it was
actually 17-tet (which I had never even heard cited as being plausible
for "normal" sounding music before), I started looking up information
on it, the only useful information on it really being the paper you
linked me to.

This paragraph:
"In spite of all this, I am forced to admit that, while I do not find
the larger semitones of 19-ET, 31-ET, and the meantone temperament
unacceptable, I still do not perceive them as being as effective
melodically as those of 12-ET or the Pythagorean tuning.

Instead, I have found that the diatonic scales that are most
melodically effective are those that have wide fifths, resulting in
diatonic semitones significantly smaller than those in 12-ET. There is
considerable evidence to indicate that I am not alone in making this
judgment, which serves as a premise upon which the following line of
reasoning is based."

Generally did wonders for pointing out things about the temperament
that I had suspected but lacked a way of articulating. To this day,
what still bothers me about 19-et is that all of the chord intervals,
melodic motions, and chord modulations/root movements are LESS
articulated than in 12-et. That is, they are all 'flatter.' They are
smaller in distance. There is less movement. This to me gives me the
impression of all of the motions being sort of half-assed, e.g.
they're "good enough," but not really good. We don't have
C!->G!->E!->B!->C! but rather c... g... e... b#... *sigh* and the
like. To be honest, if 19-equal were the dominant tuning system in
western music, I really suspect that this group would have three times
as many members, with most of them extolling the virtues of 12-equal
as a much more melodic and harmonic alternative.

On the other hand, I found the melodic movements of 17-et to be
extremely articulated and as such the piece I keep referring to on
Blackwood's album is the one I usually play if I'm only going to play
one. I notice now that for the chords, he used a timbre with a bit of
chorus/LFO and played extremely staccato chords, presumably to hide
the beating and out-of-tuneness of the mainly 5-limit thing he seems
to do with that piece.

This isn't to bash 19-tet too much... :) I have grown to like it, but
I view it more as some kind of "counterpart" to 17 and to some extent
12. 17 has mainly sharp intervals, 19 has mainly flat intervals, so
they're like the difference between night and day. 12 is sort of in
the middle but closer to 17 with its major third.

I am very interested though in hearing some of the pieces or musical
excerpts that you or Margo worked out as you described in your
paper... If you've find harmonic and melodic concepts that sound
similar to "standard" 5-limit ones, but sound interesting and new at
the same time, I would certainly like to hear them.

> In case you decide to read the entire paper (or to entice you to do
> so), I also made a 17-tone jazz excerpt using the 9-tone scale
> (subset of 17) that I described near the bottom of the 22nd page
> (numbered as p. 76):
> http://xenharmony.wikispaces.com/space/showimage/17WTjazz.mp3

Haha, wow. Neutral moondance. Dusk-dance? Twilight perhaps? Interesting.

> While we're on the subject of the psychology of alternative tunings,
> there's a 17-tone piece (by Aaron Krister Johnson) that you might be
> interested in listening to, Adagio for Margo, at:
> http://www.akjmusic.com/works.html
> and then read about a particular observation I made:
> /makemicromusic/topicId_15226.html#15247
> and Aaron's reply:
> /makemicromusic/topicId_15226.html#15249

Yes. Yes. Yes. Exactly. This sentence:

"In other words, the diatonic system is
really a musical language, and our success in creating music in
alternative tunings may depend on our ability to create (or discover)
other musical languages that are capable of becoming meaningful to
the general listener."

sums up perfectly everything I was trying to say in that other thread.
I'm trying to figure out, as a field of scientific inquiry, how it
works, how a listener BUILDS this language to begin with, how a
listener learns expands his language, why listeners sometimes treat
incoming musical concepts or tunings as "wrong versions" of something
else already in their existing language, and how to get them to not do
that. I don't know why I kept getting allegations of my ideas being
pseudoscientific or misguided in the other thread, but it's glad to
finally see someone else thinking along the same lines.

That being said, I also had some thoughts on this:

"When we listen to a diatonic composition with only two voice parts
(such as a Bach two-part keyboard invention), we are able to "hear"
harmonies that are there only in the sense that they are implied by
tonal relationships already familiar to both the composer and the
listener. A two-voice composition in some non-diatonic scale subset
of a non-12 tuning, on the other hand, would very likely not have the
same effect, but would be heard basically as a progression of
intervals -- unless the composer had first written other (successful)
pieces in that scale using full harmonies and the listener had also
become familiar with them."

I think there are two parts to it:

1: the sum-and-difference tones generated by a dyad
2: the cognitive labeling of the whole package by the listener

For intervals like a perfect fifth, a major third, perfect fourth,
minor third, etc... The sum and difference tones are quite pronounced
and align perfectly in a harmonic series. For intervals like a 9:11
neutral third, the sum and difference tones are going to be in a
harmonic series though, but that difference tone will be MUCH lower
than the chord tones. It will be low enough that if your focus is in
the midrange where the chord tones are, you might miss this "phantom
fundamental" virtual tone (even subconsciously). Once you meditate on
a neutral triad and grow used to it, however, you start to pick up on
the resonance of the chord and hear it in a harmonic context. However,
the average listener who hasn't been accustomed to the sound might be
confused and hear it as a mistuned major or minor chord, since that's
the only other thing they have to go by.

But just like people did eventually get used to the sound of major
chords and perfect fifths, I think there are probably clever ways to
find intervals that a listener will most likely hear as new and novel
rather than weird and disturbing. For some reason, for people
accustomed to 12-tet, the 7/6 subminor third is usually such an
"easy-to-grasp" interval, although a 9/7 supermajor third doesn't
share that characteristic and is often heard simply as a sharp 5/4.
Why this is, I haven't the foggiest, although it might be interesting
to study.

Furthermore, I hypothesize that just like perfect fifths can be played
lower than major thirds and still sound good (due to that phantom
fundamental dropping off the bottom of hearing range sooner for the
major thirds), there will be triads that sound muddy straight up until
the midrange of the piano, although I don't know what those triads are
yet.

I'm actually running on no sleep right now, so I apologize if any of
my post didn't make sense. I started writing this post last night and
just came back to it now, wrote this last paragraph

🔗Cameron Bobro <misterbobro@...>

6/12/2008 6:17:23 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:

> What gray/noble/shadow/mystic/double top secret intervals are out
> there that aren't neutral? Like one between 5/4 and 4/3 or
something?

Whoa you might want to slow down, I talked about this very one maybe
a couple of times. I'm curious how you hear this one, been using it a
quite a bit on the tonic.

🔗Mike Battaglia <battaglia01@...>

6/12/2008 6:26:04 AM

On Thu, Jun 12, 2008 at 9:17 AM, Cameron Bobro <misterbobro@...> wrote:
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
> wrote:
>
>> What gray/noble/shadow/mystic/double top secret intervals are out
>> there that aren't neutral? Like one between 5/4 and 4/3 or
> something?
>
> Whoa you might want to slow down, I talked about this very one maybe
> a couple of times. I'm curious how you hear this one, been using it a
> quite a bit on the tonic.

Where? I just reread your posts in this thread, as I thought I was
going crazy, and I couldn't find anything on it.

But to calculate, which way do I go? 4/3 -> 5/4 or 5/4 -> 4/3?

I have to use something besides n*d, right?

-Mike

🔗Cameron Bobro <misterbobro@...>

6/12/2008 6:59:00 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> On Thu, Jun 12, 2008 at 9:17 AM, Cameron Bobro <misterbobro@...>
wrote:
> > --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@>
> > wrote:
> >
> >> What gray/noble/shadow/mystic/double top secret intervals are out
> >> there that aren't neutral? Like one between 5/4 and 4/3 or
> > something?
> >
> > Whoa you might want to slow down, I talked about this very one
maybe
> > a couple of times. I'm curious how you hear this one, been using
it a
> > quite a bit on the tonic.
>
> Where? I just reread your posts in this thread, as I thought I was
> going crazy, and I couldn't find anything on it.
>
> But to calculate, which way do I go? 4/3 -> 5/4 or 5/4 -> 4/3?
>
> I have to use something besides n*d, right?
>
> -Mike
>

One phi-th of the frequency between them is how I do it, try it with
the golden section both ways and hear what you think.

🔗Graham Breed <gbreed@...>

6/12/2008 7:02:02 AM

Mike Battaglia wrote:

>> I think that given the chord A-C-E people will associate A
>> as being the root. And that association is natural and
>> connected with the virtual pitch mechanism.
> > Ah, wow. That's astounding. I have never thought of that before.
> You're talking about how they hear the root as A as opposed to the
> phantom fundamental of F, right? That makes perfect sense -- also why
> major 7 chords have a sometimes melancholy tone to them.

Yes.

> Although, I was just thinking, at least for 12tet an A-C-E minor chord
> actually HAS an A fundamental, because that A-C is pretty close to
> 16:19, so the fundamental will be 4 octaves below the A. I remember
> playing A and C simultaneously on a vibraphone and hearing that low A,
> wondering why it wasn't an F (I didn't realize the 16:19 relationship
> before). Might that have something to do with it?

It's been proposed many times but never tested. Minor chords have been around since before 12tet was ubiquitous. I don't think people suddenly hear a different root in equal temperament.

>>> What psychoacoustic results are you referring to in this case? I'd
>>> really like to see them.
>> http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/basse.html
> > I checked this one out, I'm not sure how this relates to hearing 6/5
> as a mistuning of 5/4.

He talks about Rameau. You can try other pages on the site.

>> These links are new to me:
>>
>> http://home.austin.rr.com/jmjensen/VirtualPitch.html
>> http://www.springerlink.com/content/d137684108735m25/
> > The virtual pitch one was interesting. For an equal tempered C E G,
> the fundamental that it calculated was an F, likely due to the E being
> as sharp as it is.

There you go ... I don't know how reliable the code is.

>> Incidentally, this may relate to your problem of a b9 being
>> bad in a chord without the root. The reason being that the
>> b9 is easily confused with the root if you don't reinforce
>> the latter.
> > Erm, the rule was that a b9 can be in a chord unless it is placed over
> a note that isn't the root. So the following:
> > C E G Bb Db
> > is okay, but this chord:
> > C E G B D F
> > is not, because there is a b9 between E and F, and F isn't the root.

Okay. It could be because E-F gets heard as a stretched octave, then, and supports E as the root. But probably not.

> Carl's explanation (which I am growing to understand) is that the F on
> top is right in the middle of a 4/3 ratio and so completely undermines
> the structure and resonance of the chord (at least that's what I make
> of it). It's like you have all of these tones in an otonal
> relationship, and then that F on top screws it all up.

You mean a 4/3 between C and a transposed F? Could be. I agree that it's a weaker chord, anyway, as far as I can get it to work on my magic keyboard (I haven't got meantone working yet).

> In jazz, leaving the root out of a chord is encouraged (likely because
> they've figured out you're going to hear it anyway), and you often get
> some weird situations where an E-G-B minor chord is played, but the
> right hand can play melodies so that you hear the root as the C below
> it, and the chord stops sounding minor (although it sounds precarious,
> as though at any point it could slip back into minor). Weirdness, I
> tell you.

This is the point where I'm glad I don't have to study jazz harmony :P

> I think this rule is probably a rough attempt at figuring out some
> considerably more difficult harmonic principles, but it is sort of
> accurate.

Or it's a language that made sense to musicians as they were fitting tunes to chords.

>> If you care about your listeners, the lesson to take from
>> this is that they won't be as familiar with the intervals
>> you're working with as you are. So they'll naturally hear
>> them relative to some other intervals. You can either help
>> them to hear things the way you do or play with their confusion.
> > Precisely. From a musical standpoint, indeed. I would also like to
> figure out precisely how this works, as I find it a fascinating
> mechanism that would likely have a lot of useful results for tuning
> theory. It seems to be based entirely off of cognitive/gestalt psych
> (or both), although the assertion earlier that there are purely
> psychoacoustic fields of attraction completely threw a wrench into the
> works in terms of how I was figuring this all out. I can't tell if
> they are simply not entirely psychoacoustic after all, and any theory
> saying that they are is wrong, or if I'm missing something obvious.

There's a book by Krumhansl that has some interesting research into how tonal harmony is perceived.

>> A nearby noble number interval is (5+6*phi)/(4+5*phi) at 339
>> cents. Simplifies as (1+5*phi)/(1+4*phi).
> > Interesting. I actually posted the wrong number - I was looking at 366
> cents, which doesn't have any noble anything near it. It had the
> feeling of slightly major, but musically gray at the same time. I'm
> not sure what that's about.

Kraig and Cameron have both reported that 366.9 cents is the ratio between the golden ratio and on octave. That's an interesting idea -- the interval between a shadow interval and a just one. You can call it (2+2*phi)/(1+2*phi)

> One thing I've noticed about the noble numbers is that two of them
> exist between any interval. You have the one generated by going from
> 5/4, 6/5, etc... And the one from 6/5, 5/4, etc. You'll end up at
> different places.

The true one is the zig-zag starting on the simpler interval. That means the multipliers by phi should be in the more complex one. So the true shadow between 5/4 and 6/5 is the target of the sequence 5/4, 6/5, 11/9, 17/14, 28/23, ... or

5 + 6*phi
---------
4 + 4*phi

which is 339.3 cents. You can also take the sequence backwards to get

1 + 5*phi
---------
1 + 4*phi

Your alternative is

6 + 5*phi
---------
5 + 4*phi

or 355.9 cents. That's properly described as the shadow between 5/4 and 11/9. You can see that by replacing phi with 1+1/phi

6 + 5*(1 + 1/phi) 6 + 5 + 5/phi 11 + 5/phi 11*phi + 5
----------------- = ------------- = ---------- = ----------
5 + 4*(1 + 1/phi) 5 + 4 + 4/phi 9 + 4/phi 9*phi + 4

It's also close to your target. The sequence goes 5/4 11/9 16/13 27/22, ...

Temperament classes that equate 16:13 and 17:22 may get close to it. These are interesting because they have neutral triads made of different sized neutral thirds that both have a 13-limit approximation -- 11:9 and 16:13. It's one of the simplest ways of accommodating the 13-limit.

Of course, if you look at enough shadow intervals you can get close to any interval you like. Same as with just intervals.

> Either way I have enough information in this thread to publish a book.

I've noticed another thing. You can think of phi as the shadow between a unison and an octave

1 + 2*phi 1/phi + 2 1 + phi 1/phi + 1 phi
--------- = --------- = ------- = --------- = ---
1 + phi 1/phi + 1 phi 1 1

The next simplest shadow within an octave is then logically the one between 2/1 and 3/2.

2 + phi
-------
1 + phi

This is 560.1 cents. A narrow tritone. As it happens it's within 2.4 cents of an interval in TOP-RMS magic temperament consisting of 8 descending minor third generators. It can also be thought of as an approximation to 11:8 but it's much closer to this shadow interval. It's the obvious "characteristic dissonance" that's big enough to be a consonance but outside the 11-limit. I was thinking it sounded good despite the large error relative to the 11-limit. And there I was theorizing that temperament classes like magic were avoiding the shadows by aiming for just intervals...

Other approximations are in 43- and 45-equal.

Graham

🔗Carl Lumma <carl@...>

6/12/2008 8:26:51 AM

Mike wrote:
> Here is the pattern that persisted throughout the whole thread:
>
> 1) I post some idea that I came up with by applying psychological
> concepts to my conscious experience of microtonal music
> 2) you give me a theory that is well-known and established but,
> on the surface, seems to contradict my experience. I feel that
> we are on different pages and that you misunderstand what I am
> saying.

Then maybe I should ask some questions: Which of my explanations
have contradicted your experience?

> 5) I give up as I am aware there is no point bickering about
> what is on or off topic, as you used to moderate and likely
> get to determine these things. i never get to really explain
> my idea, give up and am frustrated

If you gave up it wasn't until after you outposted everyone
else by a wide margin. I don't get to determine such things
by the way but I can tell you that this isn't a gestalt
psychology mailing list, but that if you have a theory of
intonation that relies on gestalt psychology you can present
the theory along with any background you think may be helpful.

> Most of what you would label the "stratosphere" I would wager are
> places where I was either first trying to explain a general
> concept before specifically applying it to music theory or places
> where I was applying the general concept to music theory before I
> applied it to tuning theory.

The places I was thinking of where when you made sweeping calls
for radical reform that are beyond anyone's power to implement.
I did however suggest a practical approach and I thought we
seemed to be on the road to a pleasant offlist discussion on
the matter before you got your panties in a bunch.

-Carl

🔗Carl Lumma <carl@...>

6/12/2008 8:44:28 AM

> So transcendental numbers have their use in JI after all :P

Transcendental != transfinite, if that's what you were referring
to here. Also it wouldn't be JI, would it, but microtonal tuning
generally?

-Carl

🔗Carl Lumma <carl@...>

6/12/2008 8:54:14 AM

> >> So transcendental numbers have their use in JI after all :P
> >
> > Noble numbers are not transcendental as far as I know. Phi
> > certainly isn't since it is (sqrt(5)+1)/2, the solution of
> > x^2 -x -1 = 0.
>
> Oh yeah. Whoops. I meant "irrational numbers that are not the
> root of some rational number". E.g. phi, although having
> sqrt(5) in it, is not going to give you a rational when you do
> phi^5. In fact, phi^anything will never be a rational number.

That's true of any irrational number.

-Carl

🔗Andreas Sparschuh <a_sparschuh@...>

6/12/2008 12:53:40 PM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@>
> wrote:
> > > measured a field recording of a cuckoo bird (who sing with
> astounding
> > > regularity of pitch) singing 368 cent thirds and I call it a
> "cuckoo
> > > third" rather than a phi third.

> > Although now I hear a bird in the
> > distance singing some kind of flat major third, and it does seem >to
> > sound like the 366 one I was saying that stuck out as a grey
> interval
> > in the other thread. Definitely sharp of 11/9 but flat of 5/4.
> >
> > > The cuckoo I listened to each dawn over a good period of time sang
> > > lower, always the same interval as far as I could tell, somewhere
> > > between a 6/5 and an 11/9.
> >
> > Erm, do you mean between 5/4 and 11/9? Or was it the 333 cent third
> you meant?
> >
>
> Two different cuckoos, one more major in a field recording,one more
> minor and about 10 yards from my front door.
>
Hi Cameron & all others cuckoo's call observers,

http://www.xs4all.nl/~huygensf/doc/fokkerorg.html
claims:
"These are superseconds, which have the relationship 7:8. They are
elementary steps in the gamelan of Java and Bali. Again, the fifth may
be divided into two equal parts. The result is a pair of "thirds"
intermediate between minor and major thirds. These intermediate thirds
make a very beautiful rendering of the cuckoo's call."

but I'm sceptical because:
http://www.tribuneindia.com/2008/20080413/spectrum/nature.htm
"Each of the 15 cuckoo species is gifted with an exclusive call and
bird song."
imitated by corresponding human-made pipes with variable pitch:
http://memory.loc.gov/cgi-bin/query/f?dcm:0:./temp/~ammem_1zwO:
http://www.dolmetsch.com/defsc3.htm
"or 'cuckoo whistle', a simple two-note wind-instrument; it is
interesting to observe that though the musical 'cuckoo' has a fixed
interval between the two notes it can produce, the real bird has a
call the interval of which narrows over the course of a season"

That narrowing agrees
with my own experience
when listening to the same bird
over some weeks during the season.

http://mq.oxfordjournals.org/cgi/reprint/VII/2/261.pdf

just for fun:
http://www.electronics-lab.com/projects/misc/011/index.html
"The frequency of the higher one (667Hz) is set by means of Trimmer
R2. When IC2D output goes low, a further Trimmer (R22) is added to IC1
timing components via D6, and the lower tone (545Hz) is generated."

1200Cents * ln(667/545)/ln(2) = ~349.716638...Cents

alternative tuning instructions for laypersons:
http://www.redcircuits.com/Page76.htm

But if you do prefer real bird singing audio-files:
that can be found in:
http://www.tau.ac.il/~tsurxx/Cuckoo_onomatopoeia.html

Yours Sincerely
A.S.

🔗George D. Secor <gdsecor@...>

6/12/2008 1:43:11 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> Hello George,

Hi Mike,

> This is extremely ironic, but a lot of my statements made in the
post
> you referenced up there were actually ideas that I was sparked onto
by
> reading your paper about 6 months ago. At the time, I had just heard
> for the first time Easley Blackwood's 17-tet "con moto" work from
his
> Twelve Microtonal Etudes album and found it extraordinarily
beautiful
> in its mood, and immediately set out about finding information as
much
> information on the tuning as I could.
>
> The only other equal tuning I was familiar with at the time that
> sounded even plausible for western music was 19-tet, which at the
time
> I found to be somewhat unsatisfactory, as the only compositions that
> I'd heard in the tuning sounded at the time really "dirty" and with
a
> very "nervous" feel to them at the time. To put it bluntly, it
sounded
> "out of tune." Most of my friends who I was trying to get into
> microtonal music felt the same way about it. Either way, we all
> thought the 17-tet piece sounded amazing, particularly with regards
to
> the melody. If anything, it sounded MORE "in tune" than 12-tet,
which
> is more than I could say for 19-tet.
>
> Actually, upon hearing this piece for the first time, I thought that
> perhaps it WAS the much-heralded 19-tet that was so often cited as
> being such an improvement on 12-equal. After I saw that it was
> actually 17-tet (which I had never even heard cited as being
plausible
> for "normal" sounding music before), I started looking up
information
> on it, the only useful information on it really being the paper you
> linked me to.
>
> This paragraph:
[quoting GS:]
> "In spite of all this, I am forced to admit that, while I do not
find
> the larger semitones of 19-ET, 31-ET, and the meantone temperament
> unacceptable, I still do not perceive them as being as effective
> melodically as those of 12-ET or the Pythagorean tuning.
>
> Instead, I have found that the diatonic scales that are most
> melodically effective are those that have wide fifths, resulting in
> diatonic semitones significantly smaller than those in 12-ET. There
is
> considerable evidence to indicate that I am not alone in making this
> judgment, which serves as a premise upon which the following line of
> reasoning is based."
>
> Generally did wonders for pointing out things about the temperament
> that I had suspected but lacked a way of articulating. To this day,
> what still bothers me about 19-et is that all of the chord
intervals,
> melodic motions, and chord modulations/root movements are LESS
> articulated than in 12-et. That is, they are all 'flatter.' They are
> smaller in distance. There is less movement.

The diatonic semitone in 19-ET is larger than in 12-ET and much more
so than that of 17-ET. So there's actually a greater distance to be
traversed, which one might think of as *more* movement. But I think
what you're getting at is that, because of the lower leading tone of
19-ET, the greater distance results in less *attraction* (think of a
sort of tonal gravity) to its resolution to the neighboring tonic.

But this is true only up to a point: if the leading tone is so high
that it's only a quartertone (or especially a lesser amount) away,
then the effect is one of less attraction or articulation. As I
wrote in my 17-tone paper, there's an optimal value of greatest
attraction somewhere around 70 cents. Since I wrote the paper, I've
concluded that it's perhaps closer to 67 cents (for an interval
approaching a unison), and probably smaller than that for an interval
approaching an octave. I had Paul Erlich run a harmonic entropy
curve with the parameters tweaked so that they would agree with some
empirical observations I made many years ago (using a retuned
electronic organ) to identify intervals with maximum dissonance
between a unison and octave with middle C fixed as the lower tone of
the interval. If I was able to hear (no matter how faintly) the
difference between a rational interval and its slight mistuning, then
that interval would be a point of local minimum on the curve, but if
I was not able, then it would be a local maximum. The resulting
curve was tweaked so that the global maximum (approaching a unison)
is at 67 cents, which put a local maximum at 1139 cents (approaching
an octave).

There are more details about this (and also mention of the noble
mediant) here:
/tuning/topicId_73794.html#73816
as well as links to Paul's and my actual discussion (on the harmonic
entropy group) and to the raw data that resulted.

> This to me gives me the
> impression of all of the motions being sort of half-assed, e.g.
> they're "good enough," but not really good. We don't have
> C!->G!->E!->B!->C! but rather c... g... e... b#... *sigh* and the
> like. To be honest, if 19-equal were the dominant tuning system in
> western music, I really suspect that this group would have three
times
> as many members, with most of them extolling the virtues of 12-equal
> as a much more melodic and harmonic alternative.

I find something rather interesting about 19-ET, that, in spite of
its many advantages -- complete compatibility with conventional
diatonic harmony (excepting 12-ET enharmonic equivalency), no special
symbols required for notation, and membership in many temperament
classes (magic, hanson, keemun, negipent/sept, flattone, liese,
semaphore, sensipent/sept, wurschmidt) -- it continues to engender
strong feelings of acceptance or rejection. I happen to be among
those who accept it (particularly vs. 22-ET). Sure, the 7ths are
either much narrower (major and harmonic) or wider (minor) than I
might prefer, but pre-romantic-era music played in 19-ET speaks to me
with a more relaxed mood that seems appropriate to times when life
was simpler and technology progressed at a much slower pace -- as if
I might expect a 19-tone musician, asking how I liked the
performance, to speak Elizabethan English.

A person from another part of the world who speaks English will
probably pronounce vowels somewhat differently than you prefer, but
that's part of what makes up "culture". If you spend a few weeks in
19-tone land, you may discover (as Ivor Darreg did) that a single
degree of 19 is a melodic interval with a lot of "zonk" that can be
exploited very effectively (e.g., in MOS scales of the magic, hanson,
or keemun generators).

> On the other hand, I found the melodic movements of 17-et to be
> extremely articulated and as such the piece I keep referring to on
> Blackwood's album is the one I usually play if I'm only going to
play
> one. I notice now that for the chords, he used a timbre with a bit
of
> chorus/LFO and played extremely staccato chords, presumably to hide
> the beating and out-of-tuneness of the mainly 5-limit thing he seems
> to do with that piece.

Yes. When these pieces first came out on vinyl, Erv Wilson and I
listened to them together. Although we greatly admired Blackwood's
meticulous craftsmanship, we were a bit disappointed that he adhered
so closely to a major-minor way of thinking. We found 13 and 23 more
refreshing in that he *had* to do something different.

> This isn't to bash 19-tet too much... :) I have grown to like it,
but
> I view it more as some kind of "counterpart" to 17 and to some
extent
> 12. 17 has mainly sharp intervals, 19 has mainly flat intervals, so
> they're like the difference between night and day. 12 is sort of in
> the middle but closer to 17 with its major third.

Funny, but I've always thought of 12 as closer to 19, because 17 is
the one with all the neutral (11- or 13-prime) intervals.

> I am very interested though in hearing some of the pieces or musical
> excerpts that you or Margo worked out as you described in your
> paper... If you've find harmonic and melodic concepts that sound
> similar to "standard" 5-limit ones, but sound interesting and new at
> the same time, I would certainly like to hear them.

Yeah, I really should make sound files of all the examples and link
them to the paper.

> > In case you decide to read the entire paper (or to entice you to
do
> > so), I also made a 17-tone jazz excerpt using the 9-tone scale
> > (subset of 17) that I described near the bottom of the 22nd page
> > (numbered as p. 76):
> > http://xenharmony.wikispaces.com/space/showimage/17WTjazz.mp3
>
> Haha, wow. Neutral moondance. Dusk-dance? Twilight perhaps?
Interesting.

I though it would be good theme music for a TV night-life detective
series. Although the neutral intervals are unmistakable, the tonic
triad is a 6:7:9 (subminor). One property of the tuning that I like
is that 6:7:9:11 and 7:9:11:13 (tempered) chords can be transformed
into one another simply by changing the two inner tones. (There
aren't many tunings in which 11:12, 12:13, and 13:14 are all
represented by the same interval.)

> > While we're on the subject of the psychology of alternative
tunings,
> > there's a 17-tone piece (by Aaron Krister Johnson) that you might
be
> > interested in listening to, Adagio for Margo, at:
> > http://www.akjmusic.com/works.html
> > and then read about a particular observation I made:
> > /makemicromusic/topicId_15226.html#15247
> > and Aaron's reply:
> > /makemicromusic/topicId_15226.html#15249
>
> Yes. Yes. Yes. Exactly. This sentence:
>
[quoting GS again:]
> "In other words, the diatonic system is
> really a musical language, and our success in creating music in
> alternative tunings may depend on our ability to create (or
discover)
> other musical languages that are capable of becoming meaningful to
> the general listener."
>
> sums up perfectly everything I was trying to say in that other
thread.
> I'm trying to figure out, as a field of scientific inquiry, how it
> works, how a listener BUILDS this language to begin with, how a
> listener learns expands his language, why listeners sometimes treat
> incoming musical concepts or tunings as "wrong versions" of
something
> else already in their existing language, and how to get them to not
do
> that. I don't know why I kept getting allegations of my ideas being
> pseudoscientific or misguided in the other thread, but it's glad to
> finally see someone else thinking along the same lines.
>
> That being said, I also had some thoughts on this:
>
[quoting GS again:]
> "When we listen to a diatonic composition with only two voice parts
> (such as a Bach two-part keyboard invention), we are able to "hear"
> harmonies that are there only in the sense that they are implied by
> tonal relationships already familiar to both the composer and the
> listener. A two-voice composition in some non-diatonic scale subset
> of a non-12 tuning, on the other hand, would very likely not have
the
> same effect, but would be heard basically as a progression of
> intervals -- unless the composer had first written other
(successful)
> pieces in that scale using full harmonies and the listener had also
> become familiar with them."

I was thinking that perhaps folks in the early Middle Ages heard a
two-voice texture without any implied harmonies and that we could
have some idea of what they experienced by listening to two-part
music in a non-diatonic non-12 tuning.

> I think there are two parts to it:
>
> 1: the sum-and-difference tones generated by a dyad
> 2: the cognitive labeling of the whole package by the listener
>
> For intervals like a perfect fifth, a major third, perfect fourth,
> minor third, etc... The sum and difference tones are quite
pronounced
> and align perfectly in a harmonic series. For intervals like a 9:11
> neutral third, the sum and difference tones are going to be in a
> harmonic series though, but that difference tone will be MUCH lower
> than the chord tones. It will be low enough that if your focus is in
> the midrange where the chord tones are, you might miss this "phantom
> fundamental" virtual tone (even subconsciously).

Thus I'm rather skeptical that this would be of any influence in 17-
tone for anything other than the 3-limit intervals.

There's also the ambiguity of multiple harmonic roles for the various
intervals: is 6deg17 in a 2-voice texture going to be heard as a
tempered 7:9 or 11:14? Will 15deg (a neutral 6th) be interpreted as
6:11 or 7:13 (or possibly 13:24)? Will 14deg be 4:7 or 9:16? It
will have to be determined by the musical context, e.g., the scale
(if any) that the composer is using.

One reason that I devised 17-tone and 19-tone well-temperaments was
to tweak the intervals by a few cents so as to influence how they're
more likely to be interpreted in various keys. One problem with 19-
ET is that 6:7 and 7:8 are represented by the same interval. For
example, my 19-WT tips the balance in such a way that C:D# sounds
more like 6:7 but D#:F more like 7:8.

> Once you meditate on
> a neutral triad and grow used to it, however, you start to pick up
on
> the resonance of the chord and hear it in a harmonic context.
However,
> the average listener who hasn't been accustomed to the sound might
be
> confused and hear it as a mistuned major or minor chord, since
that's
> the only other thing they have to go by.

Yep. That's why I've gravitated toward isoharmonic chords when using
neutral intervals. They're consonant in the sense that you can
easily distinguish ones that are in JI from ones that are even
moderately tempered, because disturbances between combinational tones
are minimized. With 18:22:27, OTOH, there are no prominent beats to
distinguish it from 26:32:39, or from anything in-between.

> But just like people did eventually get used to the sound of major
> chords and perfect fifths, I think there are probably clever ways to
> find intervals that a listener will most likely hear as new and
novel
> rather than weird and disturbing. For some reason, for people
> accustomed to 12-tet, the 7/6 subminor third is usually such an
> "easy-to-grasp" interval, although a 9/7 supermajor third doesn't
> share that characteristic and is often heard simply as a sharp 5/4.
> Why this is, I haven't the foggiest, although it might be
interesting
> to study.

For 6:7:9 vs. 14:18:21 (same intervals in reverse order), e.g., a lot
of it has to do with the relationships between combinational tones
(particularly first-order difference tones).

> Furthermore, I hypothesize that just like perfect fifths can be
played
> lower than major thirds and still sound good (due to that phantom
> fundamental dropping off the bottom of hearing range sooner for the
> major thirds), there will be triads that sound muddy straight up
until
> the midrange of the piano, although I don't know what those triads
are
> yet.
>
> I'm actually running on no sleep right now, so I apologize if any of
> my post didn't make sense.

It all makes sense to me -- but take care yourself and get enough
sleep.

--George

🔗Dave Keenan <d.keenan@...>

6/12/2008 3:17:43 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> What gray/noble/shadow/mystic/double top secret intervals are out
> there that aren't neutral? Like one between 5/4 and 4/3 or something?
>

Sure. The relevant noble number is (4+5phi)/(3+4phi). At around 422
cents that's a supermajor third. And we were just talking about the
minor seventh, the noble version being around 1002 cents.

> >> "grey intervals?" They're
> >> definitely gray to me, though I propose that if we call them gray
> >> intervals, we spell it "grey," for various aesthetic reasons.
> >
> > "Grey" is fine with me too. "Shadowy" and "grey" are of course quite
> > similar in meaning.
>
> Yeah, but gray is a color, and they have blue notes, and I want my
> gray notes, god damn it! That's all I'm saying. Chrominance-free
> neutral gray notes.
>
> Oddly enough, the more I see "grey" intervals, the more apt I am to
> want to just call them "gray" with the normal spelling. Whatever.

In Australia and the UK, the colour _is_ spelled "grey", and "gray" is
a unit of radiation dose, or with a capital letter it's someones surname.

-- Dave Keenan

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:12:27 PM

On Thu, Jun 12, 2008 at 11:54 AM, Carl Lumma <carl@...> wrote:
>> >> So transcendental numbers have their use in JI after all :P
>> >
>> > Noble numbers are not transcendental as far as I know. Phi
>> > certainly isn't since it is (sqrt(5)+1)/2, the solution of
>> > x^2 -x -1 = 0.
>>
>> Oh yeah. Whoops. I meant "irrational numbers that are not the
>> root of some rational number". E.g. phi, although having
>> sqrt(5) in it, is not going to give you a rational when you do
>> phi^5. In fact, phi^anything will never be a rational number.
>
> That's true of any irrational number.
>
> -Carl

Not true of 2^(1/12) and the like.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/12/2008 4:23:20 PM

> Sure. The relevant noble number is (4+5phi)/(3+4phi). At around 422
> cents that's a supermajor third. And we were just talking about the
> minor seventh, the noble version being around 1002 cents.

I'm confused as to how to calculate these. I was trying to find the
gray tone between a 400 cent major third and a pure 4/3. 400 cents is
a ratio of 1.2599210498948732.

So I did (1.2599 + 4phi)/(1+3phi). Somehow the answer is larger than
(9 + 4phi)/(1+7phi).

Furthermore, (1.25 + 1.333phi)/(1+1phi) is significantly different
from (5 + 4phi)/(4 + 3phi). Somehow, the former seems to have more of
the "gray interval" neutral-zone quality, even though I've been
calculating them using the latter. What's the proper way to calculate
these?

>> >> "grey intervals?" They're
>> >> definitely gray to me, though I propose that if we call them gray
>> >> intervals, we spell it "grey," for various aesthetic reasons.
>> >
>> > "Grey" is fine with me too. "Shadowy" and "grey" are of course quite
>> > similar in meaning.
>>
>> Yeah, but gray is a color, and they have blue notes, and I want my
>> gray notes, god damn it! That's all I'm saying. Chrominance-free
>> neutral gray notes.
>>
>> Oddly enough, the more I see "grey" intervals, the more apt I am to
>> want to just call them "gray" with the normal spelling. Whatever.
>
> In Australia and the UK, the colour _is_ spelled "grey", and "gray" is
> a unit of radiation dose, or with a capital letter it's someones surname.

Yeah, well in the US, the _color_ is spelled "gray." You call em grey,
and I'll call em gray, and at the end of the day, it'll be okay.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/12/2008 5:04:00 PM

> The diatonic semitone in 19-ET is larger than in 12-ET and much more
> so than that of 17-ET. So there's actually a greater distance to be
> traversed, which one might think of as *more* movement. But I think
> what you're getting at is that, because of the lower leading tone of
> 19-ET, the greater distance results in less *attraction* (think of a
> sort of tonal gravity) to its resolution to the neighboring tonic.

Well, I was talking mainly about chordal root movement, which is
usually by fifth. The fifth of 19-tet is so much flatter than 12-tet
that I find the root movement to be a bit "compressed" sounding, as if
it doesn't move as much as 12's (because it doesn't). This could give
a very stagnant or relaxed feel, I suppose, depending on how you look
at it. But I think what I was getting at was what you said - the 15/8
resolving to 2/1 doesn't work very well, and neither does 19-tet's
even flatter interval. Perhaps there's some kind of noble
interval/gray tone that needs to be hit to maximize the effect?

> But this is true only up to a point: if the leading tone is so high
> that it's only a quartertone (or especially a lesser amount) away,
> then the effect is one of less attraction or articulation. As I
> wrote in my 17-tone paper, there's an optimal value of greatest
> attraction somewhere around 70 cents. Since I wrote the paper, I've
> concluded that it's perhaps closer to 67 cents (for an interval
> approaching a unison), and probably smaller than that for an interval
> approaching an octave. I had Paul Erlich run a harmonic entropy
> curve with the parameters tweaked so that they would agree with some
> empirical observations I made many years ago (using a retuned
> electronic organ) to identify intervals with maximum dissonance
> between a unison and octave with middle C fixed as the lower tone of
> the interval. If I was able to hear (no matter how faintly) the
> difference between a rational interval and its slight mistuning, then
> that interval would be a point of local minimum on the curve, but if
> I was not able, then it would be a local maximum. The resulting
> curve was tweaked so that the global maximum (approaching a unison)
> is at 67 cents, which put a local maximum at 1139 cents (approaching
> an octave).
>
> There are more details about this (and also mention of the noble
> mediant) here:
> /tuning/topicId_73794.html#73816
> as well as links to Paul's and my actual discussion (on the harmonic
> entropy group) and to the raw data that resulted.

I have to get this harmonic entropy concept down a little bit
better... I'll read. Thanks.

>> This to me gives me the
>> impression of all of the motions being sort of half-assed, e.g.
>> they're "good enough," but not really good. We don't have
>> C!->G!->E!->B!->C! but rather c... g... e... b#... *sigh* and the
>> like. To be honest, if 19-equal were the dominant tuning system in
>> western music, I really suspect that this group would have three
> times
>> as many members, with most of them extolling the virtues of 12-equal
>> as a much more melodic and harmonic alternative.
>
> I find something rather interesting about 19-ET, that, in spite of
> its many advantages -- complete compatibility with conventional
> diatonic harmony (excepting 12-ET enharmonic equivalency), no special
> symbols required for notation, and membership in many temperament
> classes (magic, hanson, keemun, negipent/sept, flattone, liese,
> semaphore, sensipent/sept, wurschmidt) -- it continues to engender
> strong feelings of acceptance or rejection. I happen to be among
> those who accept it (particularly vs. 22-ET). Sure, the 7ths are
> either much narrower (major and harmonic) or wider (minor) than I
> might prefer, but pre-romantic-era music played in 19-ET speaks to me
> with a more relaxed mood that seems appropriate to times when life
> was simpler and technology progressed at a much slower pace -- as if
> I might expect a 19-tone musician, asking how I liked the
> performance, to speak Elizabethan English.

Oh no, I really like 19-tet. It just took me a while to get used to
it. At first, I thought it sounded... unsettling, and I think it's
because of the narrow fifths and major thirds, so that chord movements
sounded like they were lacking something. On the other hand, 17-tet's
wider intervals made it seem like they were "accentuated," so it was a
big hit right away. That's the best I can describe it. Nowadays, I
like both 19-tet and 17-tet, and as I said before, I feel like 19-tet
is like the night/day "counterpart" to 12-tet and in some ways 17 as
well.

> A person from another part of the world who speaks English will
> probably pronounce vowels somewhat differently than you prefer, but
> that's part of what makes up "culture". If you spend a few weeks in
> 19-tone land, you may discover (as Ivor Darreg did) that a single
> degree of 19 is a melodic interval with a lot of "zonk" that can be
> exploited very effectively (e.g., in MOS scales of the magic, hanson,
> or keemun generators).

Yeah, that's what I've come to realize... I personally find that music
written specifically for 19-tet can sound amazing, much better imo
than music written for 12-tet or 1/6 comma meantone or something that
is being "re-done" in 19-tet as an exercise. I haven't heard any
Renaissance or Baroque-era music in 19-tet, but I can imagine that
that would likely sound pretty decent in 19-tet as well, much better
than say, Debussy or something. Actually, I was listening to
Blackwood's 19-tet piece off of that album (not the "fanfare" that is
usually attached to the beginning), and up until he goes into
full-blown xenharmonic mode, I can tell why you like the character of
it for that kind of music - it is fairly relaxing.

I was mainly just describing 17 as potentially a good temperament to
"hook" someone into microtonal music, especially if the chords are
finessed just right so that they don't sound particularly weird to
someone with a 12-tet vocabulary.

>> On the other hand, I found the melodic movements of 17-et to be
>> extremely articulated and as such the piece I keep referring to on
>> Blackwood's album is the one I usually play if I'm only going to
> play
>> one. I notice now that for the chords, he used a timbre with a bit
> of
>> chorus/LFO and played extremely staccato chords, presumably to hide
>> the beating and out-of-tuneness of the mainly 5-limit thing he seems
>> to do with that piece.
>
> Yes. When these pieces first came out on vinyl, Erv Wilson and I
> listened to them together. Although we greatly admired Blackwood's
> meticulous craftsmanship, we were a bit disappointed that he adhered
> so closely to a major-minor way of thinking. We found 13 and 23 more
> refreshing in that he *had* to do something different.

The 23-tone one is amazing. I haven't heard the 13-tone one because I
bought the album off of Napster, and they screwed up and made both of
the tracks the 23-tone one. (Incidentally, if anyone's feeling
generous today... *cough*)

>> This isn't to bash 19-tet too much... :) I have grown to like it,
> but
>> I view it more as some kind of "counterpart" to 17 and to some
> extent
>> 12. 17 has mainly sharp intervals, 19 has mainly flat intervals, so
>> they're like the difference between night and day. 12 is sort of in
>> the middle but closer to 17 with its major third.
>
> Funny, but I've always thought of 12 as closer to 19, because 17 is
> the one with all the neutral (11- or 13-prime) intervals.

Hm. Maybe you're right. From a theoretical standpoint, that's
definitely the case. I just feel like 17 has a "brighter," more
vibrant feel to it, where as 19 has a more "low-key" and relaxed feel
to it. 12 I feel is more on the vibrant side. How 22 fits into this
setup I don't know.

>> I am very interested though in hearing some of the pieces or musical
>> excerpts that you or Margo worked out as you described in your
>> paper... If you've find harmonic and melodic concepts that sound
>> similar to "standard" 5-limit ones, but sound interesting and new at
>> the same time, I would certainly like to hear them.
>
> Yeah, I really should make sound files of all the examples and link
> them to the paper.
>
>> > In case you decide to read the entire paper (or to entice you to
> do
>> > so), I also made a 17-tone jazz excerpt using the 9-tone scale
>> > (subset of 17) that I described near the bottom of the 22nd page
>> > (numbered as p. 76):
>> > http://xenharmony.wikispaces.com/space/showimage/17WTjazz.mp3
>>
>> Haha, wow. Neutral moondance. Dusk-dance? Twilight perhaps?
> Interesting.
>
> I though it would be good theme music for a TV night-life detective
> series. Although the neutral intervals are unmistakable, the tonic
> triad is a 6:7:9 (subminor). One property of the tuning that I like
> is that 6:7:9:11 and 7:9:11:13 (tempered) chords can be transformed
> into one another simply by changing the two inner tones. (There
> aren't many tunings in which 11:12, 12:13, and 13:14 are all
> represented by the same interval.)

Just out of curiosity, do you have a scala file for this well temperament?

>> > While we're on the subject of the psychology of alternative
> tunings,
>> > there's a 17-tone piece (by Aaron Krister Johnson) that you might
> be
>> > interested in listening to, Adagio for Margo, at:
>> > http://www.akjmusic.com/works.html
>> > and then read about a particular observation I made:
>> > /makemicromusic/topicId_15226.html#15247
>> > and Aaron's reply:
>> > /makemicromusic/topicId_15226.html#15249
>>
>> Yes. Yes. Yes. Exactly. This sentence:
>>
> [quoting GS again:]
>> "In other words, the diatonic system is
>> really a musical language, and our success in creating music in
>> alternative tunings may depend on our ability to create (or
> discover)
>> other musical languages that are capable of becoming meaningful to
>> the general listener."
>>
>> sums up perfectly everything I was trying to say in that other
> thread.
>> I'm trying to figure out, as a field of scientific inquiry, how it
>> works, how a listener BUILDS this language to begin with, how a
>> listener learns expands his language, why listeners sometimes treat
>> incoming musical concepts or tunings as "wrong versions" of
> something
>> else already in their existing language, and how to get them to not
> do
>> that. I don't know why I kept getting allegations of my ideas being
>> pseudoscientific or misguided in the other thread, but it's glad to
>> finally see someone else thinking along the same lines.
>>
>> That being said, I also had some thoughts on this:
>>
> [quoting GS again:]
>> "When we listen to a diatonic composition with only two voice parts
>> (such as a Bach two-part keyboard invention), we are able to "hear"
>> harmonies that are there only in the sense that they are implied by
>> tonal relationships already familiar to both the composer and the
>> listener. A two-voice composition in some non-diatonic scale subset
>> of a non-12 tuning, on the other hand, would very likely not have
> the
>> same effect, but would be heard basically as a progression of
>> intervals -- unless the composer had first written other
> (successful)
>> pieces in that scale using full harmonies and the listener had also
>> become familiar with them."
>
> I was thinking that perhaps folks in the early Middle Ages heard a
> two-voice texture without any implied harmonies and that we could
> have some idea of what they experienced by listening to two-part
> music in a non-diatonic non-12 tuning.

I find that meditation helps me to get into a state where I -CAN- hear
2-part harmonies that way. It's not so much that I stop noticing the
harmonic sum and difference tones... It's more like I stop "filling"
in extra notes or chord qualities mentally. I.E., if I hear C and E
sung simultaneously, I don't think "this is C major, there is a G in
this triad, on the piano it's played right here, etc." I find that
cutting out all of that mental clutter makes it a lot easier to hear
the music for what it is, and I wouldn't be surprised if many folks
from back in the Middle Ages did in fact notice the sum and difference
tones, and so I'd be on the same page as them in this case.

>> I think there are two parts to it:
>>
>> 1: the sum-and-difference tones generated by a dyad
>> 2: the cognitive labeling of the whole package by the listener
>>
>> For intervals like a perfect fifth, a major third, perfect fourth,
>> minor third, etc... The sum and difference tones are quite
> pronounced
>> and align perfectly in a harmonic series. For intervals like a 9:11
>> neutral third, the sum and difference tones are going to be in a
>> harmonic series though, but that difference tone will be MUCH lower
>> than the chord tones. It will be low enough that if your focus is in
>> the midrange where the chord tones are, you might miss this "phantom
>> fundamental" virtual tone (even subconsciously).
>
> Thus I'm rather skeptical that this would be of any influence in 17-
> tone for anything other than the 3-limit intervals.
>
> There's also the ambiguity of multiple harmonic roles for the various
> intervals: is 6deg17 in a 2-voice texture going to be heard as a
> tempered 7:9 or 11:14? Will 15deg (a neutral 6th) be interpreted as
> 6:11 or 7:13 (or possibly 13:24)? Will 14deg be 4:7 or 9:16? It
> will have to be determined by the musical context, e.g., the scale
> (if any) that the composer is using.
>
> One reason that I devised 17-tone and 19-tone well-temperaments was
> to tweak the intervals by a few cents so as to influence how they're
> more likely to be interpreted in various keys. One problem with 19-
> ET is that 6:7 and 7:8 are represented by the same interval. For
> example, my 19-WT tips the balance in such a way that C:D# sounds
> more like 6:7 but D#:F more like 7:8.

I would really like to hear this well temperament. Do you have a scala
file or something of the like for it?

>> Once you meditate on
>> a neutral triad and grow used to it, however, you start to pick up
> on
>> the resonance of the chord and hear it in a harmonic context.
> However,
>> the average listener who hasn't been accustomed to the sound might
> be
>> confused and hear it as a mistuned major or minor chord, since
> that's
>> the only other thing they have to go by.
>
> Yep. That's why I've gravitated toward isoharmonic chords when using
> neutral intervals. They're consonant in the sense that you can
> easily distinguish ones that are in JI from ones that are even
> moderately tempered, because disturbances between combinational tones
> are minimized. With 18:22:27, OTOH, there are no prominent beats to
> distinguish it from 26:32:39, or from anything in-between.

Yeah, definitely. Like I was sayin above, I really don't find 18:22:27
to be of much use unless it's played at a high enough register that
the "Rameau" tone is perceivable. 9:11:13, on the other hand, doesn't
have that problem.

I make an exception for the gray tone between 5/4 and 6/5... At around
356 cents, I find a triad with that and 3/2 in it to serve a musical
function all of its own.

>> But just like people did eventually get used to the sound of major
>> chords and perfect fifths, I think there are probably clever ways to
>> find intervals that a listener will most likely hear as new and
> novel
>> rather than weird and disturbing. For some reason, for people
>> accustomed to 12-tet, the 7/6 subminor third is usually such an
>> "easy-to-grasp" interval, although a 9/7 supermajor third doesn't
>> share that characteristic and is often heard simply as a sharp 5/4.
>> Why this is, I haven't the foggiest, although it might be
> interesting
>> to study.
>
> For 6:7:9 vs. 14:18:21 (same intervals in reverse order), e.g., a lot
> of it has to do with the relationships between combinational tones
> (particularly first-order difference tones).

What do you mean here? This seems like precisely the answer I'm looking for.

>> Furthermore, I hypothesize that just like perfect fifths can be
> played
>> lower than major thirds and still sound good (due to that phantom
>> fundamental dropping off the bottom of hearing range sooner for the
>> major thirds), there will be triads that sound muddy straight up
> until
>> the midrange of the piano, although I don't know what those triads
> are
>> yet.
>>
>> I'm actually running on no sleep right now, so I apologize if any of
>> my post didn't make sense.
>
> It all makes sense to me -- but take care yourself and get enough
> sleep.

Indeed. I'm more awake now, things were rough.

-Mike

🔗Dave Keenan <d.keenan@...>

6/12/2008 5:18:29 PM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@>
> wrote:
>
> > Interesting. I actually posted the wrong number - I was looking at
> 366
> > cents, which doesn't have any noble anything near it. It had the
> > feeling of slightly major, but musically gray at the same time. I'm
> > not sure what that's about.
>
> It's right there at the inversion of 1 phi-th of the octave.

That's not a noble frequency ratio. That's a noble fraction of an
octave, considered logarithmically.

That's the other way of using noble numbers that Kraig and I were
talking about. It doesn't relate to harmony, but to scale generators
for melodic purposes. It has no necessary relationship to coincidence
of partials or the lack thereof.

> > One thing I've noticed about the noble numbers is that two of them
> > exist between any interval. You have the one generated by going from
> > 5/4, 6/5, etc... And the one from 6/5, 5/4, etc. You'll end up at
> > different places.

As Graham said, the limit of 6/5, 5/4, 11/9, 16/13, 27/22, ... is
better described as the noble mediant of 5/4 and 9/11. That way the
sequence steadily increased in n*d complexity.

The limit of the sequence 5/4, 6/5, 11/9, 17/14, 28/23, ... is the
true noble mediant of 5/4 and 6/5. But we can also run it backwards
one step before complexity starts to increase again,
1/1, 5/4, 6/5, 11/9, 17/14, 28/23, ...
so it is also the noble mediant of 1/1 and 5/4.

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/12/2008 5:43:28 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Sure. The relevant noble number is (4+5phi)/(3+4phi). At around 422
> > cents that's a supermajor third. And we were just talking about the
> > minor seventh, the noble version being around 1002 cents.
>
> I'm confused as to how to calculate these. I was trying to find the
> gray tone between a 400 cent major third and a pure 4/3. 400 cents is
> a ratio of 1.2599210498948732.
>
> So I did (1.2599 + 4phi)/(1+3phi). Somehow the answer is larger than
> (9 + 4phi)/(1+7phi).
>
> Furthermore, (1.25 + 1.333phi)/(1+1phi) is significantly different
> from (5 + 4phi)/(4 + 3phi). Somehow, the former seems to have more of
> the "gray interval" neutral-zone quality, even though I've been
> calculating them using the latter. What's the proper way to calculate
> these?

Man! You sure are confused. Calculating a mediant with an irrational
argument is utterly meaningless.

I suggest you go cold-turkey from the list for a while and get some sleep.

Then read Margo's and my paper on the subject, which URL I emailed you
as well as posted to the list. And like I said in earlier posts, the
"grayest" sound may not occur exactly at the noble number frequency
ratio. It probably occurs at the maximum of harmonic entropy, but
unfortunately the modelling of that has a free parameter that makes
the predicted maxima wander around a lot.

> Yeah, well in the US, the _color_ is spelled "gray."

We knew that.

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/12/2008 6:00:25 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> Although, I was just thinking, at least for 12tet an A-C-E minor chord
> actually HAS an A fundamental, because that A-C is pretty close to
> 16:19, so the fundamental will be 4 octaves below the A. I remember
> playing A and C simultaneously on a vibraphone and hearing that low A,
> wondering why it wasn't an F (I didn't realize the 16:19 relationship
> before). Might that have something to do with it?

Maybe so in the case of a bare 16:19 dyad on something as high pitched
as a vibraphone (otherwise the virtual fundamental would be subsonic),
but generally, in the case of the triad I'd suggest it's simply
because there's one highly consonant interval in there, the fifth, and
the perceived root is simply the virtual fundamental of that.

Looking at 16:19:24 and failing to consider that there's a 2:3 in
there is what I'd call "can't see the trees for the forest". ;-)

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/12/2008 6:53:13 PM

I think allot of this could be explained simpler by referring to the scale tree.
Which has the noble mediants between the ratios. ( i guess this is one distinction from the stern brocot tree). It seems more relevant than HE which as you point out does not coincide yet here you have the same numbers
http://anaphoria.com/sctree.PDF
see page 19 and 18
It also is quite clearer in showing the whole territory at a glance.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Cameron,
>
> Yo
>
> Margo (no "t") and I called their sound "metastable", for reasons we
> explained in the paper.
> http://dkeenan.com/Music/NobleMediant.txt > <http://dkeenan.com/Music/NobleMediant.txt>
> but maybe that sounds too much like physics, and not enough like
> auditory perception.
>
>
>
>
>

🔗Kraig Grady <kraiggrady@...>

6/12/2008 7:04:26 PM

I now see a mention at the end.
But i think all this was put forth at the time as i remember it before HE was finished?

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
>
> I think allot of this could be explained simpler by referring to the
> scale tree.
> Which has the noble mediants between the ratios. ( i guess this is one
> distinction from the stern brocot tree). It seems more relevant than HE
> which as you point out does not coincide yet here you have the same > numbers
> http://anaphoria.com/sctree.PDF <http://anaphoria.com/sctree.PDF>
> see page 19 and 18
> It also is quite clearer in showing the whole territory at a glance.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Dave Keenan wrote:
> >
> > Hi Cameron,
> >
> > Yo
> >
> > Margo (no "t") and I called their sound "metastable", for reasons we
> > explained in the paper.
> > http://dkeenan.com/Music/NobleMediant.txt > <http://dkeenan.com/Music/NobleMediant.txt>
> > <http://dkeenan.com/Music/NobleMediant.txt > <http://dkeenan.com/Music/NobleMediant.txt>>
> > but maybe that sounds too much like physics, and not enough like
> > auditory perception.
> >
> >
> >
> >
> >
>
>

🔗Dave Keenan <d.keenan@...>

6/12/2008 7:50:24 PM

Yes! Thanks for that Kraig. http://anaphoria.com/sctree.PDF

See page 1 and then pages 18 thru 25 which zoom in on the region
that's relevant to noble intervals (as opposed to noble scale
generators). The nobles are the bottom row of decimal ratios.

I note that without explanation, many people could have looked at
those diagrams for years without figuring out what the numbers at the
bottom were about. So I wouldn't say it's a simpler way of explaining
it. But they certainly complement one another. I shall update the
article to refer to Erv's scale tree.

Someone should do a version of these diagrams with cents instead of
decimal ratios. And they could leave off the bottom row of rationals
in pages 18 thru 25 so we could get it down to 4 pages. Hmm. We could
put the sagittal notation for them too, relative to say Partch's G = 1/1.

Although Harmonic Entropy is not very specific about exactly where
some shadow/grey intervals should be, at least it predicts the general
vicinity of some that the noble numbers completely fail to predict at
all, i.e. those close to the unison, octave and fifth.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I think allot of this could be explained simpler by referring to the
> scale tree.
> Which has the noble mediants between the ratios. ( i guess this is one
> distinction from the stern brocot tree). It seems more relevant than HE
> which as you point out does not coincide yet here you have the same
numbers
> http://anaphoria.com/sctree.PDF
> see page 19 and 18
> It also is quite clearer in showing the whole territory at a glance.

🔗Herman Miller <hmiller@...>

6/12/2008 8:08:02 PM

Dave Keenan wrote:

> Cameron, you have called them "shadow" intervals below, which I like.
> They could also be called "dark" intervals.
> > Margo (no "t") and I called their sound "metastable", for reasons we
> explained in the paper.
> http://dkeenan.com/Music/NobleMediant.txt
> but maybe that sounds too much like physics, and not enough like
> auditory perception.
> > I couldn't help thinking that Justice and Mercy are cardinal vitues
> that are often considered together, and I couldn't help noticing how
> similar the words "metastable" and "merciful" sound. I then googled:
> "mercy justice", and could hardly believe it when the first article I
> read had the words "golden mean" in the second paragraph! It all fits
> so well. See
> http://atheism.about.com/library/FAQs/phil/blphil_eth_mercyjustice.htm
> > So what do you think? Merciful intonation, mercifully intoned
> intervals, merciful intervals, MI?

Murky intervals?

🔗Kraig Grady <kraiggrady@...>

6/12/2008 8:39:38 PM

The problem with converting to cents is that , as we have mentioned. the tree is used in both ways.
I am not sure about mediants around these intervals cause one could focus the tree and expand it in these areas. I still find the concept unclear of harmonic entropy. First harmony is normally measured with three tones , not two. With three you have something much closer to entropy and that is 'turbulence'.
If the mediants have a strong characteristics that are immediately perceivable ( which must be the case since there are people around the world who tune to such things) them there is nothing 'uncertain' about them. The notion of lower simpler ratios as a gauge is also still in the background. There are some for instance that find 13 more consonant than 11. and then how does one quantify these relations without picking some arbitrary formula. The notion also that uncertainly= dissonance is a very equal tempered idea as this is how it manifest itself. Certainly some of Kyle Gann music illustrates that one can be very very dissonant and be very very precise and certain in what is being sounded. I can say that to my ear it can exceed the dissonances of 12 ET. On the other hand not matter how many notes i put down in my 12 note meta slendro, it will not exceed a certain dissonant which in way less that 12 equal, yet the intervals would have to be considered higher in Entropy.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Yes! Thanks for that Kraig. http://anaphoria.com/sctree.PDF > <http://anaphoria.com/sctree.PDF>
>
> See page 1 and then pages 18 thru 25 which zoom in on the region
> that's relevant to noble intervals (as opposed to noble scale
> generators). The nobles are the bottom row of decimal ratios.
>
> I note that without explanation, many people could have looked at
> those diagrams for years without figuring out what the numbers at the
> bottom were about. So I wouldn't say it's a simpler way of explaining
> it. But they certainly complement one another. I shall update the
> article to refer to Erv's scale tree.
>
> Someone should do a version of these diagrams with cents instead of
> decimal ratios. And they could leave off the bottom row of rationals
> in pages 18 thru 25 so we could get it down to 4 pages. Hmm. We could
> put the sagittal notation for them too, relative to say Partch's G = 1/1.
>
> Although Harmonic Entropy is not very specific about exactly where
> some shadow/grey intervals should be, at least it predicts the general
> vicinity of some that the noble numbers completely fail to predict at
> all, i.e. those close to the unison, octave and fifth.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > I think allot of this could be explained simpler by referring to the
> > scale tree.
> > Which has the noble mediants between the ratios. ( i guess this is one
> > distinction from the stern brocot tree). It seems more relevant than HE
> > which as you point out does not coincide yet here you have the same
> numbers
> > http://anaphoria.com/sctree.PDF <http://anaphoria.com/sctree.PDF>
> > see page 19 and 18
> > It also is quite clearer in showing the whole territory at a glance.
>
>

🔗Dave Keenan <d.keenan@...>

6/12/2008 8:41:33 PM

Hee hee. Good one.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> Dave Keenan wrote:
> > So what do you think? Merciful intonation, mercifully intoned
> > intervals, merciful intervals, MI?
>
> Murky intervals?
>

🔗Carl Lumma <carl@...>

6/12/2008 8:56:07 PM

> >> >> So transcendental numbers have their use in JI after all :P
> >> >
> >> > Noble numbers are not transcendental as far as I know. Phi
> >> > certainly isn't since it is (sqrt(5)+1)/2, the solution of
> >> > x^2 -x -1 = 0.
> >>
> >> Oh yeah. Whoops. I meant "irrational numbers that are not the
> >> root of some rational number". E.g. phi, although having
> >> sqrt(5) in it, is not going to give you a rational when you do
> >> phi^5. In fact, phi^anything will never be a rational number.
> >
> > That's true of any irrational number.
> >
> > -Carl
>
> Not true of 2^(1/12) and the like.

Very right you are. I'm definitely overextending myself.
I'll shut up now. -Carl

🔗Cameron Bobro <misterbobro@...>

6/12/2008 10:14:24 PM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I think allot of this could be explained simpler by referring to
the
> scale tree.
> Which has the noble mediants between the ratios. ( i guess this
is one
> distinction from the stern brocot tree). It seems more relevant
than HE
> which as you point out does not coincide yet here you have the
same numbers
> http://anaphoria.com/sctree.PDF
> see page 19 and 18
> It also is quite clearer in showing the whole territory at a
glance.

And there they are. Lessee... I've been going about this "wrong" but
finding them all the same, LOL. Hmmm, must be one the one a hair
above 13/10 and a hair above 27/22...yes... hahaha! back in a couple
of hours, found something very funny indeed. :)

🔗Kraig Grady <kraiggrady@...>

6/12/2008 10:49:26 PM

One interesting application , like Margo's and Dave's where one could decide what interval would be dissonant and/or consonant
would be to apply Viggo Brun's algorithm as well of determining specific context in which they appear.
the question of dark, shadowy or cloudy might be based, thinking about it on there combination with simple ratios. whereas by themselves they might not sound that way(?)
[as we hear in much S.E. Asian music/tunings)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Cameron Bobro wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > I think allot of this could be explained simpler by referring to
> the
> > scale tree.
> > Which has the noble mediants between the ratios. ( i guess this
> is one
> > distinction from the stern brocot tree). It seems more relevant
> than HE
> > which as you point out does not coincide yet here you have the
> same numbers
> > http://anaphoria.com/sctree.PDF <http://anaphoria.com/sctree.PDF>
> > see page 19 and 18
> > It also is quite clearer in showing the whole territory at a
> glance.
>
> And there they are. Lessee... I've been going about this "wrong" but
> finding them all the same, LOL. Hmmm, must be one the one a hair
> above 13/10 and a hair above 27/22...yes... hahaha! back in a couple
> of hours, found something very funny indeed. :)
>
>

🔗Dave Keenan <d.keenan@...>

6/13/2008 12:45:41 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> One interesting application , like Margo's and Dave's where one could
> decide what interval would be dissonant and/or consonant
> would be to apply Viggo Brun's algorithm

Can you point me to something on the musical application of his
continued fraction algorithm (which I assume is the one you mean).

> as well of determining specific
> context in which they appear.
> the question of dark, shadowy or cloudy might be based, thinking about
> it on there combination with simple ratios. whereas by themselves they
> might not sound that way(?)
> [as we hear in much S.E. Asian music/tunings)

I think you're probably right there.

In searching for info on Viggo Brun's algorithm I learned from the
Wikipedia continued fractions article that a simple check for whether
a number of the form

i + m*phi
---------
j + n*phi

is actually a noble number (and therefore has the same
maximum-avoidance-of-rationals property as phi itself) is that firstly
1, j, m, n must be integers, and secondly |i*n - m*j| = 1
In other words, perform two diagonal multiplications and ensure the
results differ by 1.

So the phi-weighted-mediant of 3/2 and 4/3 is noble since when we
cross multiply we get 3*3 = 9 and 2*4 = 8, differing by 1.

But the phi-weighet mediant of 3/2 and 5/4 is not noble because we get
3*4 = 12 and 2*5 = 10, differing by 2.

-- Dave Keenan

🔗Graham Breed <gbreed@...>

6/13/2008 1:17:39 AM

Dave Keenan wrote:

> In searching for info on Viggo Brun's algorithm I learned from the
> Wikipedia continued fractions article that a simple check for whether
> a number of the form
> > i + m*phi
> ---------
> j + n*phi
> > is actually a noble number (and therefore has the same
> maximum-avoidance-of-rationals property as phi itself) is that firstly
> 1, j, m, n must be integers, and secondly |i*n - m*j| = 1
> In other words, perform two diagonal multiplications and ensure the
> results differ by 1.

That condition's the same as being adjacent on the Stern-Brocot tree.

Graham

🔗Kraig Grady <kraiggrady@...>

6/13/2008 1:39:48 AM

I can see that on the scale tree that 3/2 and 5/4 are not directly connected.
The Diophantine Equation is what you have there. Mentioned in the Treasure chest BTW.
http://anaphoria.com/tres.PDF
looking at how he slyly gets around the tetrachord with 4/4---4/3 makes me wonder if there is a way to do it with the 3/2 and 5/4 spelled differently
He has mentioned to me that one could generate a Diophantine Equation where you had 2 instead of 1.

On Viggo Brun....
even though this beyond me, but in case not for you there is this original document
http://anaphoria.com/viggo0.PDF <http://anaphoria.com/viggoO.PDF>

We are aware of this thanks to Mandelbaum who discusses it in his book. I had the excerpt up before he let me put the whole thing up and happy to find i hadn't taken it down
http://anaphoria.com/mandelbaum.PDF

then look at page 2 of
http://anaphoria.com/viggo3.PDF
and one could insert Margo and yours merci third or Cameron's
in place of 5/4 and try it out in either sequence

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > One interesting application , like Margo's and Dave's where one could
> > decide what interval would be dissonant and/or consonant
> > would be to apply Viggo Brun's algorithm
>
> Can you point me to something on the musical application of his
> continued fraction algorithm (which I assume is the one you mean).
>
> > as well of determining specific
> > context in which they appear.
> > the question of dark, shadowy or cloudy might be based, thinking about
> > it on there combination with simple ratios. whereas by themselves they
> > might not sound that way(?)
> > [as we hear in much S.E. Asian music/tunings)
>
> I think you're probably right there.
>
> In searching for info on Viggo Brun's algorithm I learned from the
> Wikipedia continued fractions article that a simple check for whether
> a number of the form
>
> i + m*phi
> ---------
> j + n*phi
>
> is actually a noble number (and therefore has the same
> maximum-avoidance-of-rationals property as phi itself) is that firstly
> 1, j, m, n must be integers, and secondly |i*n - m*j| = 1
> In other words, perform two diagonal multiplications and ensure the
> results differ by 1.
>
> So the phi-weighted-mediant of 3/2 and 4/3 is noble since when we
> cross multiply we get 3*3 = 9 and 2*4 = 8, differing by 1.
>
> But the phi-weighet mediant of 3/2 and 5/4 is not noble because we get
> 3*4 = 12 and 2*5 = 10, differing by 2.
>
> -- Dave Keenan
>
>

🔗Cameron Bobro <misterbobro@...>

6/13/2008 3:03:06 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:

> the question of dark, shadowy or cloudy might be based, thinking
>about
> it on there combination with simple ratios. whereas by themselves
>they
> might not sound that way(?)
> [as we hear in much S.E. Asian music/tunings)

I'd say that by themselves they can be used like modes with all kinds
of colors. Check this out:

On Mon Feb 12, 2007

I had the following exchange with Carl, as part of my persistent
insistence that there are audible "character families" and
continuities of color/feeling that can't be explained by audibly Just
intervals or approximations of them.

Carl:
Do you have a list of all the character families you've
discovered?

Cameron:

Nope.

Carl:

Do you have anything at all that would enable another person to
actually know what a character family is?

Cameron:

Obviously, and some people knew what I meant from the expression
alone. (snip)
Okay, here's a tuning. If you play in it melodically, it is very
cohesive as far as character, to my ears. Just noodle around over a
couple of octaves, don't need to pay attention to key centers or
whatever, the point is whether or not the colors "go together".

I chose a pretty lumpy tuning to avoid being mislead by a strong
regularity in interval size, and which probably scores disasterously
in Scala's "show data" pageant- not proper, 73-limit...

(snip)

0: 1/1 0.000
1: 73/70 72.650
2: 35/32 155.140
3: 81/70 252.680
4: 729/560 456.590
5: 146/105 570.695
6: 219/140 774.605
7: 105/64 857.095
8: 243/140 954.635
9: 2/1 1200.000

Cameron contining:
I started with one interval and had a synaesthesic
experience, "Gingko!", so that's what I call this
character family. Then I went about by ear, using my working
theories as to what all makes a tuning cohesive as far as character-
the whole thing took about twenty minutes.

If you do agree that it's cohesive in color, tell me why you think
it is- you may have a better explanation than mine. I don't have a
simple explanation, only a working approach. It works nicely, to my
ears, but I could be completely wrong as to why.

-Cameron Bobro

And now that I've seen the Scale Tree of Noble intervals at
Anaphoria, and even know what it is, I went through and find this:

Scale Tree 252.005 cents 252.005
Ginkgo 81/70 252.680

Ginkgo 729/560 456.590
Scale Tree 457.610 cents 457.610

Ginkgo 146/105 570.695
Scale Tree 570.746 cents 570.746

Ginkgo 219/140 774.605
Scale Tree 774.732 cents 774.732

Ginkgo 105/64 857.095 septimal neutral sixth
Scale Tree 857.210 cents 857.210

Scale Tree 954.613 cents 954.613
Ginkgo 243/140 954.635

and
73/70 72.650 4/3 below the 146/105
35/32 155.140 3/2 below the 105/64

Well there's six convergences in the Scale Tree, found by ear.
Maximum difference: 1.019 cents. This is not as impressive as it may
sound, for the convergences in the scale tree are also related to
each by simple Just intervals, so if you get just one or two you can
get other just by going up 9/8 for example and listening if it fits
the characer (surely exactly what I did with the 81/70 and 729/560
for example).

At the time as you can tell if you wade through the ungainly threads,
I thought what I was hearing had to do with some kind of regular
pattern in difference tones or something like that. Didn't know at
all, and certainly didn't think of Phi.

Hopefully it is also clear why I agree with Kraig that the shadows
are part of Just intonation.

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

6/13/2008 3:04:43 AM

> Then maybe I should ask some questions: Which of my explanations
> have contradicted your experience?

Well, the concept of intervals having certain fields of attraction
seems to be solid, but there are some things I've noticed in my
experience of it that differ from the model.

As far as I understand it, the idea is that the user will consciously
perceive an interval as a mistuning of some other interval if the
weaker interval falls into the stronger interval's field of
attraction. This makes sense. But I think that these "fields of
attraction" change depending on what register the interval is in and
depending on how long an interval has been held, to name a few things.

For example, if you go stay on a major triad for a while, and then go
down to a neutral triad (let's say that the neutral third is 11/9),
you will likely hear the neutral triad as having more of a "minor"
quality to it than if you just hit that triad out of the blue. But if
you start on 6/5 and go up to the neutral triad, you'll likely hear it
as having more of a "major" quality to it. You gave a link to the
anchoring effect as an example of why this could be, and it seems
plausible.

An alternative explanation that I've been considering has to do with
the concept of entropy, though possibly not in the same sense as the
harmonic entropy that Paul Erlich wrote about. When you grow used to
that major chord for a while, the amount of "novel information" or
"entropy," as is defined in information theory, steadily declines from
your first exposure to the chord. When you move to the neutral triad,
you hear motion AWAY from the major triad. What is happening, in
effect, is that the field of attraction around the 5/4 has effectively
DECREASED.

Try this: Listen to a major triad with the major third sharp at 400
cents. Then drop the major third to an 11/9 at around 350 cents. That
chord will most likely have a very strong "minor" quality to it, as
the entropy of the new minor chord exceeds the entropy of the old
major chord. You are used to the major chord, and so there is no new
information there. There is information coming in when you hit the
neutral triad: that the triad is both "minor and major." You are used
to the major, and so that field of attraction is redundant - i.e. it
is low entropy. The higher entropy quality that sticks out to you is
the minor quality, which is novel. This effect is accentuated by the
major third being sharp at 400 cents, but it works for the 386 cent
third as well, although you might have to tweak the numbers a bit.

This works even better in reverse. Listen to a 10:12:15 minor triad
for a minute. Then go up to the 11/9. That 11/9 will likely have a
strong "major" feel to it.

You said that Rothenburg spoke of this effect in terms of its melodic
sense, and I think it applies to harmony as well. If you feel that the
scale degree has dropped from M3 to m3, it seems, at least in my
perception, to change the quality of the chord you're on as well,
regardless of the actual just interval.

This might be due to the anchoring effect or it might not be. It might
be a cognitive bias, or it might be a psychoacoustic phenomenon. I'm
not sure. Either way, the way I see it manifesting itself in the
"fields of attraction" model is to have a time component in which the
field of attraction of an interval decreases over time.

This leads to a model in which the right "noble" interval to go to to
really hit that neutral, "gray" sound might be entirely different if
you're going from a major chord to a neutral chord rather than if you
hit the neutral chord right away. I'm not sure how the exact math for
both this and the above time component mentioned would work right now,
especially for the noble interval side of it.

Also...

You are likely to perceive an interval much more likely to be a
mistuning of some other interval if it is in a lower register.

For example, take the 18:22:27 neutral triad again. Play that around
an octave below middle C. For me, the sound of it is, to quote from a
gestalt term, "multistable" - you might hear it flip back and forth
between sounding major and minor. I at least hear it as a flat major
chord mainly, but I can "flip" my perception to hear it as a sharp
minor chord if I try hard enough (or if I play a major chord first).

Now raise it up 3 octaves. For me, I start to hear it as a neutral
triad, with its own color. It isn't so much a major and minor chord as
much as it is a NEUTRAL chord in its own right. Just like we're used
to not being able to play major chords really low on a piano because
they get muddy, we can't play upper-limit chords too low because they
also get muddy. The only difference is that they start to get muddy
much more quickly. Many musicians intuitively know this from that they
can't play all kinds of even 12-tet upper chord extensions really low
- but the same thing also applies to simple triads such as the neutral
triad that are upper limit.

I hypothesize that this has to do with the phantom fundamental of the
chord being below the limit of human hearing -- and the phantom
fundamental of the chord for a major triad is much higher than it is
for the corresponding neutral triad. So there are triads that don't
become resonant until like the 4th or 5th octave of the piano or so.

What is happening is that the field of attraction for 11/9 diminishes
as the register drops, and conversely increases as it increases. Below
a certain threshold, the field of attraction for 11/9 will be
nonexistent. Modeling this behavior as well might make for some
interesting results.

This also makes sense if you listen to a 400-cent 12tet major third on
a piano. When it starts to get low, you really and very obviously hear
it as an out of tune major third. The beating/phantom fundamental
becomes almost untolerable. But as it gets higher, it starts to
develop its own characteristic that is slightly different from a
386-cent major third. The beating has at that point become a
legitimate virtual frequency as it reaches the hearing register - you
can hear it if you try hard enough, and especially if there is
distortion on an instrument playing it. So even irrational intervals
have a phantom fundamental as well.

>> 5) I give up as I am aware there is no point bickering about
>> what is on or off topic, as you used to moderate and likely
>> get to determine these things. i never get to really explain
>> my idea, give up and am frustrated
>
> If you gave up it wasn't until after you outposted everyone
> else by a wide margin. I don't get to determine such things
> by the way but I can tell you that this isn't a gestalt
> psychology mailing list, but that if you have a theory of
> intonation that relies on gestalt psychology you can present
> the theory along with any background you think may be helpful.

It was never my intent to discuss gestalt psychology just for the hell
of it. I'm currently caught up in this endeavor to understand why the
"end appearance" of a piece music is the way it is for a certain
person. It's sort of the same approach that is used in the study of
pedagogy: students will have schemas for things, and you as the
teacher have learn how to to build on those schemas in such a way that
students understand you.

This applies to microtonal music because when I listen to a lot of it,
in terms of what I can digest musically, I don't like a lot of it
right away. The more I get into it, the more I start to become aware
of what otherwise seems like noise and then I can start to hear it
musically. I also notice with that microtonal pieces that -I- like, my
friends often hear it as "noise" in the same way.

Furthermore, they hear pieces in 5-limit JI often as "out-of-tune"
versions of pieces in 12-tet. This applies even if they hear just
straight major chords in certain contexts (the major chord will sound
"flat" to them).

So I'm merely trying to study this issue because I find it
interesting. It isn't really meant to be about gestalt psychology.
It's more about the psychology of music, and for this forum, how it
specifically relates to tuning. And for this forum, I mainly asked
questions about how the psychology of music _relates_ to tuning theory
to see if this field has been really explored yet. It has become
apparent to me that in some places it has, and in others it has not.

>> Most of what you would label the "stratosphere" I would wager are
>> places where I was either first trying to explain a general
>> concept before specifically applying it to music theory or places
>> where I was applying the general concept to music theory before I
>> applied it to tuning theory.
>
> The places I was thinking of where when you made sweeping calls
> for radical reform that are beyond anyone's power to implement.

Then we just disagree on that. I feel strongly that if there were a
formal doctoral thesis on this subject, people would listen. To be
honest, as you know, in academic "music theory/comp" circles many of
the concepts we talk about here are often either unknown or eschewed
in favor of things like "music set theory" and such. Elucidating these
concepts formally might just bring to light things that people don't
realize, and could very well have a positive effect on the way theory
is taught.

I can tell you first-hand that music theory is often taught in schools
in a way that contradicts empirical evidence to the contrary. Proof of
this can be found in the fact that people who are often too obsessed
with theory write profoundly unmusical works, as you yourself stated
above. In fact, there are usually two camps: the people who are overly
obsessed with theory, and the people who react strongly enough against
that camp that they "hate all theory." And then you have those in the
middle who know the theory but acknowledge its flaws. All I propose is
that time be spent on fixing these flaws so that this problem no
longer exists.

In any field, you will have the teachers who can explain extremely
obtuse concepts, such as the uncountability of the reals or the
Jungian collective unconscious or what have you, in a way that makes
students go "aha!" and realize the insight there for themselves. In
all of my time spent in music education, I have never once heard any
theory concept taught that made me go "aha" and gain any significant
insight into the nature of music or sound. I have mainly gained the
"aha" moments from classes in acoustics/psychoacoustics or from
information I've gotten on the internet on tuning theory or from this
very thread. I think that the reason why this is is because common
practice music theory, as it stands and is taught right now, is
basically a mixed up jumble of brilliant psychoacoustic realizations
and "frozen accidents" that are often presented together in a way that
students can't tell which is which. Furthermore, the frozen accidents
often have fake rules applied to them as if they WERE derived from
some legitimate psychoacoustic or acoustic concept. These rules are
often imposed as gospel and the students are graded on them. It's no
wonder everyone hates theory.

Some of the offenders:
1) any concept that treats the diatonic scale as if it were
responsible for music in its entirety
2) any concept that treats music as a function of 12-tet (even IN
12-tet, people don't think in 12-tet until they're forced to)
3) any concept that says anything simply just "sounds good" or "sounds bad"
the list could go on for weeks.

The concepts taught are also usually not applicable to any style of
music except for that common-practice style. So what I was trying to
do in this thread is find a better "core set" of concepts that:

a) makes intuitive sense (e.g. Aha! moments occur upon hearing them)
b) can be applied to music in all sorts of different styles
c) explain musical things in terms of the EFFECTS they will have (i.e.
a 4:5:6:7:9:11 chord will be strongly resonant) rather than that they
just "sound good" or "sound bad"
d) then, from there, work up to the bigger picture of how priming
effects will play into it, how different things can affect the
perception of a chord/tuning/whatever of a listener (which is where
"gestalt psychology" plays a role), how priming effects basically on a
huge scale ARE what musical context is, and so on.
e) and then from THERE, perhaps tie the whole thing together by
studying how people become accustomed to NEW musical phenomena, and
what might cause them to view new musical phenomena as messed up
versions of OLD musical phenomena. This is what David Rothenburg
studied as it relates to scales, and I find his results fairly
revealing. This general field has a huge application in tuning with
regards to how is taught; e.g. it directly relates to how to best work
students into different tunings, which ones might be logical leaps
after 12-tet, etc. In other words, it relates to workshops like the
one you and I were discussing. I just think Rothenburg's results are
the tip of the iceberg.

So I'm trying to tie together a lot of disparate concepts from music
education, acoustics/psychoacoustics, gestalt psychology, music
theory, and so on together to make a better "formalized" music theory
just because the current one legitimately bothers me. Of course, I
can't do that until I actually figure out why three frequencies in a
10:12:15 triad have the quality to them that they do. Why they make
people feel the way they do. Or, maybe a better way to look at it, is
what IS the feeling of a minor chord? Is it that a minor third is
basically an out of tune major third? What is it?

So how this all relates back to tuning is that I lack the knowledge of
what this "core set" of principles might be. I've gotten a pretty good
starting point from this thread, but with regards to the stuff I
posted above there still seem to be a few holes in what I've gotten,
or places where I'm misinterpreting the theory. But we'll see.

Hopefully we're on the same page now though.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/13/2008 3:06:56 AM

> Very right you are. I'm definitely overextending myself.
> I'll shut up now. -Carl

That's quite alright. BTW, if you'd like to learn more about this
stuff, I'd recommend this book "Math for Liberal Arts Majors." You'll
want the 3rd ed.

-Mike

🔗Mike Battaglia <battaglia01@...>

6/13/2008 3:26:06 AM

> Man! You sure are confused. Calculating a mediant with an irrational
> argument is utterly meaningless.

Whoa, calm down. I was trying to go for Cameron's approach:

> One phi-th of the frequency between them is how I do it, try it with
> the golden section both ways and hear what you think.

which doesn't seem to be limited to only rational numbers. The noble
interval between 5/4 and 4/3 sounded much more like a major third than
it did a perfect fourth. I think that being used to a 12-tet major
third means that I am much more used to hearing sharp major thirds as
still being major thirds, and so that might explain it, so to test
this, I wanted to find some "gray" interval between a slightly sharp
major third and a perfect fourth. Being as the approach of using
repeated mediants is useless for irrational numbers, I thought perhaps
people used a noble mean or something. I'm not sure, but it would be
nice to have some equivalent for irrational numbers. Maybe just
running the HE curve is the only way.

> I suggest you go cold-turkey from the list for a while and get some sleep.

Probably sage advice.

> Then read Margo's and my paper on the subject, which URL I emailed you
> as well as posted to the list. And like I said in earlier posts, the
> "grayest" sound may not occur exactly at the noble number frequency
> ratio. It probably occurs at the maximum of harmonic entropy, but
> unfortunately the modelling of that has a free parameter that makes
> the predicted maxima wander around a lot.

Don't remember getting any email from you with the paper. Either way,
I read it, and it certainly makes a lot of sense. Maybe the only way
to get the grayest/most merciful intervals is just to screw around by
ear, I guess.

>> Yeah, well in the US, the _color_ is spelled "gray."
>
> We knew that.

We also spell it "noo" over here. You should come to the states
sometime, you'd probably lyke it.

-Mike

🔗Cameron Bobro <misterbobro@...>

6/13/2008 3:57:16 AM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> > Man! You sure are confused. Calculating a mediant with an
irrational
> > argument is utterly meaningless.
>
> Whoa, calm down. I was trying to go for Cameron's approach:

Haha, I wouldn't recommend my approach- I monkey around by ear then
try to find the most clean way to write it down, looking for patterns.
>
> > One phi-th of the frequency between them is how I do it, try it
with
> > the golden section both ways and hear what you think.

And I guess I'm just really really "lucky" as my wrong ways get me so
close... Get the Scale Tree .pdf at anaphoria and you're set. I'm
tickled pink about it.

Anyway there are more convergences in the area you're looking at, see
page 19. The one you're looking for is between 56/43 and 73/56, the
same one I was listening for ("a hair above 13/10", I've described it
with a cent or two with number of different intervals in my long
search to pin it down).

🔗Carl Lumma <carl@...>

6/13/2008 8:24:52 AM

Mike wrote:
> > Then maybe I should ask some questions: Which of my
> > explanations have contradicted your experience?
>
> As far as I understand it, the idea is that the user will
> consciously perceive an interval as a mistuning of some other
> interval if the weaker interval falls into the stronger
> interval's field of attraction. This makes sense. But I
> think that these "fields of attraction" change depending on
> what register the interval is in and depending on how long an
> interval has been held, to name a few things.

If fields of attraction are related to the virtual pitch
mechanism, they should cease to operate in the higher
registers, as groups of neurons responsible for periodicity
counting can only fire up to about 4KHz.

> For example, if you go stay on a major triad for a while, and
> then go down to a neutral triad (let's say that the neutral
> third is 11/9), you will likely hear the neutral triad as having
> more of a "minor" quality to it than if you just hit that triad
> out of the blue. But if you start on 6/5 and go up to the neutral
> triad, you'll likely hear it as having more of a "major" quality
> to it. You gave a link to the anchoring effect as an example of
> why this could be, and it seems plausible.
>
> An alternative explanation that I've been considering has to do
> with the concept of entropy, though possibly not in the same sense
> as the harmonic entropy that Paul Erlich wrote about. When you
> grow used to that major chord for a while, the amount of "novel
> information" or "entropy," as is defined in information theory,
> steadily declines from your first exposure to the chord. When you
> move to the neutral triad, you hear motion AWAY from the major
> triad. What is happening, in effect, is that the field of
> attraction around the 5/4 has effectively DECREASED.

That sounds like a plausible explanation for the anchoring effect.
I don't know if it's related to fields of attraction.

> You said that Rothenburg spoke of this effect in terms of its
> melodic sense,

I did? I don't recall anything in Rothenberg about this effect.
How did you make out with the papers btw?

> You are likely to perceive an interval much more likely to be a
> mistuning of some other interval if it is in a lower register.
>
> For example, take the 18:22:27 neutral triad again. Play that
> around an octave below middle C. For me, the sound of it is, to
> quote from

Yeah.

> I hypothesize that this has to do with the phantom fundamental
> of the chord being below the limit of human hearing

I don't think so. The virtual fundamental will by definition
always be in the range of hearing since it is something we hear.

> What is happening is that the field of attraction for 11/9
> diminishes as the register drops, and conversely increases as
> it increases.

What I think: the probability of hearing a neutral triad is
almost always lower than the probability of hearing a major
triad, even if the stimulus is 1/1-11/9-3/2 in JI. When you
raise the pitch of the stimulus the virtual pitch mechanism
gives up the ghost and you no longer hear the identity of
the triad at all, but instead hear only the lack of roughness,
which is even more of a lack at in register due to the
narrowing of the critical band there. So roughness dominates
consonance in higher registers.

> This also makes sense if you listen to a 400-cent 12tet major
> third on a piano. When it starts to get low, you really and
> very obviously hear it as an out of tune major third. The
> beating/phantom fundamental becomes almost untolerable.

What's happening the partials in the complex start to fall
within the critical band, which is quite large in the lower
register. A just 5/4 has the same problem as 400 cents.

> Some of the offenders:
> 1) any concept that treats the diatonic scale as if it were
> responsible for music in its entirety
> 2) any concept that treats music as a function of 12-tet (even IN
> 12-tet, people don't think in 12-tet until they're forced to)
> 3) any concept that says anything simply just "sounds good" or
> "sounds bad"
> the list could go on for weeks.

You won't find many on this list who disagree with you here.

> Hopefully we're on the same page now though.

So far you've got me, Dave, and Cameron all telling you to slow
down and study some of the materials you've been given.

I don't know how old you are, but you sound just like me when
I was 20 -- we've got to reform education! Why isn't this
reforming education?? I sent letters to the JI Network proposing
we open a school (was shot down hard), moved to California to
meet and study with microtonalists (big success), called faculty
at Berkeley and Mills and urged them to buy a generalized
keyboard (shot down hard), built a 15-limit slide guitar to
demonstrate JI to students (before cheap microtonal synths were
readily available), became a barbershop singer and went
to Harmony College to see what was going on there (they know
quite a bit about JI). So more power to you.

Going back to the two sentences of mine that spawned this
gigantic message, I don't see a single example of an
explanation I'd given you that your experience contradicts.
So I'm still waiting for that.

-Carl

🔗Carl Lumma <carl@...>

6/13/2008 8:40:13 AM

Snap.

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Very right you are. I'm definitely overextending myself.
> > I'll shut up now. -Carl
>
> That's quite alright. BTW, if you'd like to learn more about this
> stuff, I'd recommend this book "Math for Liberal Arts Majors." You'll
> want the 3rd ed.
>
> -Mike

🔗Michael Sheiman <djtrancendance@...>

6/13/2008 10:46:42 AM

This is mind-bogglingly useful.
I recently came up with a tuning I just posted using square roots IE

1
1.11803 = sqrt(5/4) or 1.1547 = sqrt(4/3)
1.224744 = sqrt(3/2)
1.29099444 = sqrt(5/3)

1.41421 = sqrt(2)
1.5 = 3/2

1.66666 = 5/3
1.7320508 = sqrt(3)
1.87082 = sqrt(3.5) = sqrt(7/2)

   That goes across MANY of the same tones as the Gingko "character scale" you all
are discussing.
   I think one thing is blatantly clear, though. High consonance alone, obeying critical band limits, matching harmonics....does not make a scale work emotionally by itself.
   There is another "character" factor needed to make a scale work and, coincidentally,
I think the fact we both arrived at 9-note scales with very similar ratios shows huge promise.

-Michael
*****************original post************************************

-----"Okay, here's a tuning. If you play in it melodically, it is very

cohesive as far as character, to my ears. Just noodle around over a

couple of octaves, don't need to pay attention to key centers or

whatever, the point is whether or not the colors "go together".

I chose a pretty lumpy tuning to avoid being mislead by a strong

regularity in interval size, and which probably scores disasterously

in Scala's "show data" pageant- not proper, 73-limit...

(snip)

0: 1/1 0.000

1: 73/70 72.650

2: 35/32 155.140

3: 81/70 252.680

4: 729/560 456.590

5: 146/105 570.695

6: 219/140 774.605

7: 105/64 857.095

8: 243/140 954.635

9: 2/1 1200.000_
------------

,_._,___

🔗George D. Secor <gdsecor@...>

6/13/2008 12:15:58 PM

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> > The diatonic semitone in 19-ET is larger than in 12-ET and much
more
> > so than that of 17-ET. So there's actually a greater distance to
be
> > traversed, which one might think of as *more* movement. But I
think
> > what you're getting at is that, because of the lower leading tone
of
> > 19-ET, the greater distance results in less *attraction* (think
of a
> > sort of tonal gravity) to its resolution to the neighboring tonic.
>
> Well, I was talking mainly about chordal root movement, which is
> usually by fifth. The fifth of 19-tet is so much flatter than 12-tet
> that I find the root movement to be a bit "compressed" sounding, as
if
> it doesn't move as much as 12's (because it doesn't). This could
give
> a very stagnant or relaxed feel, I suppose, depending on how you
look
> at it. But I think what I was getting at was what you said - the
15/8
> resolving to 2/1 doesn't work very well, and neither does 19-tet's
> even flatter interval. Perhaps there's some kind of noble
> interval/gray tone that needs to be hit to maximize the effect?

Try ~56/29 at 1139 cents, which is the 2nd highest HE peak in the
data in file raw-entr.xls, found here:
/tuning/files/secor/
Paul Erlich ran this for me as a Vos-curve with n*d<65536, s=1%:
/harmonic_entropy/topicId_652.html#667
for which I asked for raw data in increments of 1 cent, which Paul
supplied:
/harmonic_entropy/topicId_652.html#669
from which the raw figures have been transferred to the above
spreadsheet.

The raw entropy numbers are in column C, for intervals ranging
between a unison and octave (in column A). (I was experimenting with
a formula to convert these numbers to reflect consonance relative to
1:1 in Col. B, which you can ignore.) Local maxima (and minima) are
identified in col. D.

To calculate metastable intervals, enter ratios in the cyan-colored
cells.

> >...
> > There are more details about this (and also mention of the noble
> > mediant) here:
> > /tuning/topicId_73794.html#73816
> > as well as links to Paul's and my actual discussion (on the
harmonic
> > entropy group) and to the raw data that resulted.
>
> I have to get this harmonic entropy concept down a little bit
> better... I'll read. Thanks.

That will give you some idea of how Paul & I arrived at the raw
data. You can also browse thru some of the other messages there.
Posting is rather sporadic, and I haven't looked there for quite a
long time.

> >...
> > I find something rather interesting about 19-ET, that, in spite of
> > its many advantages -- ... -- it continues to engender
> > strong feelings of acceptance or rejection. ...
>
> Oh no, I really like 19-tet. It just took me a while to get used to
> it.

I agree. Some tunings sound good right out of the box, but for most
of us it takes some time to get acclimated to the melodic properties
of 19. Some like it right away, but some others never take to it.

> At first, I thought it sounded... unsettling, and I think it's
> because of the narrow fifths and major thirds, so that chord
movements
> sounded like they were lacking something. On the other hand, 17-
tet's
> wider intervals made it seem like they were "accentuated," so it
was a
> big hit right away. That's the best I can describe it. Nowadays, I
> like both 19-tet and 17-tet, and as I said before, I feel like 19-
tet
> is like the night/day "counterpart" to 12-tet and in some ways 17 as
> well.

I agree.

> > A person from another part of the world who speaks English will
> > probably pronounce vowels somewhat differently than you prefer,
but
> > that's part of what makes up "culture". If you spend a few weeks
in
> > 19-tone land, you may discover (as Ivor Darreg did) that a single
> > degree of 19 is a melodic interval with a lot of "zonk" that can
be
> > exploited very effectively (e.g., in MOS scales of the magic,
hanson,
> > or keemun generators).
>
> Yeah, that's what I've come to realize... I personally find that
music
> written specifically for 19-tet can sound amazing, much better imo
> than music written for 12-tet or 1/6 comma meantone or something
that
> is being "re-done" in 19-tet as an exercise. I haven't heard any
> Renaissance or Baroque-era music in 19-tet, but I can imagine that
> that would likely sound pretty decent in 19-tet as well, much better
> than say, Debussy or something.

Go to:
http://www.akjmusic.com/works.html
and listen to "John Bull - Ut,re,mi,fa,sol,la" (at bottom, right
side), which is in 19-ET.

> Actually, I was listening to
> Blackwood's 19-tet piece off of that album (not the "fanfare" that
is
> usually attached to the beginning), and up until he goes into
> full-blown xenharmonic mode, I can tell why you like the character
of
> it for that kind of music - it is fairly relaxing.
>
> I was mainly just describing 17 as potentially a good temperament to
> "hook" someone into microtonal music, especially if the chords are
> finessed just right so that they don't sound particularly weird to
> someone with a 12-tet vocabulary.

> >...
> >> > In case you decide to read the entire paper (or to entice you
to do
> >> > so), I also made a 17-tone jazz excerpt using the 9-tone scale
> >> > (subset of 17) that I described near the bottom of the 22nd
page
> >> > (numbered as p. 76):
> >> > http://xenharmony.wikispaces.com/space/showimage/17WTjazz.mp3
> >>
> >> Haha, wow. Neutral moondance. Dusk-dance? Twilight perhaps?
> > Interesting.
> >
> > I though it would be good theme music for a TV night-life
detective
> > series. Although the neutral intervals are unmistakable, the tonic
> > triad is a 6:7:9 (subminor). One property of the tuning that I
like
> > is that 6:7:9:11 and 7:9:11:13 (tempered) chords can be
transformed
> > into one another simply by changing the two inner tones. (There
> > aren't many tunings in which 11:12, 12:13, and 13:14 are all
> > represented by the same interval.)
>
> Just out of curiosity, do you have a scala file for this well
temperament?

Yep. Setting the notation for 17-equal should work just fine.

! secor_17wt.scl
!
George Secor's well temperament with 5 pure 11/7 and 3 near just
11/6
17
!
66.74120
144.85624
214.44090
278.33864
353.61023
428.88181
492.77955
562.36421
640.47925
707.22045
771.11819
849.23324
921.66136
985.55910
1057.98722
1136.10226
2/1

> >...
> > There's also the ambiguity of multiple harmonic roles for the
various
> > intervals: is 6deg17 in a 2-voice texture going to be heard as a
> > tempered 7:9 or 11:14? Will 15deg (a neutral 6th) be interpreted
as
> > 6:11 or 7:13 (or possibly 13:24)? Will 14deg be 4:7 or 9:16? It
> > will have to be determined by the musical context, e.g., the scale
> > (if any) that the composer is using.
> >
> > One reason that I devised 17-tone and 19-tone well-temperaments
was
> > to tweak the intervals by a few cents so as to influence how
they're
> > more likely to be interpreted in various keys. One problem with
19-
> > ET is that 6:7 and 7:8 are represented by the same interval. For
> > example, my 19-WT tips the balance in such a way that C:D# sounds
> > more like 6:7 but D#:F more like 7:8.
>
> I would really like to hear this well temperament. Do you have a
scala
> file or something of the like for it?

! secor_19wt.scl
!
George Secor's 19-tone proportional-beating (5/17-comma) well
temperament
19
!
69.41306
131.54971
191.26088
260.67394
317.95963
382.52175
451.93481
504.36956
573.78263
638.34474
695.63044
765.04350
824.75467
886.89131
956.30438
1011.16460
1078.15219
1145.13978
2/1

> >> Once you meditate on
> >> a neutral triad and grow used to it, however, you start to pick
up on
> >> the resonance of the chord and hear it in a harmonic context.
However,
> >> the average listener who hasn't been accustomed to the sound
might be
> >> confused and hear it as a mistuned major or minor chord, since
that's
> >> the only other thing they have to go by.
> >
> > Yep. That's why I've gravitated toward isoharmonic chords when
using
> > neutral intervals. They're consonant in the sense that you can
> > easily distinguish ones that are in JI from ones that are even
> > moderately tempered, because disturbances between combinational
tones
> > are minimized. With 18:22:27, OTOH, there are no prominent beats
to
> > distinguish it from 26:32:39, or from anything in-between.
>
> Yeah, definitely. Like I was sayin above, I really don't find
18:22:27
> to be of much use unless it's played at a high enough register that
> the "Rameau" tone is perceivable. 9:11:13, on the other hand,
doesn't
> have that problem.

Yes, a higher pitch does make larger-number ratios sound more
consonant.

> I make an exception for the gray tone between 5/4 and 6/5... At
around
> 356 cents, I find a triad with that and 3/2 in it to serve a musical
> function all of its own.

That's a local HE maximum, close to 27/22.

> >> But just like people did eventually get used to the sound of
major
> >> chords and perfect fifths, I think there are probably clever
ways to
> >> find intervals that a listener will most likely hear as new and
novel
> >> rather than weird and disturbing. For some reason, for people
> >> accustomed to 12-tet, the 7/6 subminor third is usually such an
> >> "easy-to-grasp" interval, although a 9/7 supermajor third doesn't
> >> share that characteristic and is often heard simply as a sharp
5/4.
> >> Why this is, I haven't the foggiest, although it might be
interesting
> >> to study.
> >
> > For 6:7:9 vs. 14:18:21 (same intervals in reverse order), e.g., a
lot
> > of it has to do with the relationships between combinational tones
> > (particularly first-order difference tones).
>
> What do you mean here? This seems like precisely the answer I'm
looking for.

For 6:7:9 the first order difference tones are 1, 2, and 3. For
14:18:21 they're 4, 3, and 7. The former are in much simpler
relationships to one another than the latter. Any isoharmonic chord,
e.g. 10:13:16:19 or 18:22:27:32, is going to be distinguishable from
its mistuning, because it's easy to hear whether or not the first-
order difference tones exactly coincide. It's not a matter of
actually hearing the difference tones themselves, but rather that you
can hear a certain smoothness when they coincide and disturbances
(similar to beating) when they don't. These aren't as consonant as
chords with simpler ratios, but they're musically useful because they
exhibit what I would call difference-tone stabilization.

> >> Furthermore, I hypothesize that just like perfect fifths can be
played
> >> lower than major thirds and still sound good (due to that phantom
> >> fundamental dropping off the bottom of hearing range sooner for
the
> >> major thirds), there will be triads that sound muddy straight up
until
> >> the midrange of the piano, although I don't know what those
triads are
> >> yet.

When you play thirds in the bass range, the beat rate between the
fundamental frequencies is slow enough for the individual beats to be
heard, and it's the beating that produces the muddiness.

--George

🔗Cameron Bobro <misterbobro@...>

6/14/2008 6:17:42 AM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>

>
> And now that I've seen the Scale Tree of Noble intervals at
> Anaphoria, and even know what it is, I went through and find this:
>
>
> Scale Tree 252.005 cents 252.005
> Ginkgo 81/70 252.680
>
> Ginkgo 729/560 456.590
> Scale Tree 457.610 cents 457.610
>
> Ginkgo 146/105 570.695
> Scale Tree 570.746 cents 570.746
>
> Ginkgo 219/140 774.605
> Scale Tree 774.732 cents 774.732
>
> Ginkgo 105/64 857.095 septimal neutral sixth
> Scale Tree 857.210 cents 857.210
>
> Scale Tree 954.613 cents 954.613
> Ginkgo 243/140 954.635
>
>
> and
> 73/70 72.650 4/3 below the 146/105
> 35/32 155.140 3/2 below the 105/64

Correction on the last two. I was trying to think of the most simple
explanation vis a vis the Scale Tree, and I remembered that I've been
continually working for the last two years now with 11, 22, and 23
o- and u-' tonalities.

So it seems plausible that when I was making Ginkgo it was a matter
of floating those diamonds, so to speak, and that's how I stumbled on
the scale. So I just checked-

Noble Mediant of 23/22 and 11/10...........71.855
Ginkgo..........................73/70 .....72.650

Ginkgo........35/32............155.140
NM of 11/10 and 1/1............155.819

It looks like the whole dang tuning might be just Noble Mediants
between 22 and 23 diamonds.

The next step is obvious- to figure out the the NMs between 22 and 23
diamonds, 22 and 23 o- and u-.

I'd like to ask Dave Keenan to check some of these out if he has the
time, errors in my reckonings are far from impossible. :-)

-Cameron Bobro

🔗Dave Keenan <d.keenan@...>

6/14/2008 9:42:30 PM

Hi Cameron,

Thanks for inviting me to check your numbers.

Those you have read from
http://www.anaphoria.com/sctree.PDF
you have correctly converted to cents.

However, we should note that Erv's scale-tree gives 256 noble numbers
within the octave, so on average they are only 4.7 cents apart, and
therefore you will always find one of these noble numbers within a few
cents of almost anything.

You can go on adding more levels to the scale-tree indefinitely,
doubling the number of nobles each time.

Erv probably took the tree out to 11 levels
(a) to include 11/10 for use as a frequency ratio, and
(b) for the tree's other use, in finding scale generators. For this
purpose the denominators of the ratios can be read as -EDOs, and the
numerator as the number of degrees of that EDO that the generator
corresponds to.

But I severely doubt that all of the given 256 noble frequency ratios
are audibly shadowy or gray.

For a noble number to correspond to a shadow interval, I think it has
to be the noble mediant of two just intervals, i.e. two intervals that
can be tuned by ear through the locking-in of partials, i.e. two
ratios which are sufficiently simple, say n*d <= 120. So I'd expect
maybe only about 20 of the simplest nobles to correspond to shadow
regions, within the octave.

In other words, I'd suggest only those nobles whose dashed lines
originate from blobs above about level 7 of the scale tree (the level
containing 7/6 11/9 14/11 13/10 15/11 18/13 17/12 13/9 19/12 21/13
18/11 17/10 19/11 16/9 11/6). That's only one more level than is shown
on page 1. Except that close to the unison and octave you might go
down another level or two.

I note that there is no point in restricting ourselves to the first
octave when calculating nobles that may correspond to shadow
intervals. The octave extensions and inversions of noble numbers are
not (in general) noble numbers. The noble numbers above 2/1 are quite
independent of those below.

Your calculation of the noble mediant of 1/1 and 11/10 below is quite
correct. It is also the noble mediant of 11/10 and 12/11.

However something must have gone wrong in your calculation of the
phi-weighted mediant of 11/10 and 23/22 since your result is not even
between those two ratios.

I say "phi-weighted mediant" because in this case, even the correct
result does not correspond to a noble number. You can see this by
applying the cross-multiplication check I mentioned. 11*22 = 242,
10*23 = 230. They differ by more than 1, so this is not noble.

To get an idea of which nobles might be shadows, I suggest looking at
this Harmonic Entropy chart that Paul Erlich calculated based on
George Secor's requirements.
/tuning/files/dyadic/secor4.gif

The data for this is in an Excel spreadsheet at
/tuning/files/Secor/raw-entr.xls
with the maxima (to the nearest cent) labelled, and the minima
labelled with their ratios.

Of course the ears must be the final arbiter, but I don't find that
any of the Ginkgo intervals from the 1/1 are "explained" by the noble
numbers you gave, as these are too complex.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
>
> >
> > And now that I've seen the Scale Tree of Noble intervals at
> > Anaphoria, and even know what it is, I went through and find this:
> >
> >
> > Scale Tree 252.005 cents 252.005
> > Ginkgo 81/70 252.680
> >
> > Ginkgo 729/560 456.590
> > Scale Tree 457.610 cents 457.610
> >
> > Ginkgo 146/105 570.695
> > Scale Tree 570.746 cents 570.746
> >
> > Ginkgo 219/140 774.605
> > Scale Tree 774.732 cents 774.732
> >
> > Ginkgo 105/64 857.095 septimal neutral sixth
> > Scale Tree 857.210 cents 857.210
> >
> > Scale Tree 954.613 cents 954.613
> > Ginkgo 243/140 954.635
> >
> >
> > and
> > 73/70 72.650 4/3 below the 146/105
> > 35/32 155.140 3/2 below the 105/64
>
> Correction on the last two. I was trying to think of the most simple
> explanation vis a vis the Scale Tree, and I remembered that I've been
> continually working for the last two years now with 11, 22, and 23
> o- and u-' tonalities.
>
> So it seems plausible that when I was making Ginkgo it was a matter
> of floating those diamonds, so to speak, and that's how I stumbled on
> the scale. So I just checked-
>
> Noble Mediant of 23/22 and 11/10...........71.855
> Ginkgo..........................73/70 .....72.650
>
> Ginkgo........35/32............155.140
> NM of 11/10 and 1/1............155.819
>
> It looks like the whole dang tuning might be just Noble Mediants
> between 22 and 23 diamonds.
>
> The next step is obvious- to figure out the the NMs between 22 and 23
> diamonds, 22 and 23 o- and u-.
>
> I'd like to ask Dave Keenan to check some of these out if he has the
> time, errors in my reckonings are far from impossible. :-)
>
> -Cameron Bobro
>

🔗Dave Keenan <d.keenan@...>

6/14/2008 11:40:41 PM

--- I wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@>
> > wrote:
> >
> > > Interesting. I actually posted the wrong number - I was looking at
> > 366
> > > cents, which doesn't have any noble anything near it. It had the
> > > feeling of slightly major, but musically gray at the same time. I'm
> > > not sure what that's about.
> >
> > It's right there at the inversion of 1 phi-th of the octave.
>
> That's not a noble frequency ratio. That's a noble fraction of an
> octave, considered logarithmically.
>
> That's the other way of using noble numbers that Kraig and I were
> talking about. It doesn't relate to harmony, but to scale generators
> for melodic purposes. It has no necessary relationship to coincidence
> of partials or the lack thereof.

That was wrong. But the thing that caused my confusion there, probably
confused Mike Battaglia too.

When you say "1 phi-th of the octave" the obvious interpretation seems
to me to be 1200 * 1/phi ~= 742 cents. That would be the "other way"
of using nobles (for melody, rather than harmony).

But you seem to mean the phi-weighted (or noble) mediant of 1/1 and
2/1. In other words

1 * 2*phi
---------
1 * 1*phi

which reduces to simply phi which, as a frequenct ratio, corresponds
to 833 cents.

So the 367 cents interval could better have been described as "the
octave inversion of phi".

You're right that it is not noble, but it wouldn't surprise me if it
was semi-noble in some mathematical sense (which I can't articulate).

Here are the 31 noble intervals up to level 7 of the scale-tree, to
the nearest cent, in order of increasing complexity (not limited to
the first octave).

Golden
833 narrow neutral sixth

Silver
2226 narrow neutral 14th
560 narrow augmented fourth

Titanium
2649
1503 narrow minor tenth
943 narrow subminor seventh
422 narrow supermajor third

Chrome
2988
2109 narrow supermajor 13th
1735 narrow super 11th
1424 narrow supermajor 9th
1002 minor seventh
792 narrow minor sixth
607 narrow diminished fifth or tritone
339 narrow neutral third

Nickel (of doubtful use )
3272
2558
2276 major 14th
2055 neutral 13th
1772 narrow augmented 11th
1641 narrow sub 11th
1530 narrow neutral 10th
1378 narrow major 9th
1039 narrow neutral seventh
923 narrow supermajor sixth
849 neutral sixth
771 subminor sixth
630 wide diminished fifth
541 narrow super fourth
448 narrow sub fourth
284 wide subminor third

Copper
... unlikely to be near the centre of any audibly shadowy/gray regions.

See http://en.wikipedia.org/wiki/Galvanic_series
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
http://dkeenan.com/Music/IntervalNaming.htm

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/15/2008 1:32:20 AM

if this list can talk about ET exceeding 256 i see no reason to limit the discussion of noble mediant a priori. It is just as much a valid continuum worthy of study as any other.
The only correct attitudo wecan haveis that we don't know at the moment.
HE has not proven itself as valid from my perspective, i am sorry. My problems with it which i posted maybe two post ago have not been dealt with or even acknowledged. I can take it that there is more interest in preserving this monumental tower regardless of how many examples can be put forth that it doesn't hold up.
I repeat why does Metaslendro taken to 12 pitches sound more consonant than 12 ET if i play all the pitches, even though is closer to simpler ratios and Meta Slendro closer to supposed more 'dissonant' points .
minor points might be why does the 7-9-11 sound so consonant then,
or why does a C6 chord sound more consonant that a C triad to many people.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Cameron,
>
> Thanks for inviting me to check your numbers.
>
> Those you have read from
> http://www.anaphoria.com/sctree.PDF <http://www.anaphoria.com/sctree.PDF>
> you have correctly converted to cents.
>
> However, we should note that Erv's scale-tree gives 256 noble numbers
> within the octave, so on average they are only 4.7 cents apart, and
> therefore you will always find one of these noble numbers within a few
> cents of almost anything.
>
> You can go on adding more levels to the scale-tree indefinitely,
> doubling the number of nobles each time.
>
> Erv probably took the tree out to 11 levels
> (a) to include 11/10 for use as a frequency ratio, and
> (b) for the tree's other use, in finding scale generators. For this
> purpose the denominators of the ratios can be read as -EDOs, and the
> numerator as the number of degrees of that EDO that the generator
> corresponds to.
>
> But I severely doubt that all of the given 256 noble frequency ratios
> are audibly shadowy or gray.
>
> For a noble number to correspond to a shadow interval, I think it has
> to be the noble mediant of two just intervals, i.e. two intervals that
> can be tuned by ear through the locking-in of partials, i.e. two
> ratios which are sufficiently simple, say n*d <= 120. So I'd expect
> maybe only about 20 of the simplest nobles to correspond to shadow
> regions, within the octave.
>
> In other words, I'd suggest only those nobles whose dashed lines
> originate from blobs above about level 7 of the scale tree (the level
> containing 7/6 11/9 14/11 13/10 15/11 18/13 17/12 13/9 19/12 21/13
> 18/11 17/10 19/11 16/9 11/6). That's only one more level than is shown
> on page 1. Except that close to the unison and octave you might go
> down another level or two.
>
> I note that there is no point in restricting ourselves to the first
> octave when calculating nobles that may correspond to shadow
> intervals. The octave extensions and inversions of noble numbers are
> not (in general) noble numbers. The noble numbers above 2/1 are quite
> independent of those below.
>
> Your calculation of the noble mediant of 1/1 and 11/10 below is quite
> correct. It is also the noble mediant of 11/10 and 12/11.
>
> However something must have gone wrong in your calculation of the
> phi-weighted mediant of 11/10 and 23/22 since your result is not even
> between those two ratios.
>
> I say "phi-weighted mediant" because in this case, even the correct
> result does not correspond to a noble number. You can see this by
> applying the cross-multiplication check I mentioned. 11*22 = 242,
> 10*23 = 230. They differ by more than 1, so this is not noble.
>
> To get an idea of which nobles might be shadows, I suggest looking at
> this Harmonic Entropy chart that Paul Erlich calculated based on
> George Secor's requirements.
> /tuning/files/dyadic/secor4.gif > </tuning/files/dyadic/secor4.gif>
>
> The data for this is in an Excel spreadsheet at
> /tuning/files/Secor/raw-entr.xls > </tuning/files/Secor/raw-entr.xls>
> with the maxima (to the nearest cent) labelled, and the minima
> labelled with their ratios.
>
> Of course the ears must be the final arbiter, but I don't find that
> any of the Ginkgo intervals from the 1/1 are "explained" by the noble
> numbers you gave, as these are too complex.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "Cameron Bobro" <misterbobro@...> wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "Cameron Bobro" <misterbobro@>
> >
> > >
> > > And now that I've seen the Scale Tree of Noble intervals at
> > > Anaphoria, and even know what it is, I went through and find this:
> > >
> > >
> > > Scale Tree 252.005 cents 252.005
> > > Ginkgo 81/70 252.680
> > >
> > > Ginkgo 729/560 456.590
> > > Scale Tree 457.610 cents 457.610
> > >
> > > Ginkgo 146/105 570.695
> > > Scale Tree 570.746 cents 570.746
> > >
> > > Ginkgo 219/140 774.605
> > > Scale Tree 774.732 cents 774.732
> > >
> > > Ginkgo 105/64 857.095 septimal neutral sixth
> > > Scale Tree 857.210 cents 857.210
> > >
> > > Scale Tree 954.613 cents 954.613
> > > Ginkgo 243/140 954.635
> > >
> > >
> > > and
> > > 73/70 72.650 4/3 below the 146/105
> > > 35/32 155.140 3/2 below the 105/64
> >
> > Correction on the last two. I was trying to think of the most simple
> > explanation vis a vis the Scale Tree, and I remembered that I've been
> > continually working for the last two years now with 11, 22, and 23
> > o- and u-' tonalities.
> >
> > So it seems plausible that when I was making Ginkgo it was a matter
> > of floating those diamonds, so to speak, and that's how I stumbled on
> > the scale. So I just checked-
> >
> > Noble Mediant of 23/22 and 11/10...........71.855
> > Ginkgo..........................73/70 .....72.650
> >
> > Ginkgo........35/32............155.140
> > NM of 11/10 and 1/1............155.819
> >
> > It looks like the whole dang tuning might be just Noble Mediants
> > between 22 and 23 diamonds.
> >
> > The next step is obvious- to figure out the the NMs between 22 and 23
> > diamonds, 22 and 23 o- and u-.
> >
> > I'd like to ask Dave Keenan to check some of these out if he has the
> > time, errors in my reckonings are far from impossible. :-)
> >
> > -Cameron Bobro
> >
>
>

🔗Charles Lucy <lucy@...>

6/15/2008 8:06:43 AM

This C6 and C Major con/dissonance thread:

Here is a theory from a scalecoding P.O.V. for you:

C Major is C G * * E = 4/34/1

A minor 7 is C G * A E = 4/3/4

C6 is C G * A E = 4/3/1

Considering a contiguous chain of four steps of fifths:

1) when you sound C Major you are excluding the notes in the 3rd and 4th positions, with the tonic in the 1st position.

2) when you sound C6 or Am7 you are only excluding the note in the 3rd position, and the tonic is either: C (first position for C6) or A (fourth position) if considered to be A

So it is a matter of how you hear it as harmony and its musical context.

If you are expecting a "fuller chord" - ; you would expect the C6 or Am7; and hear the C major triad as missing something.

If it is played in isolation you would be most likely to hear the C6/Am7 chord as an extension of an A minor with a flattened (dominant for the traditionalists) seventh, as this is a more traditional usage and way of spelling these four notes played together.

Considering it as a C6 is likely to be more "modern" and uses a spelling more likely to be hear in a "jazz" setting.

It all depends upon the context.

If you want to get into the geometry involved and actual hear how it sounds, go to this page and download the Mac application from the link below the diagram, so that you can move around the topology with you Mac, in three dimensions to get a more complete appreciation of it.

Select C6 and C Major from the pulldown menus to display the visuals and you can also sound either of the chords and/or the individual notes, and see their positions around the spiral.

http://www.lucytune.com/new_to_lt/recipe.html

If you are still living in the single OS (M$) dark ages, and want to see/hear it; you'll have to email me to make a Qucktime movie of it for you or borrow a better computer;-)

On 15 Jun 2008, at 09:32, Kraig Grady wrote:

> if this list can talk about ET exceeding 256 i see no reason to limit
> the discussion of noble mediant a priori. It is just as much a valid
> continuum worthy of study as any other.
> The only correct attitudo wecan haveis that we don't know at the > moment.
> HE has not proven itself as valid from my perspective, i am sorry. My
> problems with it which i posted maybe two post ago have not been dealt
> with or even acknowledged. I can take it that there is more interest > in
> preserving this monumental tower regardless of how many examples can > be
> put forth that it doesn't hold up.
> I repeat why does Metaslendro taken to 12 pitches sound more consonant
> than 12 ET if i play all the pitches, even though is closer to simpler
> ratios and Meta Slendro closer to supposed more 'dissonant' points .
> minor points might be why does the 7-9-11 sound so consonant then,
> or why does a C6 chord sound more consonant that a C triad to many > people.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://> anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Dave Keenan wrote:
> >
> > Hi Cameron,
> >
> > Thanks for inviting me to check your numbers.
> >
> > Those you have read from
> > http://www.anaphoria.com/sctree.PDF <http://www.anaphoria.com/sctree.PDF> >
> > you have correctly converted to cents.
> >
> > However, we should note that Erv's scale-tree gives 256 noble > numbers
> > within the octave, so on average they are only 4.7 cents apart, and
> > therefore you will always find one of these noble numbers within a > few
> > cents of almost anything.
> >
> > You can go on adding more levels to the scale-tree indefinitely,
> > doubling the number of nobles each time.
> >
> > Erv probably took the tree out to 11 levels
> > (a) to include 11/10 for use as a frequency ratio, and
> > (b) for the tree's other use, in finding scale generators. For this
> > purpose the denominators of the ratios can be read as -EDOs, and the
> > numerator as the number of degrees of that EDO that the generator
> > corresponds to.
> >
> > But I severely doubt that all of the given 256 noble frequency > ratios
> > are audibly shadowy or gray.
> >
> > For a noble number to correspond to a shadow interval, I think it > has
> > to be the noble mediant of two just intervals, i.e. two intervals > that
> > can be tuned by ear through the locking-in of partials, i.e. two
> > ratios which are sufficiently simple, say n*d <= 120. So I'd expect
> > maybe only about 20 of the simplest nobles to correspond to shadow
> > regions, within the octave.
> >
> > In other words, I'd suggest only those nobles whose dashed lines
> > originate from blobs above about level 7 of the scale tree (the > level
> > containing 7/6 11/9 14/11 13/10 15/11 18/13 17/12 13/9 19/12 21/13
> > 18/11 17/10 19/11 16/9 11/6). That's only one more level than is > shown
> > on page 1. Except that close to the unison and octave you might go
> > down another level or two.
> >
> > I note that there is no point in restricting ourselves to the first
> > octave when calculating nobles that may correspond to shadow
> > intervals. The octave extensions and inversions of noble numbers are
> > not (in general) noble numbers. The noble numbers above 2/1 are > quite
> > independent of those below.
> >
> > Your calculation of the noble mediant of 1/1 and 11/10 below is > quite
> > correct. It is also the noble mediant of 11/10 and 12/11.
> >
> > However something must have gone wrong in your calculation of the
> > phi-weighted mediant of 11/10 and 23/22 since your result is not > even
> > between those two ratios.
> >
> > I say "phi-weighted mediant" because in this case, even the correct
> > result does not correspond to a noble number. You can see this by
> > applying the cross-multiplication check I mentioned. 11*22 = 242,
> > 10*23 = 230. They differ by more than 1, so this is not noble.
> >
> > To get an idea of which nobles might be shadows, I suggest looking > at
> > this Harmonic Entropy chart that Paul Erlich calculated based on
> > George Secor's requirements.
> > /tuning/files/dyadic/secor4.gif
> > </tuning/files/dyadic/secor4.gif> >
> >
> > The data for this is in an Excel spreadsheet at
> > /tuning/files/Secor/raw-entr.xls
> > </tuning/files/Secor/raw-entr.xls> >
> > with the maxima (to the nearest cent) labelled, and the minima
> > labelled with their ratios.
> >
> > Of course the ears must be the final arbiter, but I don't find that
> > any of the Ginkgo intervals from the 1/1 are "explained" by the > noble
> > numbers you gave, as these are too complex.
> >
> > -- Dave Keenan
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
> > "Cameron Bobro" <misterbobro@...> wrote:
> > >
> > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
> > "Cameron Bobro" <misterbobro@>
> > >
> > > >
> > > > And now that I've seen the Scale Tree of Noble intervals at
> > > > Anaphoria, and even know what it is, I went through and find > this:
> > > >
> > > >
> > > > Scale Tree 252.005 cents 252.005
> > > > Ginkgo 81/70 252.680
> > > >
> > > > Ginkgo 729/560 456.590
> > > > Scale Tree 457.610 cents 457.610
> > > >
> > > > Ginkgo 146/105 570.695
> > > > Scale Tree 570.746 cents 570.746
> > > >
> > > > Ginkgo 219/140 774.605
> > > > Scale Tree 774.732 cents 774.732
> > > >
> > > > Ginkgo 105/64 857.095 septimal neutral sixth
> > > > Scale Tree 857.210 cents 857.210
> > > >
> > > > Scale Tree 954.613 cents 954.613
> > > > Ginkgo 243/140 954.635
> > > >
> > > >
> > > > and
> > > > 73/70 72.650 4/3 below the 146/105
> > > > 35/32 155.140 3/2 below the 105/64
> > >
> > > Correction on the last two. I was trying to think of the most > simple
> > > explanation vis a vis the Scale Tree, and I remembered that I've > been
> > > continually working for the last two years now with 11, 22, and 23
> > > o- and u-' tonalities.
> > >
> > > So it seems plausible that when I was making Ginkgo it was a > matter
> > > of floating those diamonds, so to speak, and that's how I > stumbled on
> > > the scale. So I just checked-
> > >
> > > Noble Mediant of 23/22 and 11/10...........71.855
> > > Ginkgo..........................73/70 .....72.650
> > >
> > > Ginkgo........35/32............155.140
> > > NM of 11/10 and 1/1............155.819
> > >
> > > It looks like the whole dang tuning might be just Noble Mediants
> > > between 22 and 23 diamonds.
> > >
> > > The next step is obvious- to figure out the the NMs between 22 > and 23
> > > diamonds, 22 and 23 o- and u-.
> > >
> > > I'd like to ask Dave Keenan to check some of these out if he has > the
> > > time, errors in my reckonings are far from impossible. :-)
> > >
> > > -Cameron Bobro
> > >
> >
> >
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗daniel_anthony_stearns <daniel_anthony_stearns@...>

6/15/2008 8:19:58 AM

hi there David.i don't really have time to participate in all this as
much as i'd like, but i thought i'd just mention that the thread i
posted a couple weeks ago--the sharp knife has a white handle--was
about exactly this (where to draw limits and what to call borders in
the "scale tree"). And what's potentially interesting on it, is that
the method is one i came up with quite a while ago (back in the late
90s on these lists) but didn't really fully notice it as i was using
the method to convert EDOs to frequency ratio series by bending
overtone and undertone series towards a median series. Anyway, the
method, while giving similar results, is quite different from those
that are usually cited--i.e, Helmholtz,Partch, Erlich's HE etc. The
results are similar, though perhaps even more "conservative" than you
suggest in this post.
take care, daniel

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Hi Cameron,
>
> Thanks for inviting me to check your numbers.
>
> Those you have read from
> http://www.anaphoria.com/sctree.PDF
> you have correctly converted to cents.
>
> However, we should note that Erv's scale-tree gives 256 noble
numbers
> within the octave, so on average they are only 4.7 cents apart, and
> therefore you will always find one of these noble numbers within a
few
> cents of almost anything.
>
> You can go on adding more levels to the scale-tree indefinitely,
> doubling the number of nobles each time.
>
> Erv probably took the tree out to 11 levels
> (a) to include 11/10 for use as a frequency ratio, and
> (b) for the tree's other use, in finding scale generators. For this
> purpose the denominators of the ratios can be read as -EDOs, and the
> numerator as the number of degrees of that EDO that the generator
> corresponds to.
>
> But I severely doubt that all of the given 256 noble frequency
ratios
> are audibly shadowy or gray.
>
> For a noble number to correspond to a shadow interval, I think it
has
> to be the noble mediant of two just intervals, i.e. two intervals
that
> can be tuned by ear through the locking-in of partials, i.e. two
> ratios which are sufficiently simple, say n*d <= 120. So I'd expect
> maybe only about 20 of the simplest nobles to correspond to shadow
> regions, within the octave.
>
> In other words, I'd suggest only those nobles whose dashed lines
> originate from blobs above about level 7 of the scale tree (the
level
> containing 7/6 11/9 14/11 13/10 15/11 18/13 17/12 13/9 19/12 21/13
> 18/11 17/10 19/11 16/9 11/6). That's only one more level than is
shown
> on page 1. Except that close to the unison and octave you might go
> down another level or two.
>
> I note that there is no point in restricting ourselves to the first
> octave when calculating nobles that may correspond to shadow
> intervals. The octave extensions and inversions of noble numbers are
> not (in general) noble numbers. The noble numbers above 2/1 are
quite
> independent of those below.
>
> Your calculation of the noble mediant of 1/1 and 11/10 below is
quite
> correct. It is also the noble mediant of 11/10 and 12/11.
>
> However something must have gone wrong in your calculation of the
> phi-weighted mediant of 11/10 and 23/22 since your result is not
even
> between those two ratios.
>
> I say "phi-weighted mediant" because in this case, even the correct
> result does not correspond to a noble number. You can see this by
> applying the cross-multiplication check I mentioned. 11*22 = 242,
> 10*23 = 230. They differ by more than 1, so this is not noble.
>
> To get an idea of which nobles might be shadows, I suggest looking
at
> this Harmonic Entropy chart that Paul Erlich calculated based on
> George Secor's requirements.
>
/tuning/files/dyadic/sec
or4.gif
>
> The data for this is in an Excel spreadsheet at
>
/tuning/files/Secor/raw-
entr.xls
> with the maxima (to the nearest cent) labelled, and the minima
> labelled with their ratios.
>
> Of course the ears must be the final arbiter, but I don't find that
> any of the Ginkgo intervals from the 1/1 are "explained" by the
noble
> numbers you gave, as these are too complex.
>
> -- Dave Keenan
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> >
> > >
> > > And now that I've seen the Scale Tree of Noble intervals at
> > > Anaphoria, and even know what it is, I went through and find
this:
> > >
> > >
> > > Scale Tree 252.005 cents 252.005
> > > Ginkgo 81/70 252.680
> > >
> > > Ginkgo 729/560 456.590
> > > Scale Tree 457.610 cents 457.610
> > >
> > > Ginkgo 146/105 570.695
> > > Scale Tree 570.746 cents 570.746
> > >
> > > Ginkgo 219/140 774.605
> > > Scale Tree 774.732 cents 774.732
> > >
> > > Ginkgo 105/64 857.095 septimal neutral sixth
> > > Scale Tree 857.210 cents 857.210
> > >
> > > Scale Tree 954.613 cents 954.613
> > > Ginkgo 243/140 954.635
> > >
> > >
> > > and
> > > 73/70 72.650 4/3 below the 146/105
> > > 35/32 155.140 3/2 below the 105/64
> >
> > Correction on the last two. I was trying to think of the most
simple
> > explanation vis a vis the Scale Tree, and I remembered that I've
been
> > continually working for the last two years now with 11, 22, and
23
> > o- and u-' tonalities.
> >
> > So it seems plausible that when I was making Ginkgo it was a
matter
> > of floating those diamonds, so to speak, and that's how I
stumbled on
> > the scale. So I just checked-
> >
> > Noble Mediant of 23/22 and 11/10...........71.855
> > Ginkgo..........................73/70 .....72.650
> >
> > Ginkgo........35/32............155.140
> > NM of 11/10 and 1/1............155.819
> >
> > It looks like the whole dang tuning might be just Noble Mediants
> > between 22 and 23 diamonds.
> >
> > The next step is obvious- to figure out the the NMs between 22
and 23
> > diamonds, 22 and 23 o- and u-.
> >
> > I'd like to ask Dave Keenan to check some of these out if he has
the
> > time, errors in my reckonings are far from impossible. :-)
> >
> > -Cameron Bobro
> >
>

🔗Carl Lumma <carl@...>

6/15/2008 10:59:29 AM

Kraig wrote:
> HE has not proven itself as valid from my perspective, i am
> sorry. My problems with it which i posted maybe two post ago
> have not been dealt with or even acknowledged.

Sorry, I didn't see them. But I'd be happy to discuss them
either here, or on the harmonic_entropy list. Could you please
summarize them so we can get a fresh start?

> I can take it that there is more interest in preserving this
> monumental tower regardless of how many examples can be
> put forth that it doesn't hold up.

Now then, there's no need for such accusations, is there?

> I repeat why does Metaslendro taken to 12 pitches sound more
> consonant than 12 ET if i play all the pitches, even though
> is closer to simpler ratios and Meta Slendro closer to
> supposed more 'dissonant' points.

I'm sorry but I can't parse this sentence.

> minor points might be why does the 7-9-11 sound so consonant
> then,

7-9-11 is a triad, and no triadic harmonic entropy data have
ever been published to my knowledge. As it exists it deals
solely with dyads. Paul figured out how to extend it to
triads but never did the calculations to my knowledge.

> or why does a C6 chord sound more consonant that a C triad
> to many people.

I've never met anyone who said so. Are you one of these
people? (Keeping in mind this is a triad and a tetrad,
so again harmonic entropy is silent for now.)

-Carl

🔗Carl Lumma <carl@...>

6/15/2008 11:30:30 AM

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> This C6 and C Major con/dissonance thread:
>
> Here is a theory from a scalecoding P.O.V. for you:
>
> C Major is C G * * E = 4/34/1
>
> A minor 7 is C G * A E = 4/3/4
>
> C6 is C G * A E = 4/3/1

Sorry, but I don't follow what happens after the = sign
at all. Can you explain?

-Carl

🔗Charles Lucy <lucy@...>

6/15/2008 11:33:05 AM

> I have looked at the spreadsheet and graph, and appreciate that the
> figures are the result of your arithmetic manipulations, yet I can
> see no reason logically and/or musically, why the interval from the
> Tonic (0) to the fifth (approx 700¢) and from the tonic to the
> fourth (approx 500¢) should have different levels of harmonic
> entropy. For they are in essence mere mirror images or
> transpositions of eachother.
>

Disregarding octaves; one is in steps of fourths, the other in steps
of fifths, so the values should be the same.

Or does a fourth plus a fifth no longer equal an octave? ;-)

I must admit this graphic does remind me of Partch's "One-footed
bride" though;-)

I even played around adding data to the spreadsheet and graphic,
expecting to find a "hidden" pattern which matched any understanding
of harmony which I have, although without success.

Is it time to abandon this "hole" and start digging a new one elsewhere?

> >To get an idea of which nobles might be shadows, I suggest looking at
> > this Harmonic Entropy chart that Paul Erlich calculated based on
> > George Secor's requirements.
> > /tuning/files/dyadic/secor4.gif
> > </tuning/files/dyadic/secor4.gif
> >
> >
> > The data for this is in an Excel spreadsheet at
> > /tuning/files/Secor/raw-entr.xls
> > </tuning/files/Secor/raw-entr.xls
> >
> > with the maxima (to the nearest cent) labelled, and the minima
> > labelled with their ratios.
> >
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Charles Lucy <lucy@...>

6/15/2008 11:43:07 AM

Hi Carl;

The stuff after the equals sign is the scalecoding.

I thought you understood this elementary stuff by now Carl.

After all you are the "expert" on microtuning, and even if you don't agree with the concepts, you could at least have taken the trouble to attempt to understand them before slagging them off;-)

Apologies,!

You did actually ask politely this time;-)

It's all explained on this page and the links at the bottom of the page are for more info:

http://www.lucytune.com/new_to_lt/pitch_05.html

best wishes

Lucy

On 15 Jun 2008, at 19:30, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > This C6 and C Major con/dissonance thread:
> >
> > Here is a theory from a scalecoding P.O.V. for you:
> >
> > C Major is C G * * E = 4/34/1
> >
> > A minor 7 is C G * A E = 4/3/4
> >
> > C6 is C G * A E = 4/3/1
>
> Sorry, but I don't follow what happens after the = sign
> at all. Can you explain?
>
> -Carl
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Kraig Grady <kraiggrady@...>

6/15/2008 12:50:54 PM

that it hasn't been taken to 3 notes has been one of my objection.
The assumption that dyads are relevant to triads is a priori idea, without any support.
But was not the intervals and octave being tempered because of the triads?
We have had 150 years of acoustician looking at dyads and i doubt if it will ever progress past that. On the other hand Helmholtz ( who has supposedly now been replaced) deals with not only triads but also inversions and range. This makes such other pet theories as harmonic distance on a grid not stand water, yet it is persisted in.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> Kraig wrote:
> > HE has not proven itself as valid from my perspective, i am
> > sorry. My problems with it which i posted maybe two post ago
> > have not been dealt with or even acknowledged.
>
> Sorry, I didn't see them. But I'd be happy to discuss them
> either here, or on the harmonic_entropy list. Could you please
> summarize them so we can get a fresh start?
>
> > I can take it that there is more interest in preserving this
> > monumental tower regardless of how many examples can be
> > put forth that it doesn't hold up.
>
> Now then, there's no need for such accusations, is there?
>
> > I repeat why does Metaslendro taken to 12 pitches sound more
> > consonant than 12 ET if i play all the pitches, even though
> > is closer to simpler ratios and Meta Slendro closer to
> > supposed more 'dissonant' points.
>
> I'm sorry but I can't parse this sentence.
>
> > minor points might be why does the 7-9-11 sound so consonant
> > then,
>
> 7-9-11 is a triad, and no triadic harmonic entropy data have
> ever been published to my knowledge. As it exists it deals
> solely with dyads. Paul figured out how to extend it to
> triads but never did the calculations to my knowledge.
>
> > or why does a C6 chord sound more consonant that a C triad
> > to many people.
>
> I've never met anyone who said so. Are you one of these
> people? (Keeping in mind this is a triad and a tetrad,
> so again harmonic entropy is silent for now.)
>
> -Carl
>
>

🔗Kraig Grady <kraiggrady@...>

6/15/2008 1:13:36 PM

to add on to this. compare the Dyad of 12 ET fourth to Meta Slendro fourth. Metaslendro 4th will be considered higher in entropy. Play a 12 pitch cluster of both though and Meta Slendro in much more consonant. I am sure we could get similar results from other such constructs
The clue is acoustical coincidence.
how this can be 'quanified' is the problem a mathematical approach will have.
good luck!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

🔗Kraig Grady <kraiggrady@...>

6/15/2008 1:13:54 PM

to add on to this. compare the Dyad of 12 ET fourth to Meta Slendro fourth. Metaslendro 4th will be considered higher in entropy. Play a 12 pitch cluster of both though and Meta Slendro in much more consonant. I am sure we could get similar results from other such constructs
The clue is acoustical coincidence.
how this can be 'quantified' is the problem a mathematical approach will have.
good luck!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

🔗Carl Lumma <carl@...>

6/15/2008 1:32:09 PM

That page refers to scales, not chords. Can you explain
the numbers you've posted without simply linking to an
external resource?

-Carl

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Hi Carl;
>
> The stuff after the equals sign is the scalecoding.
>
> I thought you understood this elementary stuff by now Carl.
>
> After all you are the "expert" on microtuning, and even if you don't
> agree with the concepts, you could at least have taken the trouble
> to attempt to understand them before slagging them off;-)
>
> Apologies,!
>
> You did actually ask politely this time;-)
>
> It's all explained on this page and the links at the bottom of the
> page are for more info:
>
> http://www.lucytune.com/new_to_lt/pitch_05.html
>
> best wishes
>
> Lucy

🔗Carl Lumma <carl@...>

6/15/2008 1:35:02 PM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> that it hasn't been taken to 3 notes has been one of my objection.
> The assumption that dyads are relevant to triads is a priori idea,
> without any support.

Huh? Who's applying it to triads???

> But was not the intervals and octave being tempered because of
> the triads?

> We have had 150 years of acoustician looking at dyads and i
> doubt if it will ever progress past that.

Some preliminary work on triads has been done. Unfortunately,
one guy (Paul) can't be expected to do it all himself. If you
perceive it to be such a grave problem perhaps you have some
ideas on how to do this computation.

> On the other hand Helmholtz (who has
> supposedly now been replaced) deals with not only triads but also
> inversions and range. This makes such other pet theories as harmonic
> distance on a grid not stand water, yet it is persisted in.

Who's talking about distance on a grid? I asked you to give
the cases that you feel harmonic entropy fails on. You haven't.

-Carl

🔗Carl Lumma <carl@...>

6/15/2008 1:44:01 PM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> to add on to this. compare the Dyad of 12 ET fourth to
> Meta Slendro fourth. Metaslendro 4th will be considered
> higher in entropy.

And how many cents have the meta-slendro 4th? 487 I suppose.
This will indeed have higher entropy than 500 cents, and
indeed I think it is less consonant after a fashion.

Harmonic entropy is only a single value, and consonance is
probably richer than can be captured completely with one
value.

How many people here think 487 cents is more consonant than
500 cents? Anyone?

-Carl

🔗Daniel Wolf <djwolf@...>

6/15/2008 2:02:47 PM

Kraig Grady wrote:

"that it hasn't been taken to 3 notes has been one of my objection.
The assumption that dyads are relevant to triads is a priori idea,
without any support.
But was not the intervals and octave being tempered because of the triads?
We have had 150 years of acoustician looking at dyads and i doubt if it
will ever progress past that. On the other hand Helmholtz ( who has
supposedly now been replaced) deals with not only triads but also
inversions and range. This makes such other pet theories as harmonic
distance on a grid not stand water, yet it is persisted in."

Kraig:

Going beyond dyads to triads is difficult, the music theorist's equivalent to the three-body problem. However, Erlich's Voronoi diagram of possible triads is the most useful treatment of the topic I've encountered and, I presume, that a triadic harmonic entropy would yield a very similar structure.

djw

🔗Cameron Bobro <misterbobro@...>

6/15/2008 3:24:55 PM

Say thanks for taking the time, Dave!

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> When you say "1 phi-th of the octave" the obvious interpretation
seems
> to me to be 1200 * 1/phi ~= 742 cents. That would be the "other way"
> of using nobles (for melody, rather than harmony).
>
> But you seem to mean the phi-weighted (or noble) mediant of 1/1 and
> 2/1. In other words
>
> 1 * 2*phi
> ---------
> 1 * 1*phi
>
> which reduces to simply phi which, as a frequenct ratio, corresponds
> to 833 cents.
>
> So the 367 cents interval could better have been described as "the
> octave inversion of phi".

Thought that's what I said- the inversion of one phi-th of the octave.
Phi-weighted mediants, yes.
>
> Here are the 31 noble intervals up to level 7 of the scale-tree, to
> the nearest cent, in order of increasing complexity (not limited to
> the first octave).
>
> Golden
> 833 narrow neutral sixth
>
> Silver
> 2226 narrow neutral 14th
> 560 narrow augmented fourth
>
> Titanium
> 2649
> 1503 narrow minor tenth
> 943 narrow subminor seventh
> 422 narrow supermajor third
>
> Chrome
> 2988
> 2109 narrow supermajor 13th
> 1735 narrow super 11th
> 1424 narrow supermajor 9th
> 1002 minor seventh
> 792 narrow minor sixth
> 607 narrow diminished fifth or tritone
> 339 narrow neutral third
>
> Nickel (of doubtful use )
> 3272
> 2558
> 2276 major 14th
> 2055 neutral 13th
> 1772 narrow augmented 11th
> 1641 narrow sub 11th
> 1530 narrow neutral 10th
> 1378 narrow major 9th
> 1039 narrow neutral seventh
> 923 narrow supermajor sixth
> 849 neutral sixth
> 771 subminor sixth
> 630 wide diminished fifth
> 541 narrow super fourth
> 448 narrow sub fourth
> 284 wide subminor third

I see the source of miscommunitcation here- I'm thinking in terms of
phi-weighted mediants "floating" intervals which are "givens", either
already literally present in the tuning, or the harmonic series, or
simple ratios. Whether or not they qualify as noble is not important-
they just have to have the appropriate character, and float (so they
don't sound like mistuned Just). And the main thing is how they all
go together.

Performing JI on a just one or two noble intervals such as the ones
you posted, whether you hit them by accident or design, will probably
"float" the entire scale. One way to find out...

-Cameron Bobro

🔗Dave Keenan <d.keenan@...>

6/15/2008 4:26:43 PM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> if this list can talk about ET exceeding 256 i see no reason to limit
> the discussion of noble mediant a priori.

I don't see the analogy. No one has ever, to my knowledge, claimed
that proximity to degrees of an ET "explains" the audible quality of
an interval. But if they did, then surely it could only be the simpler
ETs that could have such explanatory power, since you can always find
a degree of a sufficiently complex ET as close as you like to _any_
pitch. The same goes for rational numbers. The same goes for noble
numbers.

> It is just as much a valid
> continuum worthy of study as any other.
> The only correct attitudo wecan haveis that we don't know at the moment.

Sure. We can't give a reliable cutoff at this stage of
experimentation, I just gave my best guess for now. And it will always
be fuzzy and dependent on all kinds of contextual factors. But we can
say with 99.99% certainty that there can be no explanatory power in
the 16,000 or so noble numbers that appear at the 16th level of the
scale tree, because they are on average less than 0.1 of a cent apart.

> HE has not proven itself as valid from my perspective, i am sorry. My
> problems with it which i posted maybe two post ago have not been dealt
> with or even acknowledged. I can take it that there is more
interest in
> preserving this monumental tower regardless of how many examples can be
> put forth that it doesn't hold up.
> I repeat why does Metaslendro taken to 12 pitches sound more consonant
> than 12 ET if i play all the pitches, even though is closer to simpler
> ratios and Meta Slendro closer to supposed more 'dissonant' points .
> minor points might be why does the 7-9-11 sound so consonant then,
> or why does a C6 chord sound more consonant that a C triad to many
people.

Paul Erlich has always made it very clear that he believes harmonic
entropy to be modelling only one component of dissonance or
discordance (I forget which) and that dis-whatever-ance is only one
aspect of the audible quality of an interval.

In the context of the current discussion of shadow intervals I'm just
using the peaks and troughs of one parameterisation of HE as signposts
to where "something special" might happen. I'm not concerned here
whether HE accurately models dis-whatever-ance.

I don't know how to make a mathematical model that incorporates your
observations about 7:9:11, C6 chords and meta-slendro, and nor does
Paul Erlich. But that doesn't mean we ignore them. We would dearly
love to incorporate them, but we just aren't smart enough.

Physics doesn't have a single theory that covers the very large and
the very small, but that's no reason to throw out either quantum
mechanics or relativity just yet. Likewise we continue to use Harmonic
Entropy where we can.

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/15/2008 4:51:23 PM

that is exactly my point. it tells us little, cause when you have 12 of both intervals. it is reversed!
dyads tell us nothing then i am afaid.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > to add on to this. compare the Dyad of 12 ET fourth to
> > Meta Slendro fourth. Metaslendro 4th will be considered
> > higher in entropy.
>
> And how many cents have the meta-slendro 4th? 487 I suppose.
> This will indeed have higher entropy than 500 cents, and
> indeed I think it is less consonant after a fashion.
>
> Harmonic entropy is only a single value, and consonance is
> probably richer than can be captured completely with one
> value.
>
> How many people here think 487 cents is more consonant than
> 500 cents? Anyone?
>
> -Carl
>
>

🔗Dave Keenan <d.keenan@...>

6/15/2008 4:53:19 PM

Hi Charles,

The simplest formulation of harmonic entropy has no special treatment
for octaves, and so what comes out has only partial octave-equivalence.

Many people find that they hear inversions and octave extensions of
some intervals as having quite different levels of dissonance or
discordance.

But for those who experience complete octave equivalence Paul has
added it as an additional assumption to produce another chart that may
be more to your liking.
/tuning/files/dyadic/partch.bmp
with data at
/tuning/files/dyadic/partch.txt

See other HE charts in
/tuning/files/dyadic/

And voronoi diagrams of triads at
/tuning/files/Erlich/

-- Dave Keenan

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> > I have looked at the spreadsheet and graph, and appreciate that the
> > figures are the result of your arithmetic manipulations, yet I can
> > see no reason logically and/or musically, why the interval from the
> > Tonic (0) to the fifth (approx 700¢) and from the tonic to the
> > fourth (approx 500¢) should have different levels of harmonic
> > entropy. For they are in essence mere mirror images or
> > transpositions of eachother.
> >
>
> Disregarding octaves; one is in steps of fourths, the other in steps
> of fifths, so the values should be the same.
>
> Or does a fourth plus a fifth no longer equal an octave? ;-)
>
> I must admit this graphic does remind me of Partch's "One-footed
> bride" though;-)
>
> I even played around adding data to the spreadsheet and graphic,
> expecting to find a "hidden" pattern which matched any understanding
> of harmony which I have, although without success.
>
> Is it time to abandon this "hole" and start digging a new one elsewhere?

🔗Charles Lucy <lucy@...>

6/15/2008 5:05:08 PM

Thanks Dave;

I'l go get it.

On 16 Jun 2008, at 00:53, Dave Keenan wrote:

> Hi Charles,
>

>
>
> The simplest formulation of harmonic entropy has no special treatment
> for octaves, and so what comes out has only partial octave-> equivalence.
>
> Many people find that they hear inversions and octave extensions of
> some intervals as having quite different levels of dissonance or
> discordance.
>
> But for those who experience complete octave equivalence Paul has
> added it as an additional assumption to produce another chart that may
> be more to your liking.
> /tuning/files/dyadic/partch.bmp
> with data at
> /tuning/files/dyadic/partch.txt
>
> See other HE charts in
> /tuning/files/dyadic/
>
> And voronoi diagrams of triads at
> /tuning/files/Erlich/
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
>

lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Kraig Grady <kraiggrady@...>

6/15/2008 5:11:01 PM

I have missed that diagram.
My concern is with proportional triads which due to their acoustical coincidence are less dissonant that harmonic numbers would imagine. ( why i mention the 7-9-11 in this regard). I also am concerned with inversions which can vary greatly in consonance/dissonance. These are phenomena i deal with all the time. perhaps i feel like i need to stick up for them.
I do not think that Helmholtz got it right but at least aimed in the right direction looking at the difference tones and how they react. Also the effect of range on such things.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Daniel Wolf wrote:
> Kraig Grady wrote:
>
> "that it hasn't been taken to 3 notes has been one of my objection.
> The assumption that dyads are relevant to triads is a priori idea,
> without any support.
> But was not the intervals and octave being tempered because of the triads?
> We have had 150 years of acoustician looking at dyads and i doubt if it
> will ever progress past that. On the other hand Helmholtz ( who has
> supposedly now been replaced) deals with not only triads but also
> inversions and range. This makes such other pet theories as harmonic
> distance on a grid not stand water, yet it is persisted in."
>
>
> Kraig:
>
> Going beyond dyads to triads is difficult, the music theorist's equivalent > to the three-body problem. However, Erlich's Voronoi diagram of possible > triads is the most useful treatment of the topic I've encountered and, I > presume, that a triadic harmonic entropy would yield a very similar > structure.
>
> djw
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>
>
>

🔗Kraig Grady <kraiggrady@...>

6/15/2008 5:33:18 PM

Pardon my resistance but at one point the idea was put forth on these list that nothing beyond the 13th harmonic is worthy of investigation cause when you go though all the possibilities, one saturates the continuum with pitches ( possibly it was "above 13" that this was put forth). So the math breaks down to say anything. But someone thinking this way might over look something such as a recurrent sequence cause there is nothing there beyond lower points. Since the numbers get out of hand say once we get to the 19th harmonic which many find in the minor triad do we ignore it because their is no way to talk about it? or do we work backward to where we can. In which case my previous point is valid in that we are doing more to preserve the mathematical examination of, in this case harmony, than we are in pursuing the truth of the subject. I would suggest that consonance and dissonance cannot be adequately examined due to the great complexity of the variables. Ernst Toch was quite good in pointing out many problems involved in the subject.
Obviously Mathematics has much to offer music in terms of generating scales, patterns, etc.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > if this list can talk about ET exceeding 256 i see no reason to limit
> > the discussion of noble mediant a priori.
>
> I don't see the analogy. No one has ever, to my knowledge, claimed
> that proximity to degrees of an ET "explains" the audible quality of
> an interval. But if they did, then surely it could only be the simpler
> ETs that could have such explanatory power, since you can always find
> a degree of a sufficiently complex ET as close as you like to _any_
> pitch. The same goes for rational numbers. The same goes for noble
> numbers.
>
> > It is just as much a valid
> > continuum worthy of study as any other.
> > The only correct attitudo wecan haveis that we don't know at the moment.
>
> Sure. We can't give a reliable cutoff at this stage of
> experimentation, I just gave my best guess for now. And it will always
> be fuzzy and dependent on all kinds of contextual factors. But we can
> say with 99.99% certainty that there can be no explanatory power in
> the 16,000 or so noble numbers that appear at the 16th level of the
> scale tree, because they are on average less than 0.1 of a cent apart.
>
> > HE has not proven itself as valid from my perspective, i am sorry. My
> > problems with it which i posted maybe two post ago have not been dealt
> > with or even acknowledged. I can take it that there is more
> interest in
> > preserving this monumental tower regardless of how many examples can be
> > put forth that it doesn't hold up.
> > I repeat why does Metaslendro taken to 12 pitches sound more consonant
> > than 12 ET if i play all the pitches, even though is closer to simpler
> > ratios and Meta Slendro closer to supposed more 'dissonant' points .
> > minor points might be why does the 7-9-11 sound so consonant then,
> > or why does a C6 chord sound more consonant that a C triad to many
> people.
>
> Paul Erlich has always made it very clear that he believes harmonic
> entropy to be modelling only one component of dissonance or
> discordance (I forget which) and that dis-whatever-ance is only one
> aspect of the audible quality of an interval.
>
> In the context of the current discussion of shadow intervals I'm just
> using the peaks and troughs of one parameterisation of HE as signposts
> to where "something special" might happen. I'm not concerned here
> whether HE accurately models dis-whatever-ance.
>
> I don't know how to make a mathematical model that incorporates your
> observations about 7:9:11, C6 chords and meta-slendro, and nor does
> Paul Erlich. But that doesn't mean we ignore them. We would dearly
> love to incorporate them, but we just aren't smart enough.
>
> Physics doesn't have a single theory that covers the very large and
> the very small, but that's no reason to throw out either quantum
> mechanics or relativity just yet. Likewise we continue to use Harmonic
> Entropy where we can.
>
> -- Dave Keenan
>
>

🔗Dave Keenan <d.keenan@...>

6/15/2008 6:02:37 PM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
> > 1 * 2*phi
> > ---------
> > 1 * 1*phi

Oops! My typo above. That should have been

1 + 2*phi
---------
1 + 1*phi

but I expect you knew what I meant.

> > So the 367 cents interval could better have been described as "the
> > octave inversion of phi".
>
> Thought that's what I said- the inversion of one phi-th of the octave.

367 cents is the inversion of phi as a frequency ratio (nothing to do
with octaves) or it's the inversion of the phi-mediant between the
unison and octave.

The inversion of one phi-th of the octave would be 1200 - 1200/phi
cents = 458 cents.

> Phi-weighted mediants, yes.
>
> I see the source of miscommunitcation here- I'm thinking in terms of
> phi-weighted mediants "floating" intervals which are "givens", either
> already literally present in the tuning, or the harmonic series, or
> simple ratios. Whether or not they qualify as noble is not important-
> they just have to have the appropriate character, and float (so they
> don't sound like mistuned Just). And the main thing is how they all
> go together.

OK. But unless it is actually calculating a noble number, e.g. the
phi-mediant between two Just intervals adjacent on the scale-tree,
then it is mathematically "unstable" and hence musically meaningless.

This is because it depends on the actual numerator and denominator not
just the size of the interval. Many different ratios can be used to
represent what is audibly or measurably the same interval. For example
144:233 and 89:144 are probably indistinguishable but will give very
different result if a phi-mediant is taken with some other interval.

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/15/2008 6:19:21 PM

Hi Kraig,

I hear you. I understand where you are coming from. You make some good
points. Good on you for sticking up for these things, and I hope you
will likewise pardon me for sticking up for valid uses of mathematics
in modelling these things.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Pardon my resistance but at one point the idea was put forth on these
> list that nothing beyond the 13th harmonic is worthy of investigation
> cause when you go though all the possibilities, one saturates the
> continuum with pitches ( possibly it was "above 13" that this was put
> forth). So the math breaks down to say anything. But someone thinking
> this way might over look something such as a recurrent sequence cause
> there is nothing there beyond lower points. Since the numbers get
out of
> hand say once we get to the 19th harmonic which many find in the minor
> triad do we ignore it because their is no way to talk about it? or
do we
> work backward to where we can. In which case my previous point is valid
> in that we are doing more to preserve the mathematical examination of,
> in this case harmony, than we are in pursuing the truth of the subject.
> I would suggest that consonance and dissonance cannot be adequately
> examined due to the great complexity of the variables. Ernst Toch was
> quite good in pointing out many problems involved in the subject.
> Obviously Mathematics has much to offer music in terms of generating
> scales, patterns, etc.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

🔗Carl Lumma <carl@...>

6/15/2008 6:38:13 PM

Kraig wrote:
> Pardon my resistance but at one point the idea was put forth on
> these list that nothing beyond the 13th harmonic is worthy of
> investigation

Who said that???

-Carl

🔗Kraig Grady <kraiggrady@...>

6/15/2008 6:46:49 PM

agreed:)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Kraig,
>
> I hear you. I understand where you are coming from. You make some good
> points. Good on you for sticking up for these things, and I hope you
> will likewise pardon me for sticking up for valid uses of mathematics
> in modelling these things.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > Pardon my resistance but at one point the idea was put forth on these
> > list that nothing beyond the 13th harmonic is worthy of investigation
> > cause when you go though all the possibilities, one saturates the
> > continuum with pitches ( possibly it was "above 13" that this was put
> > forth). So the math breaks down to say anything. But someone thinking
> > this way might over look something such as a recurrent sequence cause
> > there is nothing there beyond lower points. Since the numbers get
> out of
> > hand say once we get to the 19th harmonic which many find in the minor
> > triad do we ignore it because their is no way to talk about it? or
> do we
> > work backward to where we can. In which case my previous point is valid
> > in that we are doing more to preserve the mathematical examination of,
> > in this case harmony, than we are in pursuing the truth of the subject.
> > I would suggest that consonance and dissonance cannot be adequately
> > examined due to the great complexity of the variables. Ernst Toch was
> > quite good in pointing out many problems involved in the subject.
> > Obviously Mathematics has much to offer music in terms of generating
> > scales, patterns, etc.
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>

🔗Kraig Grady <kraiggrady@...>

6/15/2008 6:50:40 PM

I believe when these curved graphs were being put forth.
Possibly you can point to where they diverge from Helmholtz.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> Kraig wrote:
> > Pardon my resistance but at one point the idea was put forth on
> > these list that nothing beyond the 13th harmonic is worthy of
> > investigation
>
> Who said that???
>
> -Carl
>
>

🔗Mike Battaglia <battaglia01@...>

6/15/2008 7:21:48 PM

I'm writing a 19-limit piece right now (or a piece with a few 19-limit
chords). You can definitely hear the 17th and 19th harmonics as otonal
consonances. So I disagree with that.

-Mike

On Sun, Jun 15, 2008 at 9:50 PM, Kraig Grady <kraiggrady@...> wrote:
> I believe when these curved graphs were being put forth.
> Possibly you can point to where they diverge from Helmholtz.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Carl Lumma wrote:
>>
>> Kraig wrote:
>> > Pardon my resistance but at one point the idea was put forth on
>> > these list that nothing beyond the 13th harmonic is worthy of
>> > investigation
>>
>> Who said that???
>>
>> -Carl
>>
>>
>

🔗Kraig Grady <kraiggrady@...>

6/15/2008 7:25:49 PM

Earlier i was entertaining the idea that if the minor is the 16-19-24, possibly the major is the subharmonic version of this chord:)
(i have never been a big fan of the sound of major)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> I'm writing a 19-limit piece right now (or a piece with a few 19-limit
> chords). You can definitely hear the 17th and 19th harmonics as otonal
> consonances. So I disagree with that.
>
> -Mike
>
> On Sun, Jun 15, 2008 at 9:50 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > I believe when these curved graphs were being put forth.
> > Possibly you can point to where they diverge from Helmholtz.
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Carl Lumma wrote:
> >>
> >> Kraig wrote:
> >> > Pardon my resistance but at one point the idea was put forth on
> >> > these list that nothing beyond the 13th harmonic is worthy of
> >> > investigation
> >>
> >> Who said that???
> >>
> >> -Carl
> >>
> >>
> >
>
>

🔗Dave Keenan <d.keenan@...>

6/15/2008 7:55:49 PM

Wonderful to hear from you Daniel.

Yes! This is clearly an idea whose time has come, since people seem to
be converging on it from all directions. I see this quote of yours as
capturing the essential point:

"... an 11/9 might be the simplest ratio to define a neutral third,
but whether or not that's THE interval is somewhat besides the point
in comparison to the question of whether this is an independently
articulated interval space outside the field of attraction imposed by
the long shadows of its neighbors."

It seems Mike B and Cameron agree with you that the sharp knife has a
chroma-free handle at least, but grey or shadowy rather than white.

I suppose you could equally reverse the metaphor and say: "... space
outside the field of attraction imposed by the bright (coloured)
lights of its neighbours."

So my suggestion is to avoid the confusion by not naming these shadow
regions after any particular rational fraction at all, but to
in-effect name them after the _pair_ of Just ratios being avoided. And
if a particular point is to be identified with the region then it
makes more sense not to use any rational number, but to use the
irrational noble mediant of the two Just ratios being avoided,
expressed as

5+6phi
------
4+5phi

You can see the two ratios 5/4 and 6/5 within the expression.

It simplifies to

1+5phi
------ ~= 339 cents
1+4phi

and I style it the "chrome" (narrow) neutral third in this message
/tuning/topicId_76975.html#77258
because of the level of the Stern-Brocot or scale tree where it first
appears.

I used this series of sucessively less noble commonly-known metals:
Gold, Silver, Titanium, Chrome, Nickel, Copper. But I may have grouped
some of those nobles wrongly. It's probably a silly idea anyway.
"Noble neutral third" is quite sufficient as there isn't another one
until you go down two more levels. Although it may turn out to be
useful to distinguish the golden neutral sixth at 833c from the nickel
neutral sixth at 849c (assuming 8:13 can be considered an attractor).

-- Dave Keenan

--- In tuning@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@...> wrote:
>
> hi there David.i don't really have time to participate in all this as
> much as i'd like, but i thought i'd just mention that the thread i
> posted a couple weeks ago--the sharp knife has a white handle--was
> about exactly this (where to draw limits and what to call borders in
> the "scale tree"). And what's potentially interesting on it, is that
> the method is one i came up with quite a while ago (back in the late
> 90s on these lists) but didn't really fully notice it as i was using
> the method to convert EDOs to frequency ratio series by bending
> overtone and undertone series towards a median series. Anyway, the
> method, while giving similar results, is quite different from those
> that are usually cited--i.e, Helmholtz,Partch, Erlich's HE etc. The
> results are similar, though perhaps even more "conservative" than you
> suggest in this post.
> take care, daniel

🔗Kraig Grady <kraiggrady@...>

6/15/2008 8:01:23 PM

i seem to be "diverging" from it quite greatly!:)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Wonderful to hear from you Daniel.
>
> Yes! This is clearly an idea whose time has come, since people seem to
> be converging on it from all directions. I see this quote of yours as
> capturing the essential point:
>
>

🔗Carl Lumma <carl@...>

6/15/2008 8:12:23 PM

> > Kraig wrote:
> > > Pardon my resistance but at one point the idea was put forth on
> > > these list that nothing beyond the 13th harmonic is worthy of
> > > investigation
> >
> > Who said that???
>
> I believe when these curved graphs were being put forth.
> Possibly you can point to where they diverge from Helmholtz.

Paul's been posting harmonic entropy curves here since the
late '90s, and the curved graphs in general go back to
Helmholtz at least. So you'll have to be more specific.
Needless to say, I don't think any of the major posters here
would back such a statement. If they do they are more than
welcome to speak out now.

-Carl

🔗Dave Keenan <d.keenan@...>

6/15/2008 9:44:35 PM

Kraig,

I expect I said something of the sort when I was a newbie on this list
about 15 years ago (before it was a Yahoo group) but I was soon set
straight. So now, you just seem to be setting up a straw man.

Bare dyads at ratios containing numbers higher than 13 are very
difficult to hear as anything special compared to other nearby
pitches, unless the lower note corresponds to a power of two in the
ratio (e.g. 8:13, 8:15, 16:19). But when we have triadic and larger
otonaltities we may well hear special things at higher numbers. The
more simultaneous pitches, the bigger the numbers that can be "heard".
But with 4 or less tones, I'm of the opinion that numbers beyond about
23 are more likely to relate to regions of metastability where (as Dan
Stearns said) the specific numbers in the ratio are not as important
as its distance from other simpler ratios.

Even if you want to significantly increase all my numbers above, don't
you agree that this happens _somewhere_? The idea that it could be
somehow explanatory to refer to a tuning as say "8191-limit", surely
strikes us all as somewhat ridiculous.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Kraig wrote:
> > Pardon my resistance but at one point the idea was put forth on
> > these list that nothing beyond the 13th harmonic is worthy of
> > investigation
>
> Who said that???
>
> -Carl
>

🔗Graham Breed <gbreed@...>

6/15/2008 9:49:04 PM

Dave Keenan wrote:

> I used this series of sucessively less noble commonly-known metals:
> Gold, Silver, Titanium, Chrome, Nickel, Copper. But I may have grouped
> some of those nobles wrongly. It's probably a silly idea anyway.
> "Noble neutral third" is quite sufficient as there isn't another one
> until you go down two more levels. Although it may turn out to be
> useful to distinguish the golden neutral sixth at 833c from the nickel
> neutral sixth at 849c (assuming 8:13 can be considered an attractor).

Is identifying the numbers by the sequence of metals your idea? I found a different definition of "silver ratio" and "silver means":

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html#silver

http://en.wikipedia.org/wiki/Silver_rectangle

The silver ratio (silver mean between 2 and 3) is a kind of minor third plus an octave. Thus far not even speculation about it being musically relevant.

Graham

🔗Dave Keenan <d.keenan@...>

6/15/2008 10:51:58 PM

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Dave Keenan wrote:
>
> > I used this series of sucessively less noble commonly-known metals:
> > Gold, Silver, Titanium, Chrome, Nickel, Copper. But I may have grouped
> > some of those nobles wrongly. It's probably a silly idea anyway.
> > "Noble neutral third" is quite sufficient as there isn't another one
> > until you go down two more levels. Although it may turn out to be
> > useful to distinguish the golden neutral sixth at 833c from the nickel
> > neutral sixth at 849c (assuming 8:13 can be considered an attractor).
>
> Is identifying the numbers by the sequence of metals your
> idea?

Hi Graham,

Yeah. No great thought or research went into it. Feel free to ignore
it. I just pulled them out of
http://en.wikipedia.org/wiki/Galvanic_series

> I found a different definition of "silver ratio" and
> "silver means":
>
>
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html#silver
>
> http://en.wikipedia.org/wiki/Silver_rectangle
>
> The silver ratio (silver mean between 2 and 3) is a kind of
> minor third plus an octave. Thus far not even speculation
> about it being musically relevant.

OK. Thanks for that. I see the silver ratio is not a noble number. The
sequence of "silver means" seem ill-named since the golden ratio is
one of them (the only noble one).

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/15/2008 11:33:01 PM

I don't remember you saying this, but I do not argue with the fact that if one uses limits and say you go up to 13 or especially beyond, the plethora of intervals makes it hard to find much between them except at the unison and octave. Sterns argument Parallels what i had suggested many times, that it has more to do with means between areas which appeared to be how the ancient Greeks thought. i have my own theories which has the same type of pitfalls as everyones else so i don't pretend to be immune. But i started the question at he far end of the pole- precisely.
Why and by what means causes different inversions of tetrads to sound more dissonant, and can this be quantified?
{why not triads? not enough options plus the practical and selfish applications to my own working in with the eikosany at the time}
I took this as far as i could empirically with what i had on hand. presented the results along with my own questions about it.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Kraig,
>
> I expect I said something of the sort when I was a newbie on this list
> about 15 years ago (before it was a Yahoo group) but I was soon set
> straight. So now, you just seem to be setting up a straw man.
>
> Bare dyads at ratios containing numbers higher than 13 are very
> difficult to hear as anything special compared to other nearby
> pitches, unless the lower note corresponds to a power of two in the
> ratio (e.g. 8:13, 8:15, 16:19). But when we have triadic and larger
> otonaltities we may well hear special things at higher numbers. The
> more simultaneous pitches, the bigger the numbers that can be "heard".
> But with 4 or less tones, I'm of the opinion that numbers beyond about
> 23 are more likely to relate to regions of metastability where (as Dan
> Stearns said) the specific numbers in the ratio are not as important
> as its distance from other simpler ratios.
>
> Even if you want to significantly increase all my numbers above, don't
> you agree that this happens _somewhere_? The idea that it could be
> somehow explanatory to refer to a tuning as say "8191-limit", surely
> strikes us all as somewhat ridiculous.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl > Lumma" <carl@...> wrote:
> >
> > Kraig wrote:
> > > Pardon my resistance but at one point the idea was put forth on
> > > these list that nothing beyond the 13th harmonic is worthy of
> > > investigation
> >
> > Who said that???
> >
> > -Carl
> >
>
>

🔗Kraig Grady <kraiggrady@...>

6/16/2008 12:19:45 AM

adding to previous.......
My objection is with limits at all.
Briefly
Temes attempted to find the most dissonant interval, but those (O'Connell) who looked deeper into it discovered that it produced it own types of consonance with proportional triads. (hence why metaslendro sounds so consonant). So now we have two contrary sets of 'consonances', one based on no beating and the other based on beating 'evenly'.

If one insisted in an entropic point it would seem to have to be inbetween or in combination (with more tones) where they cannot 'resolve' either way.

O Connell did an experiment in his class where he asked students to raise their hands when they heard the octave, he moved up in small steps which i do not know what they where, but over half the class raised their hand when he got to 833 cents.

AN ASIDE
{Besides being LA Monte Young's [later my own Physics teacher] he had an article published in Die Reihe of which his work with phi was a rejected one.
It appears he passed away in the last year or two without any of us knowing, finding out after much of his belongings and art were discovered by individuals who have created a cult following and a gallery show of his art and scores were going up just as i was leaving LA. He was the person who introduced me to Erv.}

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> o are not as important
> as its distance from other simpler ratios.
>
> Even if you want to significantly increase all my numbers above, don't
> you agree that this happens _somewhere_? The idea that it could be
> somehow explanatory to refer to a tuning as say "8191-limit", surely
> strikes us all as somewhat ridiculous.
>
> -- Dave Keenan
>
>

🔗Daniel Wolf <djwolf@...>

6/16/2008 1:45:52 AM

With just intonation, the use and perception of intervals based on evermore complex ratios is played out against the increasing likelihood that a given interval will be mistaken for another. At precisely which level of complexity this will occur is, most immediately, an issue of compositional context; that is to say that it is up to the composer to find ways in which intervals project their identities distinctively or ambiguously (and yes, composers do choose ambiguity over clarity when musically appropriate). Density of musical texture, tempo, amplitude, registration/timbre/orchestration: all of these elements can affect the use and perception of intervals.

Previously, in a slightly different context, I characterized the field of possible intervals as something like the burning map of the Ponderosa: we know that there's an edge beyond which distinctions are burnt up, either no longer musically meaningful or meaningful only in costly musical environments. Much of our hesistancy to precisely define just intonation is located along this edge: the set of all ratios is obviously too large, and the set of ratios of small whole numbers, while better, begs for a definition of "small" that is not immediately forthcoming. Research (particularly recent work in the neuroscience of music) gives some hints about the location of this edge, as well as the body of experience represented by real, existing musics, but for all practical purposes, the precise location of that edge is not determined, except through composition, and composers have shown some invention in creating contexts in which the usable field of intervals can be increased.

I'm not a platonist, so I'm not ready to accept the notion that the proportions of real, existing music are the shadows of ideal ratios located wherever ideals go to play. I'm inclined to a definition of just intonation based upon the real experience of tuning: a just interval is a target real musicians in a tuning process and -- pace La Monte Young, pace Fourier -- accuracy is a function of time, reduction of interference beating to local minima and contextual signals -- like the presence of consonant combination tones - can be important to our evaluation of an interval, and finally, give intervals (and the musicians who produce them) the benefit of both a doubt and a nod to Ockham: Frustra fit per plura quod potest fieri per paucior.

djw
http://renewablemusic.blogspot.com/

🔗Dave Keenan <d.keenan@...>

6/16/2008 2:50:05 AM

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i seem to be "diverging" from it quite greatly!:)

Kraig,

I completely fail to understand why you say that. You seem to be
agreeing here:

"Temes attempted to find the most dissonant interval, but those
(O'Connell) who looked deeper into it discovered that it produced it
own types of consonance with proportional triads. (hence why
metaslendro sounds so consonant). So now we have two contrary sets of
'consonances', one based on no beating and the other based on beating
'evenly'."

The way I see it, you have known about this stuff since forever --
thanks to Erv Wilson and Prof. O'Connell. You just chose to identify
these ambiguous regions (thanks Daniel Wolf) with some complex
rational number within them, and chose not to call them anything other
than Just.

Which unfortunately meant that I (and presumably many others on this
list) had no idea, until recently, that you recognised any distinction
there at all.

Your description of "two contrary sets of 'consonances', one based on
no beating and the other based on beating 'evenly'" exactly captures
the distinction that I and many others are now making.

The only disagreement seems to be one of how to name the two sides of
this (fuzzy and context dependent, but nevertheless real) distinction.

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/16/2008 3:57:05 AM

probably so.
if one insisted on another term besides just one could call them 'proportional'
or proportionally just.
which still retains the idea of ratio and says what it is directly.

for the record
Like La Monte though it wasn't until afterwards that interest in microtones came to the forefront.
I do remember Walter mentioning the former bringing in piece of page after page of a tied over b minor chord for strings.

I think Dan Wolf knows more about La Monte actual incorporation of just intonation.
(Does Conrad fit in anywhere for instance?)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
>
> The only disagreement seems to be one of how to name the two sides of
> this (fuzzy and context dependent, but nevertheless real) distinction.
>
> -- Dave Keenan
>
>

🔗djwolf_frankfurt <djwolf@...>

6/16/2008 4:49:26 AM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> So now we have two contrary sets
of
> 'consonances', one based on no beating and the other based on
beating
> 'evenly'."
>

May I also add that, assuming simple harmonic spectra, there are two
options for arriving at chords with less beating? The first is choose
tones, the lowest partials of which hew as closely as possible to
intervals found in the lower regions of the harmonic series thus
maximizing the number of coincident partials (i.e. plain vanilla just
intonation) and the second is to choose tones in which the partials
are least likely to coincide, and phi-based intervals are a likely
candidate to do this.

In the fourth movement of my string trio _Figure & Ground_, which is
all portamenti, there are several points of imitation at the minor
sixth (as an approximation of phi), which was chosen because it
creates the most dense, but not necessarily most dissonant, ensemble
spectra. I stole this insight from James Tenney who used a minor
sixth in his "barbershop pole" piece, _For Ann, Rising_. I
understand that Tenney wanted to realize this piece again with a more
precise phi interval.

djw

🔗Carl Lumma <carl@...>

6/16/2008 10:21:46 AM

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> May I also add that, assuming simple harmonic spectra, there are
> two options for arriving at chords with less beating? The first
> is choose tones, the lowest partials of which hew as closely as
> possible to intervals found in the lower regions of the harmonic
> series thus maximizing the number of coincident partials (i.e.
> plain vanilla just intonation)

But coinciding partials do not minimize beating. A lack of
multiple, non-coinciding partials falling within a critical
band does.

> and the second is to choose tones in which the partials
> are least likely to coincide, and phi-based intervals are
> a likely candidate to do this.

Just intervals also have many (usually a large majority of)
non-coinciding partials. Any irrational dyad, meanwhile,
will have zero coinciding partials for harmonic timbres,
if that's what you want.

-Carl

🔗djwolf_frankfurt <djwolf@...>

6/16/2008 11:03:00 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> >
> > May I also add that, assuming simple harmonic spectra, there are
> > two options for arriving at chords with less beating? The first
> > is choose tones, the lowest partials of which hew as closely as
> > possible to intervals found in the lower regions of the harmonic
> > series thus maximizing the number of coincident partials (i.e.
> > plain vanilla just intonation)
>
> But coinciding partials do not minimize beating. A lack of
> multiple, non-coinciding partials falling within a critical
> band does.
>

If a pair of partials coincides precisely -- for example the third
partial of a tone with fundamental 100 Hz. and the fifth partial of a
tone with 60 Hz. -- they will not beat and, of course, are
(tirivially) within a critical band of one another.

> > and the second is to choose tones in which the partials
> > are least likely to coincide, and phi-based intervals are
> > a likely candidate to do this.
>
> Just intervals also have many (usually a large majority of)
> non-coinciding partials. Any irrational dyad, meanwhile,
> will have zero coinciding partials for harmonic timbres,
> if that's what you want.
>

We're not after zero coincidence, as one could have sero coincidence
and still have every pair of successive partials lie within critical
band of one another, thus garanteeing beating; we're after maximizing
the critical band distance between partials.

🔗Carl Lumma <carl@...>

6/16/2008 11:39:22 AM

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> > But coinciding partials do not minimize beating. A lack of
> > multiple, non-coinciding partials falling within a critical
> > band does.
>
> If a pair of partials coincides precisely -- for example the third
> partial of a tone with fundamental 100 Hz. and the fifth partial
> of a tone with 60 Hz. -- they will not beat and, of course, are
> (tirivially) within a critical band of one another.

So?

> We're not after zero coincidence, as one could have sero
> coincidence and still have every pair of successive partials
> lie within critical band of one another, thus garanteeing
> beating; we're after maximizing the critical band distance
> between partials.

And how do "phi-based" intervals accomplish this?

-Carl

🔗Dave Keenan <d.keenan@...>

6/16/2008 5:06:31 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> > We're not after zero coincidence, as one could have sero
> > coincidence and still have every pair of successive partials
> > lie within critical band of one another, thus garanteeing
> > beating; we're after maximizing the critical band distance
> > between partials.
>
> And how do "phi-based" intervals accomplish this?

If by phi-based numbers here we mean specifically the noble numbers,
defined as numbers of the form

i * m*phi
---------
j + n*phi

where i,j,m,n are integers

and i*n - j*m = 1 or -1

then they accomplish this by being local maxima of "unconvergability".

Now I just made up that word "unconvergability", and I can't find the
proof I was looking at just the other day, but it's about
approximating a number by simple rationals. You can define it as some
combination of the complexity of the approximating rational (e.g. n*d)
and the percentage difference between it and the number being
approximated. Noble numbers remain a long way from even very complex
rationals. Phi itself is the global maximum of this.

Phi and its powers have the additional property (mentioned by Kraig as
requiring precise tuning of it) that the differences between
consecutive powers of phi are also powers of phi (including phi^0 =
1). There could be an argument for referring to this specific case as
one of Just intonation.

But for the evenly-distributed-beats metastable-interval property of
the simple nobles generally, they do not need to be precisely tuned
and in fact the best point may not be exactly at the simple noble
number because the sound is affected by the relative loudness of the
partials too.

But the simpler noble numbers provide cardinal points of reference for
these metastable intervals in the same way that the simpler rational
numbers provide the cardinal points for the Just intervals.

I personally think that extending the meaning of "Just" to include the
metastable intervals is too much of a stretch. We've already stretched
it beyond its early historical meaning where it was essentially
limited to coincidence or near coincidence among the first 6 partials.

To extend it to cases where we are actually doing the complete
opposite, namely trying to maximally avoid any coincidence of
partials, particularly the first six, would in my view be unreasonable.

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/16/2008 5:10:21 PM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> If by phi-based numbers here we mean specifically the noble numbers,
> defined as numbers of the form
>
> i * m*phi
> ---------
> j + n*phi

That should be

i + m*phi
---------
j + n*phi

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/16/2008 5:18:26 PM

A summary:

The simpler noble intervals are easily-calculated representatives of
the metastable regions between audibly Just ratios. The meaning of
"metastable" in this context, is explained in
http://dkeenan.com/Music/NobleMediant.txt

While it might be correct in one sense to describe the sound of
metastable intervals as maximally "dissonant", this is only in terms
of the kind of consonance we hear in Just intervals (those at, and
very close to, simple-rational intervals).

But this definitely fails to adequately describe the difference
between the sound of a metastable interval and that of a very poorly
tuned Just interval or an interval between metastable and Just which
might even be a moderately complex rational such as 8:13.

Almost everyone agrees that these latter intervals are dissonant (at
least as bare dyads), but we seem to want another word to describe the
sound of metastable intervals. Apart from "metastable", some other
descriptions people have used are: complex, shadows, murky, gray/grey,
white, vague, diffuse, impressionistic, divinity imbued, and "a
different kind of consonance".

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/16/2008 5:42:18 PM

there is little dissonance in Metaslendro for instance. i repeat- a 12 tone cluster is way more consonant to anyone than 12 ET. In fact one of the major problems i have at times is that i cannot get it to sound dissonant past a certain point.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> A summary:
>
> The simpler noble intervals are easily-calculated representatives of
> the metastable regions between audibly Just ratios. The meaning of
> "metastable" in this context, is explained in
> http://dkeenan.com/Music/NobleMediant.txt > <http://dkeenan.com/Music/NobleMediant.txt>
>
> While it might be correct in one sense to describe the sound of
> metastable intervals as maximally "dissonant", this is only in terms
> of the kind of consonance we hear in Just intervals (those at, and
> very close to, simple-rational intervals).
>
> But this definitely fails to adequately describe the difference
> between the sound of a metastable interval and that of a very poorly
> tuned Just interval or an interval between metastable and Just which
> might even be a moderately complex rational such as 8:13.
>
> Almost everyone agrees that these latter intervals are dissonant (at
> least as bare dyads), but we seem to want another word to describe the
> sound of metastable intervals. Apart from "metastable", some other
> descriptions people have used are: complex, shadows, murky, gray/grey,
> white, vague, diffuse, impressionistic, divinity imbued, and "a
> different kind of consonance".
>
> -- Dave Keenan
>
>

🔗Carl Lumma <carl@...>

6/16/2008 6:04:47 PM

--- In tuning@yahoogroups.com, "Dave Keenan" wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" wrote:
> >
> > --- In tuning@yahoogroups.com, "djwolf_frankfurt" wrote:
> > > We're not after zero coincidence, as one could have sero
> > > coincidence and still have every pair of successive partials
> > > lie within critical band of one another, thus garanteeing
> > > beating; we're after maximizing the critical band distance
> > > between partials.
> >
> > And how do "phi-based" intervals accomplish this?
>
> If by phi-based numbers here we mean specifically the noble
> numbers, defined as numbers of the form
>
> i * m*phi
> ---------
> j + n*phi
>
> where i,j,m,n are integers
>
> and i*n - j*m = 1 or -1
>
> then they accomplish this by being local maxima of
> "unconvergability".
//
> Phi and its powers have the additional property (mentioned
> by Kraig as requiring precise tuning of it) that the
> differences between consecutive powers of phi are also
//

That's all well and good, Dave, but how does this address
Daniel's point?

-Carl

🔗Carl Lumma <carl@...>

6/16/2008 6:11:31 PM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> A summary:
>
> The simpler noble intervals are easily-calculated representatives
> of the metastable regions between audibly Just ratios. The
> meaning of "metastable" in this context, is explained in
> http://dkeenan.com/Music/NobleMediant.txt
>
> While it might be correct in one sense to describe the sound of
> metastable intervals as maximally "dissonant", this is only in
> terms of the kind of consonance we hear in Just intervals (those
> at, and very close to, simple-rational intervals).
>
> But this definitely fails to adequately describe the difference
> between the sound of a metastable interval and that of a very
> poorly tuned Just interval or an interval between metastable and
> Just which might even be a moderately complex rational such as
> 8:13.

I read all of that, including the Noble Mediant paper and would
like to ask:

* What, if any, audible properties are being claimed of
"metastable" intervals?

* If "metastable" intervals are "another kind of consonance",
where are the corresponding points of "another kind of
dissonance"? '13:8 or poorly tuned just intervals' is pretty
vague.

* What are the most prominent metastable intervals between
1 and 2?

etc.

-Carl

🔗Carl Lumma <carl@...>

6/16/2008 6:36:06 PM

I wrote:
>
> That's all well and good, Dave, but how does this address
> Daniel's point?

Because like, I think the only way to minimize beating is
to minimize critical-band interactions. And the only ways
I know of to do that are:

* Use wider intervals
* Voice intervals in higher registers
* Use just intervals (or their equivalent for other timbres)
* Use timbres with little energy in higher partials

-Carl

🔗Dave Keenan <d.keenan@...>

6/17/2008 1:51:31 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> > A summary:
> >
> > The simpler noble intervals are easily-calculated representatives
> > of the metastable regions between audibly Just ratios. The
> > meaning of "metastable" in this context, is explained in
> > http://dkeenan.com/Music/NobleMediant.txt
> >
> > While it might be correct in one sense to describe the sound of
> > metastable intervals as maximally "dissonant", this is only in
> > terms of the kind of consonance we hear in Just intervals (those
> > at, and very close to, simple-rational intervals).
> >
> > But this definitely fails to adequately describe the difference
> > between the sound of a metastable interval and that of a very
> > poorly tuned Just interval or an interval between metastable and
> > Just which might even be a moderately complex rational such as
> > 8:13.
>
> I read all of that, including the Noble Mediant paper and would
> like to ask:
>
> * What, if any, audible properties are being claimed of
> "metastable" intervals?

See last sentence of
/tuning/topicId_76975.html#77354
Best if you listen for yourself. And best if you can use a wheel or
joystick or something to vary a few cents either side.

> * If "metastable" intervals are "another kind of consonance",
> where are the corresponding points of "another kind of
> dissonance"? '13:8 or poorly tuned just intervals' is pretty
> vague.

I don't know.

> * What are the most prominent metastable intervals between
> 1 and 2?

See
/tuning/topicId_76975.html#77258

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/17/2008 2:01:23 AM

I have to admit, I'm not sure if what Dan Wolf said is literally true.
Maybe not _all_ the beat rates between partials in a phi interval are
outside the critical band, unless they also partake of one of the
following that you mentioned.
* Use wider intervals
* Voice intervals in higher registers
* Use timbres with little energy in higher partials

You could soon find out with a spreadsheet.

But even those that remain within the critical band are fast and
unsynchronised such that together they form a "beat" that is chaotic
and more like white noise.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I wrote:
> >
> > That's all well and good, Dave, but how does this address
> > Daniel's point?
>
> Because like, I think the only way to minimize beating is
> to minimize critical-band interactions. And the only ways
> I know of to do that are:
>
> * Use wider intervals
> * Voice intervals in higher registers
> * Use just intervals (or their equivalent for other timbres)
> * Use timbres with little energy in higher partials
>
> -Carl
>

🔗Carl Lumma <carl@...>

6/17/2008 9:21:13 AM

Dave wrote:
> > * What are the most prominent metastable intervals between
> > 1 and 2?
>
> See
> /tuning/topicId_76975.html#77258

!
Gold, silver, titanium - strong metastable intervals between 1 and 2.
8
!
339.
422.
560.
607.
792.
833.
943.
1002.
2/1
!
! Dave Keenan, TL77258.

Do you think metastability admits to octave equivalence?

-Carl

🔗Carl Lumma <carl@...>

6/17/2008 9:39:47 AM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> I have to admit, I'm not sure if what Dan Wolf said is literally
> true. Maybe not _all_ the beat rates between partials in a phi
> interval are outside the critical band, unless they also partake
> of one of the following that you mentioned.
> * Use wider intervals
> * Voice intervals in higher registers
> * Use timbres with little energy in higher partials
> You could soon find out with a spreadsheet.

I mean, aside from those generic things, we're looking for the
intervals which maximize the energy-weighted spacing between
partials. I think those are the simple ratios.

> But even those that remain within the critical band are fast and
> unsynchronised such that together they form a "beat" that is
> chaotic and more like white noise.

Extended-JI intervals beat, but in a highly periodic manner.
7/6 and to a lesser extent 7/4 have a distinctive "periodicity
buzz" that many listeners find very pleasant. These beats
also occur only in the upper partials. I don't see how
chaotic beating is a good thing, but I guess the main question
is if it's distinct under audition (I suspect it may be, but
not to any great degree of accuracy).

-Carl

🔗Dave Keenan <d.keenan@...>

6/17/2008 3:25:21 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> > I have to admit, I'm not sure if what Dan Wolf said is literally
> > true. Maybe not _all_ the beat rates between partials in a phi
> > interval are outside the critical band, unless they also partake
> > of one of the following that you mentioned.
> > * Use wider intervals
> > * Voice intervals in higher registers
> > * Use timbres with little energy in higher partials
> > You could soon find out with a spreadsheet.
>
> I mean, aside from those generic things, we're looking for the
> intervals which maximize the energy-weighted spacing between
> partials. I think those are the simple ratios.

Certainly. But we're claiming that something else audible, worth
distinguishing and giving its own name, happens near the nobles or HE
maxima. Maybe they are local maxima of energy-weighted spacing between
partials. Maybe not.

> > But even those that remain within the critical band are fast and
> > unsynchronised such that together they form a "beat" that is
> > chaotic and more like white noise.
>
> Extended-JI intervals beat, but in a highly periodic manner.
> 7/6 and to a lesser extent 7/4 have a distinctive "periodicity
> buzz" that many listeners find very pleasant. These beats
> also occur only in the upper partials. I don't see how
> chaotic beating is a good thing, but I guess the main question
> is if it's distinct under audition

Exactly.

> (I suspect it may be, but
> not to any great degree of accuracy).

I'm certainly not claiming any great degree of accuracy for it, except
possibly for the difference-tone effect that Kraig and Dan Wolf
mentioned in the case of phi itself (not any other nobles, except
possibly other powers of phi), e.g. in Tenney's 'For Ann (rising)'.

> Do you think metastability admits to octave equivalence?

There may be a tiny bit of octave equivalence for the stronger
metastables. But noble numbers

🔗Dave Keenan <d.keenan@...>

6/17/2008 6:03:23 PM

Oops. I sent the previous message before I'd finished it.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:

> > Do you think metastability admits to octave equivalence?

There may be a tiny bit of octave equivalence for the stronger
metastables. But no two noble numbers differ by a factor of two. A
proof of this follows from the cross-multiplication requirement, that
|i*n - j*m| = 1 for the noble number

i + m*phi
---------
j + n*phi

i,j,m,n are integers and so the cross-mutiply requirement means that
at least one of i*n or j*m must be odd, and a product can only be odd
if all its factors are odd, so at least one of the integers on the top
(i, m) must be odd and at least one on the bottom (j, n) must be odd.
So we cannot transpose the noble number by an octave by dividing top
or bottom by two (or we will not have integers). We must multiply
either top or bottom by two.

Consider multiplying the top by two. The only way to do this is to
multiply both i and m by two. This is because phi is irrational (in
fact the most irrational) and so no multiple of phi can ever be an
integer or vice versa. [Although interestingly every integer can be
generated as a finite sum of powers of phi -- so called phi-nary
number representation.]

2*i + 2*m*phi
-----------
j + n*phi

cannot be noble since |2*i*n - 2*j*m| cannot be 1. It must be 2.

The same argument applies to multiplying the bottom by two. And same
for octave inversions.

So no two nobles differ by a factor of two. But the four simplest ones
come in pairs that differ by a factor of phi. I actually missed one of
these in my earlier list, the other "golden" one at 1666 cents
(phi-squared).

So it might have been tempting to posit "phi-tave" equivalence for
noble intervals, but that's not true either (except for phi and 3-phi
having a single phi-tave extension each).

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/17/2008 9:49:42 PM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Oops. I sent the previous message before I'd finished it.
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > > Do you think metastability admits to octave equivalence?
>
> There may be a tiny bit of octave equivalence for the stronger
> metastables. But no two noble numbers differ by a factor of two.

If the audible difference you're hearing is due to the way
the partials are lining up, then adding an octave shouldn't
change that too much...

-Carl

🔗Carl Lumma <carl@...>

6/17/2008 11:50:03 PM

I wrote:

> !
> Gold, silver, titanium - strong metastable intervals
> 8
> !
> 339.
> 422.

The number under the big G should be a 9, sorry. -Carl

🔗Carl Lumma <carl@...>

6/17/2008 11:58:45 PM

> Extended-JI intervals beat, but in a highly periodic manner.
> 7/6 and to a lesser extent 7/4 have a distinctive "periodicity
> buzz" that many listeners find very pleasant. These beats
> also occur only in the upper partials. I don't see how
> chaotic beating is a good thing, but I guess the main question
> is if it's distinct under audition (I suspect it may be, but
> not to any great degree of accuracy).

Here are my notes on the gold, silver, and titanium intervals...

339. passable minor 3rd
422. dissonant and nicely ambiguous
560. passable tritone but also somewhat ambiguous
607. very like 600 cents, which is to say ambiguous
792. passable minor 6th
833. sounds like 13/8 but without the periodicity buzz
943. nicely ambiguous
1002. sounds like 1000 cents; passable 7/4

The only ones I found ambiguous-sounding were:

422. dissonant and nicely ambiguous
560. passable tritone but also somewhat ambiguous
607. very like 600 cents, which is to say ambiguous
943. nicely ambiguous

I tried these mostly as dyads, so I can't say much of
chords. I did quickly try a few things, including
playing the entire scale at one time but didn't note
anything special.

I wish I had a knob-tunable synth to hand.

What's metaslendro I wonder? (I'd like to try it.)

-Carl

🔗Dave Keenan <d.keenan@...>

6/18/2008 3:25:54 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I wrote:
>
> > !
> > Gold, silver, titanium - strong metastable intervals
> > 8
> > !
> > 339.
> > 422.
>
> The number under the big G should be a 9, sorry. -Carl
>

I also note that you (rightly) included those I called "chrome" too.

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/18/2008 1:31:54 PM

I wrote:

> Here are my notes on the gold, silver, and titanium intervals...
//
> The only ones I found ambiguous-sounding were:
> 422. dissonant and nicely ambiguous
> 560. passable tritone but also somewhat ambiguous
> 607. very like 600 cents, which is to say ambiguous
> 943. nicely ambiguous
> I tried these mostly as dyads, so I can't say much of
> chords.
//
> I wish I had a knob-tunable synth to hand.

So I played around with some chords in Scala, and for
chords it can do even better than a knob -- while keeping
a chord going in the chromatic clavier, I can type
"quantize 17" or whatever to retune it in an ET and then
"undo" to tune it back. It works in realtime.

Most things I tried were indeed less dissonant than the
metastable versions. One exception was the 422-cent
interval. It's noticeably more consonant than the 13-ET
3rd, and this agrees with harmonic entropy...

422 4.6099115
458 4.6235625

So the noble mediant procedure doesn't get us to the
harmonic entropy maximum in this case.

After a bunch of listening I think there's nothing to
the sound I'm hearing other than dissonance (I hear both
more beating and less tonalness). Dissonance isn't a
bad thing, but I hear no other kind of sensation
distinguishing these examples. Furthermore, the noble
mediant procedure generated several intervals that sounded
like just approximations to me, and missed at least one
more dissonant interval that harmonic entropy caught.
So my advice would tentatively be, if you want tonally
ambiguous scales or scales with lots of beating, use
harmonic entropy maxima instead of noble mediants.

-Carl

🔗Dave Keenan <d.keenan@...>

6/18/2008 2:54:55 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> So I played around with some chords in Scala, and for
> chords it can do even better than a knob -- while keeping
> a chord going in the chromatic clavier, I can type
> "quantize 17" or whatever to retune it in an ET and then
> "undo" to tune it back. It works in realtime.

But presumably it jumps -- it doesn't sweep?

> Most things I tried were indeed less dissonant than the
> metastable versions. One exception was the 422-cent
> interval. It's noticeably more consonant than the 13-ET
> 3rd, and this agrees with harmonic entropy...
>
> 422 4.6099115
> 458 4.6235625
>
> So the noble mediant procedure doesn't get us to the
> harmonic entropy maximum in this case.

But surely these are on separate HE humps? Surely you hear 7:9 (435
cents) as a local minimum between them? The question is whether you
hear 422 as the maximum between 4:5 and 7:9?

>
> After a bunch of listening I think there's nothing to
> the sound I'm hearing other than dissonance (I hear both
> more beating and less tonalness). Dissonance isn't a
> bad thing, but I hear no other kind of sensation
> distinguishing these examples.

But you have already said you heard "ambiguousness" at some of them.
Surely that is not the same thing as dissonance?

> Furthermore, the noble
> mediant procedure generated several intervals that sounded
> like just approximations to me,

But weren't these also HE maxima?

> and missed at least one
> more dissonant interval that harmonic entropy caught.

I have already pointed out that noble mediants fail to predict those
HE maxima closest to the unison, octave and perfect fifth. I'll now
add the one closest to the perfect fourth on the narrow side.

> So my advice would tentatively be, if you want tonally
> ambiguous scales or scales with lots of beating, use
> harmonic entropy maxima instead of noble mediants.

But which parameterisation of HE should we use for this? It is exactly
those maxima (those the noble mediant fails to predict) that move
around the most with a change in sigma or s.

There also remains a possibility that something different can be heard
at more precisely tuned nobles than we've been listening to, and in
larger tone clusters.

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/18/2008 4:23:45 PM

Dave wrote:
> > So I played around with some chords in Scala, and for
> > chords it can do even better than a knob -- while keeping
> > a chord going in the chromatic clavier, I can type
> > "quantize 17" or whatever to retune it in an ET and then
> > "undo" to tune it back. It works in realtime.
>
> But presumably it jumps -- it doesn't sweep?

I think it jumps, but it's pretty smooth.

> > Most things I tried were indeed less dissonant than the
> > metastable versions. One exception was the 422-cent
> > interval. It's noticeably more consonant than the 13-ET
> > 3rd, and this agrees with harmonic entropy...
> >
> > 422 4.6099115
> > 458 4.6235625
> >
> > So the noble mediant procedure doesn't get us to the
> > harmonic entropy maximum in this case.
>
> But surely these are on separate HE humps? Surely you hear 7:9 (435
> cents) as a local minimum between them? The question is whether you
> hear 422 as the maximum between 4:5 and 7:9?

Yes, but the point is the n strongest noble mediants don't
correspond to the n biggest h.e. maxima.

> > After a bunch of listening I think there's nothing to
> > the sound I'm hearing other than dissonance (I hear both
> > more beating and less tonalness). Dissonance isn't a
> > bad thing, but I hear no other kind of sensation
> > distinguishing these examples.
>
> But you have already said you heard "ambiguousness" at some of them.
> Surely that is not the same thing as dissonance?

Dissonance is usually seen as having two components, one of
which is roughness and the other ambiguousness (entropy).

> > Furthermore, the noble
> > mediant procedure generated several intervals that sounded
> > like just approximations to me,
>
> But weren't these also HE maxima?

Presumably, though I didn't check.

> > So my advice would tentatively be, if you want tonally
> > ambiguous scales or scales with lots of beating, use
> > harmonic entropy maxima instead of noble mediants.
>
> But which parameterisation of HE should we use for this? It is
> exactly those maxima (those the noble mediant fails to predict)
> that move around the most with a change in sigma or s.

What's sigma (the same as s I thought)? I like 1.0%. It'll
depend on the listener, so it's good that this is a free
parameter.

> There also remains a possibility that something different can
> be heard at more precisely tuned nobles than we've been
> listening to,

Unlikely based on what I've heard. Also: why suspect this?

> and in larger tone clusters.

Well that brings me to my next question, which is: should
there be anything special about one noble mediant subtracted
from another (i.e. the dyads formed in chords)?

-Carl

🔗Kraig Grady <kraiggrady@...>

6/18/2008 5:37:44 PM

yes 'usually' , but as i mentioned there are pieces of Kyle Gann's which illustrates how unambiguous dissonances can be.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
>
>
>
> Dissonance is usually seen as having two components, one of
> which is roughness and the other ambiguousness (entropy).
>
>
>

🔗Dave Keenan <d.keenan@...>

6/18/2008 11:33:25 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > > Most things I tried were indeed less dissonant than the
> > > metastable versions. One exception was the 422-cent
> > > interval. It's noticeably more consonant than the 13-ET
> > > 3rd, and this agrees with harmonic entropy...
> > >
> > > 422 4.6099115
> > > 458 4.6235625
> > >
> > > So the noble mediant procedure doesn't get us to the
> > > harmonic entropy maximum in this case.
> >
> > But surely these are on separate HE humps? Surely you hear 7:9
> > (435 cents) as a local minimum between them? The question is
> > whether you hear 422 as the maximum between 4:5 and 7:9?
>
> Yes, but the point is the n strongest noble mediants don't
> correspond to the n biggest h.e. maxima.

No one ever claimed the n strongest noble mediants corresponded to the
n biggest HE maxima. Only that the n strongest noble mediants
correspond to HE maxima.

The point is, you claimed the noble at 422 cents does not correspond
to a HE maximum at all. You were mistaken. You were looking at the
wrong HE maximum.

> What's sigma (the same as s I thought)?

Yes. It is sometimes called sigma in Paul's writings and sometimes
"s", presumably because of the lack of a greek character set.

> I like 1.0%. It'll
> depend on the listener, so it's good that this is a free
> parameter.

But _does_ the position of these maxima depend on the listener. That's
an interesting empirical question.

> > There also remains a possibility that something different can
> > be heard at more precisely tuned nobles than we've been
> > listening to,
>
> Unlikely based on what I've heard. Also: why suspect this?

Only because of some things Kraig has said including that the
difference tones become tones of the chord/scale.

> > and in larger tone clusters.
>
> Well that brings me to my next question, which is: should
> there be anything special about one noble mediant subtracted
> from another (i.e. the dyads formed in chords)?

There are usually only one or two metastable intervals in a chord.
e.g. Keenan Pepper's "crunchy" chords.

There are no saturated strictly-noble chords smaller than an octave.
However I found the following approximate one (and its inverse) which
should still qualify as saturated metastable.
0-338-944 0-606-944 cents

The simplest saturated noble triad is
0-833-1666 cents and is its own inverse.
Some others narrower than this (inverse pairs) are:
0-560-1503 0-943-1503 cents
0-422-1424 0-1002-1424
0-339-1378 0-1039-1378
0-607-1378 0-771-1378

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/19/2008 12:28:19 AM

Dave wrote:
> The point is, you claimed the noble at 422 cents does not
> correspond to a HE maximum at all. You were mistaken. You were
> looking at the wrong HE maximum.

My point was, your paper talks about finding the ambiguous
point between 5/4 and 4/3 and winds up with 422 cents, which
ain't it.

> > I like 1.0%. It'll
> > depend on the listener, so it's good that this is a free
> > parameter.
>
> But _does_ the position of these maxima depend on the listener.
> That's an interesting empirical question.

Yes, it should be tested.

> > > There also remains a possibility that something different can
> > > be heard at more precisely tuned nobles than we've been
> > > listening to,
> >
> > Unlikely based on what I've heard. Also: why suspect this?
>
> Only because of some things Kraig has said including that the
> difference tones become tones of the chord/scale.

That's pretty weak.

> > > and in larger tone clusters.
> >
> > Well that brings me to my next question, which is: should
> > there be anything special about one noble mediant subtracted
> > from another (i.e. the dyads formed in chords)?
>
> There are usually only one or two metastable intervals in a chord.

I mean, if I play a chord in the 9-tone 'scale' I made,
should there be anything special about the dyads formed?
i.e. is the difference of two noble mediant intervals
anything special?

> e.g. Keenan Pepper's "crunchy" chords.

Keenan Pepper's crunchy chords have nothing to do with
noble mediants, harmonic entropy maxima, or any of it.
At least not the way they were originally presented:
/tuning/topicId_11922.html#11922

-Carl

🔗Dave Keenan <d.keenan@...>

6/19/2008 1:54:42 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> My point was, your paper talks about finding the ambiguous
> point between 5/4 and 4/3 and winds up with 422 cents, which
> ain't it.

OK. That could be a problem. Thanks. Perhaps we chose a bad example
with which to begin our exposition, since there are two ambiguous
points between 5/4 and 4/3.

I see we wrote:
"Similarly, while both 4:3 and 5:4 are simple or "planetlike" ratios,
the 4:3 has a greater degree of simplicity or attraction, so that we
might expect the point of maximum complexity or ambiguity to be
somewhat closer to 5:4."

Can you suggest how we might fix this with minimum changes?

Certainly 422 cents is not the point of maximum harmonic entropy or
dissonance between 4:3 and 5:4 but it's an unclear whether or not it
is the point of maximum complexity or ambiguity.

A litle later we write:
"At this stage we will drop the 4:3 and consider the series to have
begun with the last two attractors to appear, 5:4 and 9:7, ...".

> > > Well that brings me to my next question, which is: should
> > > there be anything special about one noble mediant subtracted
> > > from another (i.e. the dyads formed in chords)?
> >
> > There are usually only one or two metastable intervals in a chord.
>
> I mean, if I play a chord in the 9-tone 'scale' I made,
> should there be anything special about the dyads formed?
> i.e. is the difference of two noble mediant intervals
> anything special?

No.

> > e.g. Keenan Pepper's "crunchy" chords.
>
> Keenan Pepper's crunchy chords have nothing to do with
> noble mediants, harmonic entropy maxima, or any of it.
> At least not the way they were originally presented:
> /tuning/topicId_11922.html#11922

I don't understand why you say that. Clearly a chord with one interval
at a harmonic entropy maximum and all the rest Just, would be an
exemplary crunchy chord according to Keenan's definition.

-- Dave Keenan

🔗Carl Lumma <carl@...>

6/19/2008 10:24:49 AM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > My point was, your paper talks about finding the ambiguous
> > point between 5/4 and 4/3 and winds up with 422 cents, which
> > ain't it.
>
> OK. That could be a problem. Thanks. Perhaps we chose a bad example
> with which to begin our exposition, since there are two ambiguous
> points between 5/4 and 4/3.
>
> I see we wrote:
> "Similarly, while both 4:3 and 5:4 are simple or "planetlike"
> ratios, the 4:3 has a greater degree of simplicity or
> attraction, so that we might expect the point of maximum
> complexity or ambiguity to be somewhat closer to 5:4."
>
> Can you suggest how we might fix this with minimum changes?

If you have an example that works you could put it there. :)

> Certainly 422 cents is not the point of maximum harmonic entropy
> or dissonance between 4:3 and 5:4 but it's an unclear whether or
> not it is the point of maximum complexity or ambiguity.

Well I'm reporting I didn't hear it that way. I was just randomly
retuning the interval and happened to stop within 3 cents of
the h.e. maximum.

> A litle later we write:
> "At this stage we will drop the 4:3 and consider the series to have
> begun with the last two attractors to appear, 5:4 and 9:7, ...".

Yeah, that was weird. To me, it still indicates you're thinking
in terms of finding the ambiguity between 5/4 and 4/3, but you
took the trouble to write more charactors than the 4/3 entry
would have been in the table.

> > > e.g. Keenan Pepper's "crunchy" chords.
> >
> > Keenan Pepper's crunchy chords have nothing to do with
> > noble mediants, harmonic entropy maxima, or any of it.
> > At least not the way they were originally presented:
> > /tuning/topicId_11922.html#11922
>
> I don't understand why you say that. Clearly a chord with one
> interval at a harmonic entropy maximum and all the rest Just,
> would be an exemplary crunchy chord according to Keenan's
> definition.

I see what you mean now, sorry.

-Carl

🔗Cameron Bobro <misterbobro@...>

6/20/2008 5:07:08 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > > My point was, your paper talks about finding the ambiguous
> > > point between 5/4 and 4/3 and winds up with 422 cents, which
> > > ain't it.
> >
> > OK. That could be a problem. Thanks. Perhaps we chose a bad
example
> > with which to begin our exposition, since there are two ambiguous
> > points between 5/4 and 4/3.
> >
> > I see we wrote:
> > "Similarly, while both 4:3 and 5:4 are simple or "planetlike"
> > ratios, the 4:3 has a greater degree of simplicity or
> > attraction, so that we might expect the point of maximum
> > complexity or ambiguity to be somewhat closer to 5:4."
> >
> > Can you suggest how we might fix this with minimum changes?
>
> If you have an example that works you could put it there. :)
>
> > Certainly 422 cents is not the point of maximum harmonic entropy
> > or dissonance between 4:3 and 5:4 but it's an unclear whether or
> > not it is the point of maximum complexity or ambiguity.
>
> Well I'm reporting I didn't hear it that way. I was just randomly
> retuning the interval and happened to stop within 3 cents of
> the h.e. maximum.

My "wrong way" to strike a thirth or a foird also gets the same as
the harmonic entropy maximum. I get 458 point something. I disagree
with some of Dave's assessments about noble intervals.

When I tried to sing a most inbetweeny interval there three times out
of the blue with no reference or cheating (eg up a semitone from 5/4)
I first got a 9/7, the same as HE max, and then a 9/7 again. The
accuracy of the 9/7 surpassed the measuring abilities of my equipment,
the "thirth" was somewhere from 458-464.

I'll be posting some stuff, and sound files! hear my fumbling in all
its uncensored glory! about earing in intervals over a drone.

I consider the attraction of Just intervals "quod erat demonstratum".
Speaking for myself, they are hard to avoid even if I am deliberately
trying to do so. (Physical documentary evidence following ASAP).

And so I agree with Kraig that whatever regular and predictable
"shadows" may be, they do fall under Just Intonation, for the
harmonic series is what they exist with or poised against or whatever.

More to follow, still triple-checking every dang frequency at the
sample level.

🔗daniel_anthony_stearns <daniel_anthony_stearns@...>

6/20/2008 6:51:21 AM

Hello there David et al. I think in some ways metastability is
already achieved without phi weighting--so long as you allow that the
more complex a ratio is (the larger its numbers) the higher it sits
in relation to its more stable-state neighbors. Though as an aside, I
do think phi-weighting is the best way to go to define generators for
all 2 step-size scales... that seems like a perfect generalization to
me, and same for other metallic-constants to define step sizes for
other scales of more than two step-sizes.

Anyway, what I was trying to do in the earlier White Knife post was
to model span in a simple rule-of-thumb way, like N*D, the product of
the numerator and the denominator for height. Envisioning spanhow
wide a given ratio might bemight allow one to model those places
where intervals cross into each other's field of attraction leading
to ambiguity. I know this has all been done by others in different
ways, but consider this:

If you take any given ratio and its inversion, 2:3 and 3:4 for
example, and take the sum of both you have already converted them to
an EDO:

2+3=5
3+4=7

Now to set a width you'd need to define a step out of each EDO, and
there's a type of critical band here where (LOG(N)-LOG(D))*(EDO/LOG
(2)) is the rule-of-thumb. This is simply defined as:

(N-D)*3
and,
(N-D)*4

So for the 2:3 the rule-of-thumb is 3/5 at the sharp edge and 4/7 at
the flat edge. This simple conversion formula works for any given
arbitrary frequency ratio and can generally be done in your head (or
at least scribbled on a piece of paper) in a few seconds time using
nothing more than its inherent numbers.

The charts I generated for The White Knife has a sharp Handle were
the result of intertwining to Stern-Brocot trees as Scale Trees where
the frequency ratios have been converted to EDOs using the above rule-
of-thumb. And if I allowed only ratios with shared borders (and none
with overlapping borders), you'd have the following octave:

10:11 9:10 8:9 7:8 6:7 5:6 9:11 4:5 7:9 3:4 5:7 7:10 2:3 7:11 5:8 3:5
7:12 4:7 9:16 5:9 6:11 7:13 8:15 9:17 10:19

And here's the same with the ratios given as the rule-of-thumb
conversion to EDO fractions:

(4/31 3/21) (4/28 3/19) (4/25 3/17) (4/22 3/15) (4/19 3/13) (4/16
3/11) (8/29 6/20) (4/13 3/9) (8/23 6/16) (4/10 3/7) (8/17 6/12)
(12/24 9/17) (4/7 3/5) (16/25 12/18) (12/18 9/13) (8/11 6/8) (20/26
15/19) (12/15 9/11) (28/34 21/25) (16/19 12/14) (20/23 15/17) (24/27
18/20) (28/31 21/23) (32/35 24/26) (36/39 27/29)

This would leave gray space, or pockets of ambiguity between most
ratios (though here the 10:11's upper limit is shared by the 9:10's
lower limit and the 5:7's upper limit is shared by the 7:10's lower
limit).

What's interesting on modeling span this or some other, more
sophisticated way (besides offering a nice pantheistic example of the
flexibility and interconnectedness of the pitch-space stratum theses
numbers occupy!) is that you can "see" things like a 8:11's sharp
edge crossing over into a 5:7's flat edge, suggesting that the 8:11
is more likely to be confused for a flat 5:7 than it is a sharp
3:4... or that a 11:13 is much more likely to be heard as a sharp 6:7
than it is a flat 5:6, though it also shares that border as well, so
it's somewhat even less likely to be heard as an independent interval
space of its own.

dan stearns

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Wonderful to hear from you Daniel.
>
> Yes! This is clearly an idea whose time has come, since people seem
to
> be converging on it from all directions. I see this quote of yours
as
> capturing the essential point:
>
> "... an 11/9 might be the simplest ratio to define a neutral third,
> but whether or not that's THE interval is somewhat besides the point
> in comparison to the question of whether this is an independently
> articulated interval space outside the field of attraction imposed
by
> the long shadows of its neighbors."
>
> It seems Mike B and Cameron agree with you that the sharp knife has
a
> chroma-free handle at least, but grey or shadowy rather than white.
>
> I suppose you could equally reverse the metaphor and say: "... space
> outside the field of attraction imposed by the bright (coloured)
> lights of its neighbours."
>
> So my suggestion is to avoid the confusion by not naming these
shadow
> regions after any particular rational fraction at all, but to
> in-effect name them after the _pair_ of Just ratios being avoided.
And
> if a particular point is to be identified with the region then it
> makes more sense not to use any rational number, but to use the
> irrational noble mediant of the two Just ratios being avoided,
> expressed as
>
> 5+6phi
> ------
> 4+5phi
>
> You can see the two ratios 5/4 and 6/5 within the expression.
>
> It simplifies to
>
> 1+5phi
> ------ ~= 339 cents
> 1+4phi
>
> and I style it the "chrome" (narrow) neutral third in this message
> /tuning/topicId_76975.html#77258
> because of the level of the Stern-Brocot or scale tree where it
first
> appears.
>
> I used this series of sucessively less noble commonly-known metals:
> Gold, Silver, Titanium, Chrome, Nickel, Copper. But I may have
grouped
> some of those nobles wrongly. It's probably a silly idea anyway.
> "Noble neutral third" is quite sufficient as there isn't another one
> until you go down two more levels. Although it may turn out to be
> useful to distinguish the golden neutral sixth at 833c from the
nickel
> neutral sixth at 849c (assuming 8:13 can be considered an
attractor).
>
> -- Dave Keenan
>
>
> --- In tuning@yahoogroups.com, "daniel_anthony_stearns"
> <daniel_anthony_stearns@> wrote:
> >
> > hi there David.i don't really have time to participate in all
this as
> > much as i'd like, but i thought i'd just mention that the thread
i
> > posted a couple weeks ago--the sharp knife has a white handle--
was
> > about exactly this (where to draw limits and what to call borders
in
> > the "scale tree"). And what's potentially interesting on it, is
that
> > the method is one i came up with quite a while ago (back in the
late
> > 90s on these lists) but didn't really fully notice it as i was
using
> > the method to convert EDOs to frequency ratio series by bending
> > overtone and undertone series towards a median series. Anyway,
the
> > method, while giving similar results, is quite different from
those
> > that are usually cited--i.e, Helmholtz,Partch, Erlich's HE etc.
The
> > results are similar, though perhaps even more "conservative" than
you
> > suggest in this post.
> > take care, daniel
>

🔗Carl Lumma <carl@...>

6/20/2008 10:28:07 AM

Cameron Bobro wrote:
> My "wrong way" to strike a thirth or a foird also gets the same as
> the harmonic entropy maximum. I get 458 point something.

What way is that?

-Carl

🔗Cameron Bobro <misterbobro@...>

6/20/2008 12:26:16 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Cameron Bobro wrote:
> > My "wrong way" to strike a thirth or a foird also gets the same
as
> > the harmonic entropy maximum. I get 458 point something.
>
> What way is that?

Golden cut, used just like any other mediant or mean, but it needs to
be "aimed" one way or the other when deliberately avoiding or
balancing two intervals.

The golden section is extremely simple as you know, it's just
A+B is to A as A is to B, and I do it on the frequency level. This
means of course that if you have 100 and 200 Hz, and you make the
golden section, it's at 161.83... Hz and the resulting ratios between
frequencies are the "same". In this case the "metastability" is
perhaps most obvious if you play it like C-Ab-c or use a rich timbre,
even if it's only roughly harmonic.

Some of the results are exactly the same as the Noble Mediant
procedure, the first one which Dave calls Gold, for example. The
second most obvious one, simply making a golden cut of the 833 cent
golden interval, is also one of the metastable intervals on Dave's
list. These intervals create the same difference tone- if you
continue the process you leave what Dave would find acceptable :-D
but you can have chords and scales with great "oneness" in the
difference tones, where everything is returning something else in the
tuning or the difference tones are an inverted harmonic series of one
of the tones.

Kraig is surely using chords and scales that do these things because
you can hear the "other oneness" or whatever it is. The unity and
harmonic relationships of difference tones for one thing can't be
dismissed. Rameau and Tartini might have gotten carried away but they
did describe real acoustic phenomena that are at least legitimate
components of what's going on in tonality and consonance, I think we
can agree on that?

As far as the point of balance between 5/4 and 4/3, n*d doesn't work
to determine the fields of attraction as 4/3 is simpler and lower in
the harmonic series, but 5/4 fuses with the harmonics- in wide
voicings, it IS a harmonic so to speak. And so the "thirth" or
"foird" must be closer to 4/3, not 5/4, and in this case (and others)
the golden section of frequency ratios returns the same result as
harmonic entropy. You found the same tiny region by ear as I did, and
it corresponds both to HE and to the method I'm using.

My problem with HE is that I can't hear the "red thread". It's like
members of different character families, some of which correspond
with accuracy that makes sheer accident suspect to intervals I hear
and others which don't.

These things work in different voicings and inversions.

Hasn't anyone else noticed that yee olde "consonant interval" of Ibn
Sin, 196/169, which I brought up quite some time ago on this as a
strange "far-away consonance" which I couldn't properly explain, is
the inversion of one of the first-families Noble intervals?

-Cameron Bobro

🔗Carl Lumma <carl@...>

6/20/2008 1:28:22 PM

Cameron wrote:
> The golden section is extremely simple as you know, it's just
> A+B is to A as A is to B, and I do it on the frequency level. This
> means of course that if you have 100 and 200 Hz, and you make the
> golden section, it's at 161.83... Hz

Can you show me step-by-step?

> Kraig is surely using chords and scales that do these things
> because you can hear the "other oneness" or whatever it is.
> The unity and harmonic relationships of difference tones for
> one thing can't be dismissed. Rameau and Tartini might have
> gotten carried away but they did describe real acoustic
> phenomena that are at least legitimate components of what's
> going on in tonality and consonance, I think we can agree
> on that?

I don't know enough about your technique or Erv's to say
if they're the same, though Dave might. Kraig's given me
a tutorial on MMM that I hope to tackle tonight, and
hopefully you'll respond to my question above, and then
I'll hopefully be able to understand it.

Difference tones can be used to great effect in music.
When Kraig and Erin played me a melody in difference
tones I had a revelatory experience on the spot. But
that was a live performance, on a metallophone, played
at high volume in a confined space. You simply don't
get that kind of thing in common musical situations.

> As far as the point of balance between 5/4 and 4/3, n*d
> doesn't work to determine the fields of attraction as
> 4/3 is simpler and lower in the harmonic series, but 5/4
> fuses with the harmonics- in wide voicings, it IS a
> harmonic so to speak. And so the "thirth" or "foird" must
> be closer to 4/3, not 5/4,

First off, n*d isn't an octave equivalence thing.
5*2 is < 4*3. Secondly, it isn't meant to predict
fields of attraction. It gives good results for
consonance rankings, and indeed I think it nails
5/2 4/3 and 5/4 in that regard. Mediant-to-mediant
widths are also *approximately* 1/sqrt(n*d) over a
large Farey series, according to Paul Erlich.

> and in this case (and others)
> the golden section of frequency ratios returns the same
> result as harmonic entropy.

Can you give specific examples? Does it work
regardless of where I put the intervals in frequency
space, e.g. if I start between 100 and 200 Hz or if
I instead go between 200 and 400 Hz?

> My problem with HE is that I can't hear the "red thread".

Have you auditioned the local minima and maxima?

> These things work in different voicings and inversions.

Harmonic entropy is most definitely not octave-symmetric.

-Carl

🔗Dave Keenan <d.keenan@...>

6/20/2008 3:00:03 PM

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
> My "wrong way" to strike a thirth or a foird also gets the same as
> the harmonic entropy maximum. I get 458 point something. I disagree
> with some of Dave's assessments about noble intervals.

This is great. Thanks Cameron. If it's my maths versus your ears, I'm
gonna go with your ears every time. I suspect I only said it was the
wrong way to calculate the simplest noble between 5/4 and 4/3. But
clearly the simplest noble does not give the strongest metastable in
this case.

So it seems that HE maxima are good predictors of shadows (metastable
sounding intervals) and simple noble numbers are good predictors of
_some_ HE maxima -- not those closest to the really strong consonances
of unison, octave, fifth or fourth.

I look forward to hearing what else your experiments disagree with.

-- Dave Keenan

🔗Cameron Bobro <misterbobro@...>

6/20/2008 3:40:56 PM

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> > My "wrong way" to strike a thirth or a foird also gets the same
as
> > the harmonic entropy maximum. I get 458 point something. I
disagree
> > with some of Dave's assessments about noble intervals.
>
> This is great. Thanks Cameron. If it's my maths versus your ears,
I'm
> gonna go with your ears every time. I suspect I only said it was the
> wrong way to calculate the simplest noble between 5/4 and 4/3. But
> clearly the simplest noble does not give the strongest metastable in
> this case.
>
> So it seems that HE maxima are good predictors of shadows
(metastable
> sounding intervals) and simple noble numbers are good predictors of
> _some_ HE maxima -- not those closest to the really strong
consonances
> of unison, octave, fifth or fourth.
>
> I look forward to hearing what else your experiments disagree with.
>
> -- Dave Keenan

It is interesting to note that Carl eared in to the same place. But
also note what Kraig said about subjectivity on MMM. I completely
agree that subjectivity is good and I won't try to conceal it.

I'm dead sure I'm listening with a lot of subjectivity and am sure to
label some intervals as "floating" simply because they are to my
taste, and miss others because I just don't like them. At any rate
let's go for the simplest explanations- when I get a chance to upload
some notes tuned in over a drone using an analog knob, I think you'll
agree that the 765 cent interval I tuned in by feel is best explained
as a 14/9 (.1 cent away). :-D

And strange intervals can even be explained with "5-limit" Just- we
will never know for sure if I or Carl actually unconciously just
went up a 25/24 from 5/4, which is simply moving m3 and M3 up one
slot so to speak, or simply detuned 13/10 a hair high, thereby
arriving at the same place, will we?

-Cameron Bobro

🔗Dave Keenan <d.keenan@...>

6/20/2008 4:16:25 PM

--- In tuning@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@...> wrote:
>
> Hello there David et al. I think in some ways metastability is
> already achieved without phi weighting--so long as you allow that the
> more complex a ratio is (the larger its numbers) the higher it sits
> in relation to its more stable-state neighbors.

I agree. I recently suggested that the range of metastability between
two Just intervals i:j and m:n should be considered to be bounded
(inclusively) on one side by their classic mediant (i+m):(j+n).

Your rule of thumb for the range of attraction of a just interval is
fascinating since it gives a result in logarithmic pitch space (EDOs)
without the use of any log function.

I note that for a ratio N/D (in lowest terms), if N is even, the
inversion of N/D in lowest terms is D/(N/2), otherwise it is 2D/N.

So you're saying that a frequency ratio N/D (in lowest terms, with
N>=D) can be considered to have a range:
if N is even, from 4(N-D)/(N+D) octave to 3(N-D)/(D+N/2) octave, or
if N is odd, from 4(N-D)/(N+2D) octave to 3(N-D)/(D+N) octave.

Or more simply, as you had it, if n/d is the octave-inversion of N/D
then it ranges
from 4(N-D)/(N+n) octave to 3(N-D)/(D+d) octave.

Wow! That's a brilliantly simple rule. It's not perfect of course
since it seems to give 10:19 more importance than it deserves, but as
a rule-of-thumb it's great.

-- Dave Keenan

🔗Dave Keenan <d.keenan@...>

6/20/2008 5:19:09 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I don't know enough about your technique or Erv's to say
> if they're the same, though Dave might. Kraig's given me
> a tutorial on MMM that I hope to tackle tonight, and
> hopefully you'll respond to my question above, and then
> I'll hopefully be able to understand it.

I've only sorted this stuff out myself very recently.

On the scale tree, Erv is using the same thing as Margo and I, the
noble _mediant_. That's where you phi-weight the numerators and
denominators individually.

NMed(i/j, n/m) = (i + m*phi)/(j + n*phi), where i*j < n*m

Cameron is using two golden _means_

GMeanUp(i/j, n/m) = (i/j + phi*m/n)/(1+phi)
GMeanDn(i/j, n/m) = (phi*i/j + m/n)/(1+phi)

The interesting thing is that Cameron's golden means give results that
are very close to noble numbers. They are identical to noble numbers
if the two ratios have denominators of 1. They are within a few cents
of the noble numbers if the denominators are greater than 2, getting
closer the more complex the ratios are. The worst case difference is
with the simplest noble between 3/2 and 4/3 (which I acknowledge is
not the maximum HE). The noble mediant gives 560 cents while the
golden mean gives 579 cents, a 19 cent discrepancy.

Within the octave, the next worst discrepancy is between 5/3 and 7/4.
Noble mediant is 943 c, Golden mean is 937 c, only 6 cents away.

And Dan Stearns formulae have given us a way of delineating a _range_
of possible metastable values in EDO space, rather than any particular
central value.

I also note that Erv's Meru numbers are _not_ noble numbers (except
for phi itself).

Noble numbers all use the same recurrence relation, the Fibonacci
recurrence relation, namely "add the two preceding values". The
different noble numbers are the result of using different starting values.

Erv's Meru numbers, use different recurrence relations, obtained from
the diagonals of Mt Meru (Pascal's triangle), only one of which is the
Fibonacci relation. They may reach back further than the previous two
values, or they may multiply previous values by some integer before
adding them. They all start from the same initial values of 1, 1, 1, ...

-- Dave Keenan

🔗Kraig Grady <kraiggrady@...>

6/20/2008 6:06:57 PM

I am not sure at the moment what the relationship is between Erv's and the Nobles (if we for the sake of argument refer to those on the scale tree as 'noble').
The immediate thing that strikes us is it limited range.
Since one uses his i/f pattern to find the MOS pattern we can surmise that they all occur on the tree except at layers quite far below the layers pictured. It guess where i am not sure is will the meru numbers "eventually" settle into a zig zag pattern or will they as they move down continually in an uneven alternation of zig and zags. I don't know if any one has taken it down far enough or if possible before the calculator fails to give good answers. If for some reason they did do this continually unequal type of shifting one might thing of them as the 'nobles of nobles' in that it implies a tree with an infinite number of layers.
Then there is the problems of the distinction between his original numbers off the diagonals of Mt. Meru compared to the secondary sequence where one will multiply one of the factor which is how he arrived at meta-mavila and meta-meantone. These extend the range to that of the scale tree (in theory)
link http://anaphoria.com/meruthree.PDF

we also have variations on the triangle itself which seems to also produce other numbers if we look at
http://anaphoria.com/tres.PDF page 4 we can see that different seeds will produce different diagonal convergences. although here we are dealing with fractions whereas i assume with whole numbers the diagonals would most likely converge to the same place, having more the relationship of the Lucas series to the fibonacci series.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
>
> I also note that Erv's Meru numbers are _not_ noble numbers (except
> for phi itself).
>
> Noble numbers all use the same recurrence relation, the Fibonacci
> recurrence relation, namely "add the two preceding values". The
> different noble numbers are the result of using different starting values.
>
> Erv's Meru numbers, use different recurrence relations, obtained from
> the diagonals of Mt Meru (Pascal's triangle), only one of which is the
> Fibonacci relation. They may reach back further than the previous two
> values, or they may multiply previous values by some integer before
> adding them. They all start from the same initial values of 1, 1, 1, ...
>
> -- Dave Keenan
>
>

🔗Kraig Grady <kraiggrady@...>

6/20/2008 8:50:43 PM

http://anaphoria.com/meru13-29.PDF
looking at this seems to imply no matter how you 'seed' the triangle the diagonal will always converge on the same ratio. but the numerical sequence will be different

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
>
> I am not sure at the moment what the relationship is between Erv's
> and the Nobles (if we for the sake of argument refer to those on the
> scale tree as 'noble').
> The immediate thing that strikes us is it limited range.
> Since one uses his i/f pattern to find the MOS pattern we can surmise
> that they all occur on the tree except at layers quite far below the
> layers pictured. It guess where i am not sure is will the meru numbers
> "eventually" settle into a zig zag pattern or will they as they move
> down continually in an uneven alternation of zig and zags. I don't know
> if any one has taken it down far enough or if possible before the
> calculator fails to give good answers. If for some reason they did do
> this continually unequal type of shifting one might thing of them as the
> 'nobles of nobles' in that it implies a tree with an infinite number of
> layers.
> Then there is the problems of the distinction between his original
> numbers off the diagonals of Mt. Meru compared to the secondary sequence
> where one will multiply one of the factor which is how he arrived at
> meta-mavila and meta-meantone. These extend the range to that of the
> scale tree (in theory)
> link http://anaphoria.com/meruthree.PDF > <http://anaphoria.com/meruthree.PDF>
>
> we also have variations on the triangle itself which seems to also
> produce other numbers if we look at
> http://anaphoria.com/tres.PDF <http://anaphoria.com/tres.PDF> page 4 > we can see that different seeds
> will produce different diagonal convergences. although here we are
> dealing with fractions whereas i assume with whole numbers the diagonals
> would most likely converge to the same place, having more the
> relationship of the Lucas series to the fibonacci series.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Dave Keenan wrote:
> >
> >
> >
> > I also note that Erv's Meru numbers are _not_ noble numbers (except
> > for phi itself).
> >
> > Noble numbers all use the same recurrence relation, the Fibonacci
> > recurrence relation, namely "add the two preceding values". The
> > different noble numbers are the result of using different starting > values.
> >
> > Erv's Meru numbers, use different recurrence relations, obtained from
> > the diagonals of Mt Meru (Pascal's triangle), only one of which is the
> > Fibonacci relation. They may reach back further than the previous two
> > values, or they may multiply previous values by some integer before
> > adding them. They all start from the same initial values of 1, 1, 1, ...
> >
> > -- Dave Keenan
> >
> >
>
>

🔗Dave Seidel <dave@...>

6/21/2008 7:01:22 AM

Ahem. 249EUR is quite a bit more than 200USD. At the moment, it's about 388USD[1]

Not to cast aspersions on what looks to be a great product, but it ain't cheap.

- Dave

[1] http://uk.finance.yahoo.com/currency/convert?amt=249&from=EUR&to=USD&submit=Convert

Carl Lumma wrote:
> Yes, but the best synth in the known universe (pianoteq)
> only costs $200, and there are many excellent cheap or
> free microtonal-capable softsynths around the way.

🔗Carl Lumma <carl@...>

6/21/2008 10:28:47 AM

--- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote:
>
> > Yes, but the best synth in the known universe (pianoteq)
> > only costs $200, and there are many excellent cheap or
> > free microtonal-capable softsynths around the way.
>
> Ahem. 249EUR is quite a bit more than 200USD. At the moment, it's
> about 388USD[1]
>
> Not to cast aspersions on what looks to be a great product, but
> it ain't cheap.

My bad. -Carl

🔗Daniel Wolf <djwolf@...>

6/21/2008 11:11:16 AM

Just a small note -- it's interesting that we seem to have settled on the mediant here. Many years ago on the Mills list, I posed the question of whether the freshman sum (i.e. mediant) had precisely this function. Of course, being a message with my "from" address on it, no one followed up on this...

djw

🔗Kraig Grady <kraiggrady@...>

6/21/2008 4:07:02 PM

There was a period where i believe this would happen to myself also, or so it seemed.
Yes the scale tree is a tree of mediants and it starts with the infinitely large and small-
1/0 and 0/1.

[ At least i answered this time:)]

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Daniel Wolf wrote:
> Just a small note -- it's interesting that we seem to have settled on the > mediant here. Many years ago on the Mills list, I posed the question of > whether the freshman sum (i.e. mediant) had precisely this function. Of > course, being a message with my "from" address on it, no one followed up > on this...
>
> djw
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>
>
>

🔗daniel_anthony_stearns <daniel_anthony_stearns@...>

6/21/2008 4:31:52 PM

hi kraig.as far as metastability goes, i think there is a certain
important difference from the Scale Tree in that you have to address
the idea of "height" so that you can say that there are various
degrees of stability, no?

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> There was a period where i believe this would happen to myself
also, or
> so it seemed.
> Yes the scale tree is a tree of mediants and it starts with the
> infinitely large and small-
> 1/0 and 0/1.
>
> [ At least i answered this time:)]
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria
<http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Daniel Wolf wrote:
> > Just a small note -- it's interesting that we seem to have
settled on the
> > mediant here. Many years ago on the Mills list, I posed the
question of
> > whether the freshman sum (i.e. mediant) had precisely this
function. Of
> > course, being a message with my "from" address on it, no one
followed up
> > on this...
> >
> > djw
> >
> > ------------------------------------
> >
> > You can configure your subscription by sending an empty email to
one
> > of these addresses (from the address at which you receive the
list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual
emails.
> > tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> >
> >
> >
> >
> >
> >
>

🔗Kraig Grady <kraiggrady@...>

6/21/2008 5:28:18 PM

Doesn't the height in the scale tree reflect this?
I still have problems with looking for the roots of con/dis with dyads in general.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

daniel_anthony_stearns wrote:
>
> hi kraig.as far as metastability goes, i think there is a certain
> important difference from the Scale Tree in that you have to address
> the idea of "height" so that you can say that there are various
> degrees of stability, no?
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > There was a period where i believe this would happen to myself
> also, or
> > so it seemed.
> > Yes the scale tree is a tree of mediants and it starts with the
> > infinitely large and small-
> > 1/0 and 0/1.
> >
> > [ At least i answered this time:)]
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria
> <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Daniel Wolf wrote:
> > > Just a small note -- it's interesting that we seem to have
> settled on the
> > > mediant here. Many years ago on the Mills list, I posed the
> question of
> > > whether the freshman sum (i.e. mediant) had precisely this
> function. Of
> > > course, being a message with my "from" address on it, no one
> followed up
> > > on this...
> > >
> > > djw
> > >
> > > ------------------------------------
> > >
> > > You can configure your subscription by sending an empty email to
> one
> > > of these addresses (from the address at which you receive the
> list):
> > > tuning-subscribe@yahoogroups.com > <mailto:tuning-subscribe%40yahoogroups.com> - join the tuning group.
> > > tuning-unsubscribe@yahoogroups.com > <mailto:tuning-unsubscribe%40yahoogroups.com> - leave the group.
> > > tuning-nomail@yahoogroups.com > <mailto:tuning-nomail%40yahoogroups.com> - turn off mail from the group.
> > > tuning-digest@yahoogroups.com > <mailto:tuning-digest%40yahoogroups.com> - set group to send daily > digests.
> > > tuning-normal@yahoogroups.com > <mailto:tuning-normal%40yahoogroups.com> - set group to send individual
> emails.
> > > tuning-help@yahoogroups.com <mailto:tuning-help%40yahoogroups.com> > - receive general help information.
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> > >
> > >
> >
>
>

🔗Dave Keenan <d.keenan@...>

6/21/2008 5:31:20 PM

Hi Dan Wolf,

Ah, the loneliness of being ahead of your time. :-)

-- Dave Keenan

--- In tuning@yahoogroups.com, "Daniel Wolf" <djwolf@...> wrote:
>
> Just a small note -- it's interesting that we seem to have settled
on the
> mediant here. Many years ago on the Mills list, I posed the
question of
> whether the freshman sum (i.e. mediant) had precisely this function.
Of
> course, being a message with my "from" address on it, no one
followed up
> on this...
>
> djw
>