Clarification of my comments on Igs' 32-64 program

Since certain list members have shown a keen interest in my
comments on Igs' recent proposal, I'll try to clarify them.
My original comments to Igs are quoted at the bottom.

First, his proposal: Having enjoyed a running dialog with
Igs both on- and offlist for many months, regarding his
forthcoming EDO primer, I felt I understood what his proposal
was and what he intended to use it for. I'll summarize that
understanding:
Igs is writing an introductory survey of EDOs for beginners,
with some emphasis on guitar (his main instrument). He was
looking for a way to describe the sound and potential musical
function of intervals in these EDOs to near novices.
Recently, he announced he would scrap his previous approach
based on approximations to just intonation and instead
identify each EDO interval the nearest rational found in the
harmonic series, up to the 64th harmonic. He also announced
an 8-cent approximation threshold, though it isn't clear how
he planned to use it.

I'll define numerology as the unjustified use of numbers.
It may be as innocuous as showing precision you don't have,
or as strange as attributing magical powers to the numbers
themselves (e.g. speaking certain numbers to cure diseases).
It's a widespread and robust phenomenon, as are many forms
of magical thinking in human history, and especially common
in "just intonation" music theory (e.g. La Monte Young,
Barbara Hero, etc).

I think it's pretty obvious that numerology is the only
plausible rationale for the choice of harmonics up to 64 in
Igs' proposal. Mike said people could certainly learn to
distinguish these intervals, and that I routinely deny the
role of learning in music perception. In fact I'm one of
the most outspoken proponents of learning in the microtonal
community and have been for over a decade. (This is true
both in scale theory, where I'm one of the most vocal
proponents of using categorical perception to classify
scales, and in psychoacoustics, where I'm among the first
to mention plasticity in combination-sensitive neurons as
potentially important in the perception of harmony.)

As I've written here many times, it's the nature of
learning that nothing is impossible to learn. Here's one
example: /tuning/topicId_94046.html#94179
But there is still the question of what is practical to
learn, what is learned already by most of the public and
what is known only to specialists, etc. (Generally it's
assumed that any effect that can be heard by the audience
can be used musically.)

64/63 and 63/62 are less than half a cent apart. This is
beyond the resolution of any ordinary guitar and beyond
the limits of human perception thus far measured in
laboratories. It's also noticeably smaller than 8 cents.

Assuming this obstacle could be overcome, distinguishing
the "texture" of so many intervals is not a skill in the
general population, nor one ever documented. Igs said
it's a skill possessed by Dante Rosati and others. I
replied that there's no evidence of this and there bloody
well is none.

Even assuming Igs were not writing a general-purpose primer
for novices and their audiences, but instead a primer for
people willing to learn this exotic skill, there's still
the ugly coincidence that the standard chosen just happens
to involve those favorite playthings of the microtonal
numerologists: rational numbers. Why not any other
standard? And why the 8-cent approximation threshold?

It's also the nature of learning that older brains learn
less permanently and less easily than younger ones. The
recognition of the texture of the rationals up to Tenney
height 100 (on average) and SPAN 2-3 octaves is something
all healthy natural language speakers learn in the womb and
the first months of life. Expecting adult audiences to make
major changes in this foundation is completely unrealistic.
For comparison, it's possible to learn absolute pitch skills
in adulthood. This has been shown in university studies.
But the skills are never as robust as those who acquire them
at a young age, and outside of a paid study it's not clear
how many people have ever bothered and met with success.

In short, from what I know of reality and what I know of
Igs' long work on his primer, his recent proposal was not
a good one. And his subsequent defense of it on grounds
of cultural-relativistic B.S. didn't help.

-Carl

>> ...analyzes each EDO in terms of harmonics 32-64 and
>> "bans" any approximations worse than 8 cents off.
>
> A lot of stuff up there simply isn't audible outside
> of very specific listening conditions.
>
> Abstract models (such as analyzing an equal temperament
> in terms of a harmonic series) should aid us in reaching
> consistent conclusions about reality. Using harmonics
> 32-64 with a brick wall 8-cent error cutoff won't do that.
>
>> I disagree. The "reality" is that harmonics 32-64 each
>> have a sound (or at least a texture) that people can
>> and have learned to recognize.
>
> Who? Is there any reason to believe such a statement?
> I don't think so...
>
>> If those methods lead to good music (as they seem to do,
>> in the case of Kraig Grady and Johnny Reinhard and
>> Dante Rosati, among others), then the real fool is the
>> person who insists against the use of such approaches.
>
> I haven't heard any of them claim to be able to recognize
> every harmonic up to 64 or that such a skill has been
> useful in music-making. Other outlandish claims have been
> made though (such as the ability to distinguish and perform
> at will on a variety of instruments any interval with
> 1-cent accuracy).

A few good points, plus a few holes I see in Carl's argument/intepretation of Igs's use of harmonics up to 64 in the context of his EDO primer:

Carl>"I think it's pretty obvious that numerology is the only
plausible rationale for the choice of harmonics up to 64 in
Igs' proposal."
.............
>"64/63 and 63/62 are less than half a cent apart.  This is beyond the resolution of any ordinary guitar and beyond the limits of human perception thus far measured in

laboratories."
  Good point, but does 64 mean necessarily comparing of that resolution (in the same way "11-odd-limit resolution" does not necessarily mean up to 12/11)?
  For example, think of 64/61 vs. 63/59.  The difference there is more like 29 cents apart and definitely audible...

>"It's also noticeably smaller than 8 cents."
  I digress...I (by ear testing alone, even) am a huge fan of the idea that 8 cents is very close to a point of "just noticeable difference".  But many people (you included at times, Carl) have said the choice of 8 cents makes no sense and that the real just noticeable difference is more like 3 or even 2 cents.  If your point is that anything smaller than 8 cents "off" is likely to go virtually unacknowledged by the average listener though, and figure "why bother explaining something beyond that resolution...for example: that you likely can't hear), I certainly
agree.

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

> 64/63 and 63/62 are less than half a cent apart.

This is why I was asking if the only intervals being considered are of the form N/32--there seems to be no agreement as to what the conversation is even about.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > 64/63 and 63/62 are less than half a cent apart.
>
> This is why I was asking if the only intervals being considered are of the form N/32--there seems to be no agreement as to what the conversation is even about.
>

Yes- I was also under the impression that Igliashon meant n/2,n/4,n/8,n/16, and n/32 intervals ((33-64)/32). Jonny Reinhard, from whom Igliashon seems to have got the idea, uses this for his "overtone" tuning.

On Mon, Jun 20, 2011 at 12:44 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > 64/63 and 63/62 are less than half a cent apart.
>
> This is why I was asking if the only intervals being considered are of the form N/32--there seems to be no agreement as to what the conversation is even about.

/tuning/topicId_99859.html#99947

I've been through it all. I'll respond to Carl's post tomorrow, I'm
far too tired right now.

-Mike

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

> The
> recognition of the texture of the rationals up to Tenney
> height 100 (on average) and SPAN 2-3 octaves is something
> all healthy natural language speakers learn in the womb and
> the first months of life.

And here's a shining example of internet-kook numerological waffle. Not only is this unsupported and probably unfalsifiable goop, this gem of pseudo-science fails to function in any positive generative way in the arts: at least New Age tuning numerology is used to create music (some of it pretty darn nice music).

I agree that Igliashon's new approach (from what I have heard of it) is bad- meaningless, really. But I think that trying to drag people into the "regular mapping paradigm" via largely inharmonic tunings was a bad idea, too.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Since certain list members have shown a keen interest in my
> comments on Igs' recent proposal, I'll try to clarify them.
> My original comments to Igs are quoted at the bottom.
>
> First, his proposal: Having enjoyed a running dialog with
> Igs both on- and offlist for many months, regarding his
> forthcoming EDO primer, I felt I understood what his proposal
> was and what he intended to use it for. I'll summarize that
> understanding:
> Igs is writing an introductory survey of EDOs for beginners,
> with some emphasis on guitar (his main instrument). He was
> looking for a way to describe the sound and potential musical
> function of intervals in these EDOs to near novices.
> Recently, he announced he would scrap his previous approach
> based on approximations to just intonation and instead
> identify each EDO interval the nearest rational found in the
> harmonic series, up to the 64th harmonic. He also announced
> an 8-cent approximation threshold, though it isn't clear how
> he planned to use it.
>
> I'll define numerology as the unjustified use of numbers.
> It may be as innocuous as showing precision you don't have,
> or as strange as attributing magical powers to the numbers
> themselves (e.g. speaking certain numbers to cure diseases).
> It's a widespread and robust phenomenon, as are many forms
> of magical thinking in human history, and especially common
> in "just intonation" music theory (e.g. La Monte Young,
> Barbara Hero, etc).
>
> I think it's pretty obvious that numerology is the only
> plausible rationale for the choice of harmonics up to 64 in
> Igs' proposal. Mike said people could certainly learn to
> distinguish these intervals, and that I routinely deny the
> role of learning in music perception. In fact I'm one of
> the most outspoken proponents of learning in the microtonal
> community and have been for over a decade. (This is true
> both in scale theory, where I'm one of the most vocal
> proponents of using categorical perception to classify
> scales, and in psychoacoustics, where I'm among the first
> to mention plasticity in combination-sensitive neurons as
> potentially important in the perception of harmony.)
>
> As I've written here many times, it's the nature of
> learning that nothing is impossible to learn. Here's one
> example: /tuning/topicId_94046.html#94179
> But there is still the question of what is practical to
> learn, what is learned already by most of the public and
> what is known only to specialists, etc. (Generally it's
> assumed that any effect that can be heard by the audience
> can be used musically.)
>
> 64/63 and 63/62 are less than half a cent apart. This is
> beyond the resolution of any ordinary guitar and beyond
> the limits of human perception thus far measured in
> laboratories. It's also noticeably smaller than 8 cents.
>
> Assuming this obstacle could be overcome, distinguishing
> the "texture" of so many intervals is not a skill in the
> general population, nor one ever documented. Igs said
> it's a skill possessed by Dante Rosati and others. I
> replied that there's no evidence of this and there bloody
> well is none.
>
> Even assuming Igs were not writing a general-purpose primer
> for novices and their audiences, but instead a primer for
> people willing to learn this exotic skill, there's still
> the ugly coincidence that the standard chosen just happens
> to involve those favorite playthings of the microtonal
> numerologists: rational numbers. Why not any other
> standard? And why the 8-cent approximation threshold?
>
> It's also the nature of learning that older brains learn
> less permanently and less easily than younger ones. The
> recognition of the texture of the rationals up to Tenney
> height 100 (on average) and SPAN 2-3 octaves is something
> all healthy natural language speakers learn in the womb and
> the first months of life. Expecting adult audiences to make
> major changes in this foundation is completely unrealistic.
> For comparison, it's possible to learn absolute pitch skills
> in adulthood. This has been shown in university studies.
> But the skills are never as robust as those who acquire them
> at a young age, and outside of a paid study it's not clear
> how many people have ever bothered and met with success.
>
> In short, from what I know of reality and what I know of
> Igs' long work on his primer, his recent proposal was not
> a good one. And his subsequent defense of it on grounds
> of cultural-relativistic B.S. didn't help.
>
> -Carl
>
> >> ...analyzes each EDO in terms of harmonics 32-64 and
> >> "bans" any approximations worse than 8 cents off.
> >
> > A lot of stuff up there simply isn't audible outside
> > of very specific listening conditions.
> >
> > Abstract models (such as analyzing an equal temperament
> > in terms of a harmonic series) should aid us in reaching
> > consistent conclusions about reality. Using harmonics
> > 32-64 with a brick wall 8-cent error cutoff won't do that.
> >
> >> I disagree. The "reality" is that harmonics 32-64 each
> >> have a sound (or at least a texture) that people can
> >> and have learned to recognize.
> >
> > Who? Is there any reason to believe such a statement?
> > I don't think so...
> >
> >> If those methods lead to good music (as they seem to do,
> >> in the case of Kraig Grady and Johnny Reinhard and
> >> Dante Rosati, among others), then the real fool is the
> >> person who insists against the use of such approaches.
> >
> > I haven't heard any of them claim to be able to recognize
> > every harmonic up to 64 or that such a skill has been
> > useful in music-making. Other outlandish claims have been
> > made though (such as the ability to distinguish and perform
> > at will on a variety of instruments any interval with
> > 1-cent accuracy).
>

"genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...>
> wrote:
>
> > 64/63 and 63/62 are less than half a cent apart.
>
> This is why I was asking if the only intervals being
> considered are of the form N/32--there seems to be no
> agreement as to what the conversation is even about.

I thought it was obvious, from his first reply, that Igs's
comment about distinguishing harmonics up to 64 only
applied to N/32. Therefore Carl was arguing with a straw
man, and Mike was right to ask him to clarify.

There are cultures where pointing out that somebody made a
mistake, especially if they really did make a mistake, is
considered rude and hostile. But even if this were such a
culture, Carl would have been wrong by starting the
argument.

Now, you could say that as the 8 cent error cutoff was
clearly intended to keep the error of intervals between
harmonics below 16 cents (yes, this is clear from what Igs
said) distinguishing intervals between harmonics must be
important. But nobody did say that. It shows how poor the
argument was.

Graham

I'd like to make it known that Igs has written me offlist
to say that I've misunderstood his proposal. -Carl

I wrote:
> Since certain list members have shown a keen interest in my
> comments on Igs' recent proposal, I'll try to clarify them.
> My original comments to Igs are quoted at the bottom.
[snip]

Graham wrote:

> I thought it was obvious, from his first reply, that Igs's
> comment about distinguishing harmonics up to 64 only
> applied to N/32. Therefore Carl was arguing with a straw
> man, and Mike was right to ask him to clarify.

What in Igs' original made that obvious to you?

Most of my criticism does apply either way.

> There are cultures where pointing out that somebody made a
> mistake, especially if they really did make a mistake, is
> considered rude and hostile. But even if this were such a
> culture, Carl would have been wrong by starting the
> argument.

You mean even if this weren't such a culture? Are you
saying it is or...?

> Now, you could say that as the 8 cent error cutoff was
> clearly intended to keep the error of intervals between
> harmonics below 16 cents (yes, this is clear from what Igs
> said) distinguishing intervals between harmonics must be
> important. But nobody did say that. It shows how poor the
> argument was.

I don't follow this either. :(

-Carl

On Sun, Jun 19, 2011 at 9:27 PM, Carl Lumma <carl@...> wrote:
> I'll define numerology as the unjustified use of numbers.
> It may be as innocuous as showing precision you don't have,
> or as strange as attributing magical powers to the numbers
> themselves (e.g. speaking certain numbers to cure diseases).

Is it numerology if you develop a categorical perception for the 64
rooted intervals in the 32-64 harmonic series, and just call them
xx/64 for the sake of giving them a name? Because that's what it
sounds like learning to see everything as harmonics 32-64 would
entail.

> (This is true both in scale theory, where I'm one of the most vocal
> proponents of using categorical perception to classify
> scales, and in psychoacoustics, where I'm among the first
> to mention plasticity in combination-sensitive neurons as
> potentially important in the perception of harmony.)

I have never heard you mention neuronal plasticity as affecting the
perception of harmony or being in any way related to categorical
perception. I posted something offlist to you similar about learned
biases in preattentive F0 estimation, and I believe your response was
that they were "oh gee so what" studies. If you have proposed some
hypothesis that I've missed, please clue me in on it.

> As I've written here many times, it's the nature of
> learning that nothing is impossible to learn. Here's one
> example: /tuning/topicId_94046.html#94179
> But there is still the question of what is practical to
> learn, what is learned already by most of the public and
> what is known only to specialists, etc. (Generally it's
> assumed that any effect that can be heard by the audience
> can be used musically.)

Musicians have never been known for limiting themselves to learning
only what is practical, especially not this group.

> 64/63 and 63/62 are less than half a cent apart. This is
> beyond the resolution of any ordinary guitar and beyond
> the limits of human perception thus far measured in
> laboratories. It's also noticeably smaller than 8 cents.
>
> Assuming this obstacle could be overcome, distinguishing
> the "texture" of so many intervals is not a skill in the
> general population, nor one ever documented. Igs said
> it's a skill possessed by Dante Rosati and others. I
> replied that there's no evidence of this and there bloody
> well is none.

As we know for certain at this point, we're talking about rooted
harmonics from 32-64, not all 64-integer-limit dyads. So I'll respond
to just the "rooted" claim.

1) You can distinguish between intervals that are the same size given
the right musical context.
2) If I play 300 cents to you after exposing you to 10 minutes of
silence, and I ask you whether I just played an augmented second or a
minor third, you will fail.
3) Distinguishing the "texture" of all of the intervals in 12-tet is
not a skill that the general population possesses. Plenty of people
routinely screw up the difference between an octave and a perfect
fifth. Nonetheless, most of the same people can still carry a melody,
because musical context activates some part of musical cognition that
bare dyads don't.
5) This scale provides for some of the best contextual cues ever:
there are low-complexity ratios every eighth note (4:5:6:7) - "chord
tones", and then halfway between those are intermediate complexity
ratios (8:..:16) - "diatonic non-chord tones," and then in between
those you have higher complexity ones (16:..:32) - "chromatic
non-chord tones," and then in between those you would have ultra
high-complexity notes that are kind of like "quarter tones."
6) I can already identify harmonics 16-32 and I'm pretty sure that I
can personally get 32-64 if I work at it. 33/32 is a quarter tone,
34/32 is a half step, 35/32 is a neutral second, etc. It would get
harder as you go up more and more, but I'm not convinced that a short
bout of training would stop anyone on the list from getting it.

I wouldn't be surprised if 43/32, which is a 511 cent 26-tet sized
fourth, even acquired a secondary "rooted" sound (or perhaps
"function") after a while, given how it's going to sound if you play
it as part of any decent-sized chord in this scale. Most large chords
in this scale will evoke a single VF, and you can always just remember
that sounds after and learn to hear 43/32 as a part of that.

> Even assuming Igs were not writing a general-purpose primer
> for novices and their audiences, but instead a primer for
> people willing to learn this exotic skill, there's still
> the ugly coincidence that the standard chosen just happens
> to involve those favorite playthings of the microtonal
> numerologists: rational numbers. Why not any other
> standard? And why the 8-cent approximation threshold?

The 8-cent threshold was the only thing he said that I didn't agree with.

Nonetheless, the results are in: people like using rational numbers to
discuss categorical perceptions these days, and prefer to see a VF as
just one minor part of what can make up the sound of an interval.
People like to claim that 81/64 and 5/4 are different, and if they've
learned to distinguish the two, then to that person they are different
things, even if they share the similarity because they evoke the same
VF. Things that are different need a name, and "5/4" and "81/64" are
two decent names to use. There is a difference between making a
specific claim about VF perception, and simply using numbers to
distinguish between percepts without caring whether two intervals
share a VF or not. The former is numerological, the latter is not. I
haven't seen any artists make the former claim, but perhaps that was
all the rage before I joined the list.

VF perception is not such an overwhelming gestalt that it is worth
telling people that referring to 29/16 is numerological. It might be
worth addressing that 29/16 might evoke the same VF as 7/4, but if
someone has learned to distinguish 29/16 by its unique combination of
VF, mistuning, tonalness, and beating, then they have every right to
give that gestalt whatever name they want. I don't think that most
people would be averse to us telling them that 14/11 and 5/4 are
likely to evoke the same VF and that that fact is of prime importance
for harmony, but I think they would in fact object to us saying they
can't call an interval 14/11 at all because it's going to be heard
"as" a 5/4.

> It's also the nature of learning that older brains learn
> less permanently and less easily than younger ones. The
> recognition of the texture of the rationals up to Tenney
> height 100 (on average) and SPAN 2-3 octaves is something
> all healthy natural language speakers learn in the womb and
> the first months of life. Expecting adult audiences to make
> major changes in this foundation is completely unrealistic.

Here's my experience: when I started playing 11/8 as a dyad, it
sounded like either a flat tritone or sometimes, more rarely, a sharp
fourth. After spending months in porcupine now, and using 11/8 in
otonal chords, I've started hearing it in isolation as having that
characteristic and somewhat ominous sound of being a "rooted, complex"
dyad that most importantly evokes the proper 11/8 VF. I've even heard
the same thing happening for 11/9 - play the first five notes of a
porcupine[7] Lssssss scale (let's call those notes C D E F G), and
while holding the C, play D-F -> E-G -> D-F -> C-E -> D-F, which
should sound like you're arpeggiating 8:9:10:11:12. Then, if you let
go of the C, you hear the D-F as still having a "root" of C, and it
doesn't sound like a 6/5 at all (which it's closer to in porcupine),
nor does it sound like a "neutral third." It sounds like a "tonal"
interval that has a root that's 9/8 below the bottom note. In short,
it sounds like an 11/9.

Sometimes my perception gets "stuck" this way and I have trouble
reframing it to be a minor third again. And if, in the above example,
I stay on that D-F and suddenly modulate to D minor 9, thus taking
advantage of the 55/54 unison vector, the other perception of it
somehow colors the sound in a way that sounds really irritating and
wrong. It's not that it starts sounding like a "neutral" third, but
just that it sounds like cheese whiz. I don't know how to describe it
any other way than that, and I get stuck in it and now I can't get out
of this new "wrong" perception. Point is: I've already seen radical
changes in my perception of even bare dyads - it just took AXiS and
SSquares and several dozen hours playing on an actual instrument to
activate it.

Music theory is different from other forms of science: the burden of
proof is on us to disprove something as being unrealistic beyond the
shadow of a doubt before it can be claimed that it's unrealistic - and
let's also consider who we're saying that it's unrealistic for.
Artists tend to be extreme personalities who devote utterly
exhorbitant amounts of their time to learning to do unrealistic things
for no other reason than that they want to explore as many new forms
of perception as possible before they die. That sounds heavy, but it's
what it is. The claim that something is impractical means that it's
possible if you practice enough. Things are possible by default until
proven otherwise given the objective and work ethic of this audience.

As for whether the audience will be able to become hip to what's going
on - the concept of a musical phenomenon being targeted to a specific
audience with the same developed skill to decode the information is
certainly not unheard of in music today. Take when drummers will start
playing a fake backbeat in a different subdivision of the true tempo
(like imagine that you're in 4/4, and you accent every third sixteenth
note. Then start playing a drum beat over the new "fake tempo" while
still keeping the original in your mind). The audience that can keep
counting the 4 will get what's going on and continue to follow the
form of the song, whereas the audience that can't will lose their
place and have to get back on the train when the normal beat restarts.

-Mike

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

> People like to claim that 81/64 and 5/4 are different, and if >they've
> learned to distinguish the two, then to that person they are >different
> things, even if they share the similarity because they evoke the >same
> VF.

I suspect that it is more likely that one must learn to conflate the two, by internalizing some kind of diatonic grid. My wife and seven-year-old son distinguish them with ease, at least harmonically, by describing what each evokes.

>Things that are different need a name, and "5/4" and "81/64" are
> two decent names to use.

Respectively, "old-fashioned" vs. "soldierly" for my son, "eeewwww...church music" vs. (no reaction) for my wife.

> I don't think that most
> people would be averse to us telling them that 14/11 and 5/4 are
> likely to evoke the same VF and that that fact is of prime importance
> for harmony, but I think they would in fact object to us saying they
> can't call an interval 14/11 at all because it's going to be heard
> "as" a 5/4.

Hearing a bright, driving, beating interval as a soft smooth stable interval would be... well, unmusical. Hearing both as a "major third" isn't unmusical, it simply tells us that a "major third" can fall within a goodly range of tuning, which is in keeping with the history of Western music.

> Here's my experience: when I started playing 11/8 as a dyad, it
> sounded like either a flat tritone or sometimes, more rarely, a >sharp
> fourth. After spending months in porcupine now, and using 11/8 in
> otonal chords, I've started hearing it in isolation as having that
> characteristic and somewhat ominous sound of being a "rooted, >complex"
> dyad that most importantly evokes the proper 11/8 VF.

One guy to whom I was introducing alternative tunings had no training other than singing in acappella choirs since childhood. He immediately said, upon hearing an 11/8, "augmented fourth...perfectly in tune". Which I thought was quite interesting.

I'm not sure why you're pressing on with this conversation,
that could have been overheard on a middle school playground,
but I want nothing more to do with it. Your entire attitude
toward me is completely toxic and has been for some time.

-Carl

Mike Battaglia <battaglia01@...> wrote:

> Is it numerology if you develop a categorical perception
> for the 64 rooted intervals in the 32-64 harmonic series,
[snip]
> please clue me in on it.
[snip]
> 2) If I play 300 cents to you after exposing you to
> 10 minutes of silence, and I ask you whether I just played
> an augmented second or a minor third, you will fail.
[snip]
>> "For reasons already stated" is an escalation?
>
>It is a rude and characteristically rude statement.
[snip]

Just finished a paper called "Eighth Octave Overtone Tuning: A Perfect
Tuning" which I am just now passing around. Like so many topics, it is not
possible to explain in this medium what is really going on with higher
overtone tuning as a system for making music. However, I thought I'd make some
response (rather than remain silent).

While I haven't seen any lengthy description of what Iggs has planned with
a Primer, we have exchanged on Facebook. And reading some of the comments
here seem off base.

1. Higher overtone tuning is not numerology
2. This is proven in recent live performances: Stravinsky, Reinhard,
Improvisation, Vicentino
3. Proven means that the audience relished what they heard
4. Stravinsky is up at the AFMM website: _www.afmm.org_
(http://www.afmm.org)

Guys, for an adventurous lot, you guys really do shoot down what is new.
It's an old pattern. The 43/32 does not need ten minutes of steady
bullying to make a lasting impression. Tune it up and listen, please. And if you
don't know the terrain being discussed in the higher overtones, don't
spout nonsense, and don't insult individuals. Sure, I still think the squiggle
theory on Bach is shameful. The making of new music as a state of the art
affair seems a reasonable enough position to take, a position that anyone
on this list should be able to support. And yes, the notes are playable
for me in a scale on the bassoon and it sounds great. The notes actually
have more "tone" to the sound.

Johnny Reinhard

I'm sorry that this is your reaction to what I've said. I would like for us
to attain productive discourse, but at this point this objective is not
possible if my concerns are not addressed.

My attitude towards you is toxic for the same reason many others' are: you
can be at times very abrasive and insulting. There's no point beating around
the issue any more, and it would do you good to assess honestly the
truthhood of that statement.

The first email, which you lumped in with the second, was a straightforward
response to what you'd written about learning. There was no toxicity in it.
If you'd like for the "middle school playground" talk to end, one way is to
respond to it and make an effort to be amicable, and I will behav. I am
always willing to start from the beginning.

-Mike

On Jun 21, 2011, at 5:43 PM, "Carl Lumma" <carl@...> wrote:

I'm not sure why you're pressing on with this conversation,
that could have been overheard on a middle school playground,
but I want nothing more to do with it. Your entire attitude
toward me is completely toxic and has been for some time.

On Tue, Jun 21, 2011 at 9:30 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > People like to claim that 81/64 and 5/4 are different, and if >they've
> > learned to distinguish the two, then to that person they are >different
> > things, even if they share the similarity because they evoke the >same
> > VF.
>
> I suspect that it is more likely that one must learn to conflate the two, by internalizing some kind of diatonic grid. My wife and seven-year-old son distinguish them with ease, at least harmonically, by describing what each evokes.

Sure, but my larger point here is that virtual fundamentals are not
the only percept that matters in interval distinction. The two
obviously do sound different - one is pure and just sounding, while
the other beats like crazy and is also tuned nicely sharp (a koan for
you). For a naive listener, it's likely that they will produce the
same fundamental, which will lead to them sharing a certain similar
sound. But they do not need to produce different virtual fundamental
pitches to be perceived as having differences, and there's no need to
pretend they do.

375 cents and 400 cents are also "major thirds" that beat, but they
sound very different. There is something different in the quality of
these two intervals, despite that they both beat. That something is
what I'm pointing out.

> > I don't think that most
> > people would be averse to us telling them that 14/11 and 5/4 are
> > likely to evoke the same VF and that that fact is of prime importance
> > for harmony, but I think they would in fact object to us saying they
> > can't call an interval 14/11 at all because it's going to be heard
> > "as" a 5/4.
>
> Hearing a bright, driving, beating interval as a soft smooth stable interval would be... well, unmusical.

It is noteworthy that we do hear it as bright, driving, and beating
rather than being perfectly synchronous at the 14/11.

> Hearing both as a "major third" isn't unmusical, it simply tells us that a "major third" can fall within a goodly range of tuning, which is in keeping with the history of Western music.

Hearing both as evoking a virtual pitch two octaves below the lowest
note isn't unmusical either, and this is another similarity that they
will share outside of the "major third' category as well. A 9/7 might
only share the "major third" status and not end up sharing the same
VF.

> One guy to whom I was introducing alternative tunings had no training other than singing in acappella choirs since childhood. He immediately said, upon hearing an 11/8, "augmented fourth...perfectly in tune". Which I thought was quite interesting.

I've noticed sometimes that trumpet players in jazz bands will
sometimes lip the #11 over a dom7#11 waaaay down, so that it gets
closer to 11/8. Just saying.

-Mike

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> 1. Higher overtone tuning is not numerology

How far up do you think you can push it? One reason for asking that is that any scale in rational intonation can be converted to a higher overtone tuning if you are willing to go arbitrarily high. I'm interested in particular in dwarf scales, as they are JI scales built on an overtone plan.

On Tue, Jun 21, 2011 at 9:13 PM, <Afmmjr@...> wrote:
>
> Just finished a paper called "Eighth Octave Overtone Tuning: A Perfect Tuning" which I am just now passing around.  Like so many topics, it is not possible to explain in this medium what is really going on with higher overtone tuning as a system for making music.  However, I thought I'd make some response (rather than remain silent).
>
> While I haven't seen any lengthy description of what Iggs has planned with a Primer, we have exchanged on Facebook.  And reading some of the comments here seem off base.
>
> 1. Higher overtone tuning is not numerology
> 2. This is proven in recent live performances: Stravinsky, Reinhard, Improvisation, Vicentino
> 3. Proven means that the audience relished what they heard
> 4. Stravinsky is up at the AFMM website: www.afmm.org
>
> Guys, for an adventurous lot, you guys really do shoot down what is new.  It's an old pattern.  The 43/32 does not need ten minutes of steady bullying to make a lasting impression.  Tune it up and listen, please.  And if you don't know the terrain being discussed in the higher overtones, don't spout nonsense, and don't insult individuals.  Sure, I still think the squiggle theory on Bach is shameful.  The making of new music as a state of the art affair seems a reasonable enough position to take, a position that anyone on this list should be able to support.  And yes, the notes are playable for me in a scale on the bassoon and it sounds great.  The notes actually have more "tone" to the sound.

I'm diving in. Time to see how plastic the brain can get. Four simple
questions for you:

1) For these intervals, particularly for 43/32, do you hear them as
being "rooted" intervals, where the root is the bottom note? Or for
43/32, do you hear the root as being the top note? Or is it variable?
2) Do you find that you require brighter, harsher timbres with more
harmonics to really clearly be able to distinguish between intervals?
Do you think you'd have trouble if you used a triangle wave? For
example, do you hear 43/32 as having a beating sound, and does that
beating sound help you to identify the interval in any way?
3) Can you identify all dyads between each harmonic, or just ones that
have a root of /32? E.g. can you identify 63/37, for example?
4) Do you ever find that 43/32 sounds ambiguous with 4/3?

Just curious; your insight here would be much appreciated.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Jun 21, 2011 at 9:30 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > People like to claim that 81/64 and 5/4 are different, and if >they've
> > > learned to distinguish the two, then to that person they are >different
> > > things, even if they share the similarity because they evoke the >same
> > > VF.
> >
> > I suspect that it is more likely that one must learn to conflate the two, by internalizing some kind of diatonic grid. My wife and seven-year-old son distinguish them with ease, at least harmonically, by describing what each evokes.
>
> Sure, but my larger point here is that virtual fundamentals are not
> the only percept that matters in interval distinction.

Oh yes I agree of course.

>The two
> obviously do sound different - one is pure and just sounding, while
> the other beats like crazy and is also tuned nicely sharp (a koan >for
> you).

Did you know that lumping the two together as an interval class, yet distinguishing them by character, was documented thousands of years ago? I'll get you the reference as soon as I can (it's in M.L. West for one). One of the ancient Greek writers complains that the musician properly sings the 5/4, but tuned his lyre Pythagorean, 81/64. Of course in that case it's not a "third", the scalar identity changed according to mode, but that's even more indicative of the raw psychoacoustic relationship involved.

>For a naive listener, it's likely that they will produce the
> same fundamental, which will lead to them sharing a certain similar
> sound. But they do not need to produce different virtual fundamental
> pitches to be perceived as having differences, and there's no need >to
> pretend they do.

Keep in mind that there is a great deal of subjectivity to "virtual fundamental".

>
> 375 cents and 400 cents are also "major thirds" that beat, but they
> sound very different. There is something different in the quality of
> these two intervals, despite that they both beat. That something is
> what I'm pointing out.

Yes, I've been pointing that out for years here, in the face of jeering (for of course I'm an ignorant fool for not acknowledgeing that these are simply mistunings of their Platonian identity, 5/4).

>
> > > I don't think that most
> > > people would be averse to us telling them that 14/11 and 5/4 are
> > > likely to evoke the same VF and that that fact is of prime importance
> > > for harmony, but I think they would in fact object to us saying they
> > > can't call an interval 14/11 at all because it's going to be heard
> > > "as" a 5/4.
> >
> > Hearing a bright, driving, beating interval as a soft smooth stable interval would be... well, unmusical.
>
> It is noteworthy that we do hear it as bright, driving, and beating
> rather than being perfectly synchronous at the 14/11.

Yes: "point of reference" and "identity" are not the same thing. There's orienting beating around partials 4 and 5, it's dishonest to pretend otherwise, but that does not mean they somehow "are" 5/4 Quite the contrary, really. Early and often working with the strongly microtonal genera of enharmonic and soft chromatic, I've found that the strong lower partials help to emphasize microtonal distinctions rather than subsume small intervals into a black hole of "identity".
>
> > Hearing both as a "major third" isn't unmusical, it simply tells us that a "major third" can fall within a goodly range of tuning, which is in keeping with the history of Western music.
>
> Hearing both as evoking a virtual pitch two octaves below the lowest
> note isn't unmusical either, and this is another similarity that >they
> will share outside of the "major third' category as well. A 9/7 >might
> only share the "major third" status and not end up sharing the same
> VF.

Yes.

>
> > One guy to whom I was introducing alternative tunings had no >training other than singing in acappella choirs since childhood. He >immediately said, upon hearing an 11/8, "augmented >fourth...perfectly in tune". Which I thought was quite interesting.
>
> I've noticed sometimes that trumpet players in jazz bands will
> sometimes lip the #11 over a dom7#11 waaaay down, so that it gets
> closer to 11/8. Just saying.

I have spent some time trying to sing an isolated 7:5 cold, and haven't done it yet. I'll keep trying, but at this point it's always, without exception, 11/8, 16/11, or the 12-tET "tritone" (coupla cents plus or minus in each case). In context any interval is singable, if the structure has a sound-logic to it, there are reference pitches, etc. Just saying. :-)

Is your tuning derived from a section of the harmonic series fixed or relative? For example, do you always use 43/32 as the "fourth"? If not, and your system is fixed upon a given pitch, it can be summarily dismissed as either a particular compositional method or simply as tinfoil-hat stuff; "fa" alone ranges from a pure 4/3 to some 652 cents.

As a relative system, it has a lot of very nice features. You've got Just harmonic structure up to what Partch would call "13-limit otonality", and using 43/32 as the fourth would, for a great deal of music, especially in acoustic practice, in effect enable you to veer temporarily into 1/2 comma meantone each time you encountered the classic ii-V comma problem, halving typical sinking in overall pitch. Weird, but something that can probably easily be made to work in real life situations.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Just finished a paper called "Eighth Octave Overtone Tuning: A Perfect
> Tuning" which I am just now passing around. Like so many topics, it is not
> possible to explain in this medium what is really going on with higher
> overtone tuning as a system for making music. However, I thought I'd make some
> response (rather than remain silent).
>
> While I haven't seen any lengthy description of what Iggs has planned with
> a Primer, we have exchanged on Facebook. And reading some of the comments
> here seem off base.
>
> 1. Higher overtone tuning is not numerology
> 2. This is proven in recent live performances: Stravinsky, Reinhard,
> Improvisation, Vicentino
> 3. Proven means that the audience relished what they heard
> 4. Stravinsky is up at the AFMM website: _www.afmm.org_
> (http://www.afmm.org)
>
> Guys, for an adventurous lot, you guys really do shoot down what is new.
> It's an old pattern. The 43/32 does not need ten minutes of steady
> bullying to make a lasting impression. Tune it up and listen, please. And if you
> don't know the terrain being discussed in the higher overtones, don't
> spout nonsense, and don't insult individuals. Sure, I still think the squiggle
> theory on Bach is shameful. The making of new music as a state of the art
> affair seems a reasonable enough position to take, a position that anyone
> on this list should be able to support. And yes, the notes are playable
> for me in a scale on the bassoon and it sounds great. The notes actually
> have more "tone" to the sound.
>
> Johnny Reinhard
>

Oh, and the Stravinsky duet sounds good, and coherent, so whatever the system is, it obviously functions musically at least for some things, that is, it isn't just a paper tuning.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Is your tuning derived from a section of the harmonic series fixed or relative? For example, do you always use 43/32 as the "fourth"? If not, and your system is fixed upon a given pitch, it can be summarily dismissed as either a particular compositional method or simply as tinfoil-hat stuff; "fa" alone ranges from a pure 4/3 to some 652 cents.
>
> As a relative system, it has a lot of very nice features. You've got Just harmonic structure up to what Partch would call "13-limit otonality", and using 43/32 as the fourth would, for a great deal of music, especially in acoustic practice, in effect enable you to veer temporarily into 1/2 comma meantone each time you encountered the classic ii-V comma problem, halving typical sinking in overall pitch. Weird, but something that can probably easily be made to work in real life situations.
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> >
> > Just finished a paper called "Eighth Octave Overtone Tuning: A Perfect
> > Tuning" which I am just now passing around. Like so many topics, it is not
> > possible to explain in this medium what is really going on with higher
> > overtone tuning as a system for making music. However, I thought I'd make some
> > response (rather than remain silent).
> >
> > While I haven't seen any lengthy description of what Iggs has planned with
> > a Primer, we have exchanged on Facebook. And reading some of the comments
> > here seem off base.
> >
> > 1. Higher overtone tuning is not numerology
> > 2. This is proven in recent live performances: Stravinsky, Reinhard,
> > Improvisation, Vicentino
> > 3. Proven means that the audience relished what they heard
> > 4. Stravinsky is up at the AFMM website: _www.afmm.org_
> > (http://www.afmm.org)
> >
> > Guys, for an adventurous lot, you guys really do shoot down what is new.
> > It's an old pattern. The 43/32 does not need ten minutes of steady
> > bullying to make a lasting impression. Tune it up and listen, please. And if you
> > don't know the terrain being discussed in the higher overtones, don't
> > spout nonsense, and don't insult individuals. Sure, I still think the squiggle
> > theory on Bach is shameful. The making of new music as a state of the art
> > affair seems a reasonable enough position to take, a position that anyone
> > on this list should be able to support. And yes, the notes are playable
> > for me in a scale on the bassoon and it sounds great. The notes actually
> > have more "tone" to the sound.
> >
> > Johnny Reinhard
> >
>

Mike Battaglia wrote:
> 3) Can you identify all dyads between each harmonic, or just
> ones that have a root of /32? E.g. can you identify 63/37, for
> example?

Pff, that's nothing for AFMM musicians. They can perform
any interval to the nearest cent!

lobawad wrote:
> Oh, and the Stravinsky duet sounds good, and coherent, so
> whatever the system is, it obviously functions musically at
> least for some things, that is, it isn't just a paper tuning.

Assuming the tuning heard in the recording is the one
claimed, that is.

-Carl

Gene, there is no "pushing" as the notes are simple to fill into a scale.
And they are rather easy to find. Some we already know.

For example, the 181st harmonic is the equal tempered tritone...to the
cent. I feel it is time to disregard what has been said about it. Speaking
about the bassoon, my greatest strength in pitch accuracy and expression,
the Eb has always been a favorite note. When I want to end on a note
completely in my control, truly able to morendo on and on, I choose Eb. I hear
the pitch in my mind before I play it, and then without any vibrato I emanate
the pitch, express upon it further, and then allow it to dissolve. This
Eb is as exact in my mind's ear as any pitch could be. Whether my ear was
first bullied into hearing it, or it has certain characteristics (like its
being a half of an octave), I would doubt. I think it is an overtone point,
something like a node that rings true.

I would stop at the eighth octave because it feels like there is an
asteroid belt between it and the 9th octave. It's just more practical not to
double 128 notes. The 8th octave takes us into the sixteenthtones (a nice
comparision with Carrillo), but more in line with the human music making range
of 8 octaves.

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=7naRYDOFDs8fLi1_QqrEK_gba33UaRMw9Ox4e88VxXuzOPPYgV-eIDBYQnvUy_C
PNKTy2_9TCtylQcdO) , Afmmjr@... wrote:

> 1. Higher overtone tuning is not numerology

Gene: How far up do you think you can push it? One reason for asking that
is that any
scale in rational intonation can be converted to a higher overtone tuning
if you
are willing to go arbitrarily high. I'm interested in particular in dwarf
scales, as they are JI scales built on an overtone plan.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Gene, there is no "pushing" as the notes are simple to fill into a scale.

By "pushing" I mean going past 64.

Mike,

I will do my best to answer your questions:

Mike: I'm diving in. Time to see how plastic the brain can get. Four simple
questions for you:

1) For these intervals, particularly for 43/32, do you hear them as
being "rooted" intervals, where the root is the bottom note? Or for
43/32, do you hear the root as being the top note? Or is it variable?

The Stravinsky recording is in said tuning. Only 43/32 perfect fourths
are played. It is a happier interval than the just/pythagorean perfect
fourth. It is 12 cents higher than the "perfect fourth" of equal temperament.
I fully believe in it when I play it. It is preferable in sound both
melodically and harmonically to all the musicians that have had a long time
working with it...and they agree it sounds "better" than 4/3 or ET's "perfect"
fourth. Not sure how I would entertain "roots" here because it is a
straight switch.

Mike:
2) Do you find that you require brighter, harsher timbres with more
harmonics to really clearly be able to distinguish between intervals?

J: just the opposite, actual overtones of the instrument make the
instruments sound better. That's why the violin family of instruments tunes to
pure fifths even when they are absent in equal temperament.

M: Do you think you'd have trouble if you used a triangle wave? For
example, do you hear 43/32 as having a beating sound, and does that
beating sound help you to identify the interval in any way?

J: Can't speak to the triangle wave, being an acoustic musician. However,
beating is always to be eased out in the tuning. We did performances
recently of Nicolo Vicentino in overtone tuning. My honest response is
"pungent" and the audience found it very modern sounding, while beautifully
coherent. Clearly no one heard it stick out as inferior in the Stravinsky
recording. I played it a lot...standard D fingering with added LH pinky on the
Eb and Db keys, together.

3) Can you identify all dyads between each harmonic, or just ones that
have a root of /32? E.g. can you identify 63/37, for example?

J: 63/37 does not exist in the overtones. However, temporary tonics will
give the ear even more to digest. G major based on A overtones, has an
easily constructed major scale that sounds very 12/tet. I only began working
out the fingerings a year ago. 4 performances later, and lots of improv
performances, it's will be time this summer to dig in. :)

M: 4) Do you ever find that 43/32 sounds ambiguous with 4/3?

Never.

Just curious; your insight here would be much appreciated.

-Mike

J: I hope to put up the paper some paragraphs at a time...unless there's a
better idea. One tough challenge for all of us is that we cannot be sure
that just intonation theoretical language will work for straight overtone
tuning, no matter how high it goes.

Carl, you might want to sit this out. You are coming off surly and
sarcastic, and that's with me giving you the benefit of the doubt.

You should realize by now that the alternatives to learning music by
reading music marked with cents deviations are:
1. Perfect Pitch (which I don't have)
2. Listening to a recording to learn by rote (as with the recent Ben
Johnston string quartets)
3. Using headphones (as with Toby Twining)
4. ...or simple neglect.

The Stravinsky was my idea to perform in overtone tuning...I now imagine
doing a performance of Firebird...or the Rite! We simply used the actual
overtones rather than using ET...and basically saved the piece!

Johnny Reinhard

p.s. thanks lobawad!

Re: Clarification of my comments on Igs' 32-64 program

Mike Battaglia wrote:
> 3) Can you identify all dyads between each harmonic, or just
> ones that have a root of /32? E.g. can you identify 63/37, for
> example?

Pff, that's nothing for AFMM musicians. They can perform
any interval to the nearest cent!

lobawad wrote:
> Oh, and the Stravinsky duet sounds good, and coherent, so
> whatever the system is, it obviously functions musically at
> least for some things, that is, it isn't just a paper tuning.

Assuming the tuning heard in the recording is the one
claimed, that is.

-Carl

sorry to butt in here but I know the answer to the ratio question... it also is the key to understanding far more complex systems...the top number is the number of the harmonic series position, the bottom number is the number of notes in the scale's octave... oh wait you didnt learn it that way did you? There is a better method waiting just for you to discover....

--- On Wed, 6/22/11, Afmmjr@... <Afmmjr@...> wrote:

From: Afmmjr@aol.com <Afmmjr@...>
Subject: [tuning] Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Wednesday, June 22, 2011, 9:27 PM

Mike,
 
I will do my best to answer your questions:
 
Mike: I'm diving in. Time to see how plastic the brain can get. Four simple
questions for you:

1) For these intervals, particularly for 43/32, do you hear them as
being "rooted" intervals, where the root is the bottom note? Or for
43/32, do you hear the root as being the top note? Or is it variable?
 
The Stravinsky recording is in said tuning.  Only 43/32 perfect fourths are played.  It is a happier interval than the just/pythagorean perfect fourth.  It is 12 cents higher than the "perfect fourth" of equal temperament.  I fully believe in it when I play it.  It is preferable in sound both melodically and harmonically to all the musicians that have had a long time working with it...and they agree it sounds "better" than 4/3 or ET's "perfect" fourth.  Not sure how I would entertain "roots" here because it is a straight switch. 
 
Mike:
2) Do you find that you require brighter, harsher timbres with more
harmonics to really clearly be able to distinguish between intervals?
 
J: just the opposite, actual overtones of the instrument make the instruments sound better.  That's why the violin family of instruments tunes to pure fifths even when they are absent in equal temperament.

M: Do you think you'd have trouble if you used a triangle wave? For
example, do you hear 43/32 as having a beating sound, and does that
beating sound help you to identify the interval in any way?

J: Can't speak to the triangle wave, being an acoustic musician.  However, beating is always to be eased out in the tuning.  We did performances recently of Nicolo Vicentino in overtone tuning.  My honest response is "pungent" and the audience found it very modern sounding, while beautifully coherent.  Clearly no one heard it stick out as inferior in the Stravinsky recording.  I played it a lot...standard D fingering with added LH pinky on the Eb and Db keys, together.
 
3) Can you identify all dyads between each harmonic, or just ones that
have a root of /32? E.g. can you identify 63/37, for example?
 
J: 63/37 does not exist in the overtones.  However, temporary tonics will give the ear even more to digest.  G major based on A overtones, has an easily constructed major scale that sounds very 12/tet.  I only began working out the fingerings a year ago.  4 performances later, and lots of improv performances, it's will be time this summer to dig in. :)

M: 4) Do you ever find that 43/32 sounds ambiguous with 4/3?

Never.
 

Just curious; your insight here would be much appreciated.

-Mike

J: I hope to put up the paper some paragraphs at a time...unless there's a better idea.  One tough challenge for all of us is that we cannot be sure that just intonation theoretical language will work for straight overtone tuning, no matter how high it goes.

On Wed, Jun 22, 2011 at 5:44 PM, Tim Reeves <reevest360@...> wrote:
>
> sorry to butt in here but I know the answer to the ratio question... it also is the key to understanding far more complex systems...the top number is the number of the harmonic series position, the bottom number is the number of notes in the scale's octave... oh wait you didnt learn it that way did you? There is a better method waiting just for you to discover....

Tim, dude, it's like Chinese water torture with these posts. Please
reveal what this amazing method is already before I go into cardiac
arrest from the stress. And if your amazing method doesn't reveal the
existence of some equivalent to mavila and porcupine temperaments,
then I'm going to go back to the boring old method.

-Mike

Mr. Battaglia, it's only fair to warn you that the recent posts about "perfect" and "truth" tunings mean that we're only one Marcel short of you having to scoop your knobbly moderator's shillelagh from its case velvet lin'd, in order to beat me about the head and shoulders under authority of the Godwin Act.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jun 22, 2011 at 5:44 PM, Tim Reeves <reevest360@...> wrote:
> >
> > sorry to butt in here but I know the answer to the ratio question... it also is the key to understanding far more complex systems...the top number is the number of the harmonic series position, the bottom number is the number of notes in the scale's octave... oh wait you didnt learn it that way did you? There is a better method waiting just for you to discover....
>
> Tim, dude, it's like Chinese water torture with these posts. Please
> reveal what this amazing method is already before I go into cardiac
> arrest from the stress. And if your amazing method doesn't reveal the
> existence of some equivalent to mavila and porcupine temperaments,
> then I'm going to go back to the boring old method.
>
> -Mike
>

Maybe you shouldn't thank me just yet, Mr. Reinhard. I think AFMM has wonderful performances, and won't pass judgement on claims of pitch accuracy for the simple reason that my ears, which don't suck if I may be so bold as to say, hear pitch consistency in your work that is downright eerie. But, I think that notating by cent deviation from 12-tET is, artistically, a dreadful idea, completely out of touch with larger/deeper musical conceptualization, and am more than allergic to the idea of any "perfect" or "true" tuning.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Carl, you might want to sit this out. You are coming off surly and
> sarcastic, and that's with me giving you the benefit of the doubt.
>
> You should realize by now that the alternatives to learning music by
> reading music marked with cents deviations are:
> 1. Perfect Pitch (which I don't have)
> 2. Listening to a recording to learn by rote (as with the recent Ben
> Johnston string quartets)
> 3. Using headphones (as with Toby Twining)
> 4. ...or simple neglect.
>
> The Stravinsky was my idea to perform in overtone tuning...I now imagine
> doing a performance of Firebird...or the Rite! We simply used the actual
> overtones rather than using ET...and basically saved the piece!
>
> Johnny Reinhard
>
> p.s. thanks lobawad!
>
>
> Re: Clarification of my comments on Igs' 32-64 program
>
> Mike Battaglia wrote:
> > 3) Can you identify all dyads between each harmonic, or just
> > ones that have a root of /32? E.g. can you identify 63/37, for
> > example?
>
> Pff, that's nothing for AFMM musicians. They can perform
> any interval to the nearest cent!
>
> lobawad wrote:
> > Oh, and the Stravinsky duet sounds good, and coherent, so
> > whatever the system is, it obviously functions musically at
> > least for some things, that is, it isn't just a paper tuning.
>
> Assuming the tuning heard in the recording is the one
> claimed, that is.
>
> -Carl
>

Hi Mike,
Thanks for being real with me.  There is no "secret" other than to use what is there naturally. Most in the tuning group seem to use advanced forms of synthesis to derive divisions of an octave. I appreciate their efforts.  All I'm saying is that  the entire spectrum of possible intervals is available right from the natural harmonic series... without all the mind boggling math.
 
For instance,  most have been taught that the Pythagorean comma occurs by using the closed circle of fifths method. What usually follows in one's study of the comma is rarely explained  to the student adequately, mainly because the math can be so tough, but also because many teachers don't fully understand the subject themselves....   In contrast, my approach shows that the Pythagorean comma occurs naturally in a scale found in the NHS. I treat it as "just another note". and never have to stray far from the original procedure... which follows later in this post.
 
Let me give you some background as to my madness...
 
Many years ago, I tried to think like Pythagoras would have done, using addition and multiplication and basic algebra. With this in mind,  I "discoverd"  that he more than likely found an added factor scale that reveals itself in the sequence of theoretical frequencies from the NHS:  80 90 100 110 120 130 140 150 160.  Labeling the elements gives a scale A B C D E F G H then the octave A.   All intervals are spaced by the same number "10".  
 
 Referring back to my post, Partch wrote (and paraphrasing) "Timoteus, who used an 8 note scale" (So tell me, what ever happened to H ? )
 
 Next I wrote sound statements on my IBM PC Jr and played them back for my mom who was an accomplished singer. She had trouble distinguishing this 8 tone natural scale from the 12 TET  diatonic 7 tone major scale, mainly because the two scales have several intervals in common, with others in close proximity.
 
Most of what followed in my initial study, I wrote about in an unpublished work "The Natural Routes Of Music" copyrighted in 1981, then  I moved on to concenterating on equal temperaments and published another book " The Songwriters' Guide to Scales and Chords" copyrighted in 1982
 
More recently, I went back and realized what a mistake it was to stop at 160 in the NHS. The added factor nature of deriving scale values continues into infinity. What was once just the "added factor major" scale to me, was more appropriately named the "natural whole tone scale".
 
 Each succeeding octave then contains the natural microtuning of half tones quarter tones, etc... nested within the whole tone values that continue indefinitely. in the series. This is natural microtuning in a nut shell. 
 
Note:This is easily applied using Scala but the software wants to "correct you" as you fight against the more commonly accepted proceedures of scale building that are incorporated into the program.
 
There are more than a few short cuts that i use in my study.One that I touched on briefly is the practice of identifying the parts of a ratio (n / m ) as n = harmonic position, m = the number of notes in the octave. A good example is in the interval 9 / 8 where 9 is the harmonic position, 8 is the number of notes in the octave ( at that point in the NHS)
 
Another short cut (for me) is abondoning the practice of viewing the NHS as 1/2, 2/3, 3/4... but instead just comparing the interval with the root position as the relative term 1/2, 1/3, 1/4... not the adjacent NHS position..  Still another that should be no surprise to you, is using the octave factor to reduce any interval  to a value between 1 and 2 and then applying the Ellis cent formula to give a  letter value to the interval       See... I'm not claiming to have re invinted the wheel here.
 
So I could go on and on, but I'll spare you that torture. Is all this groundbreaking development?
It depends on whether you have studied microtuning for years and still don't quite get it ( not necessarily referring to you, of course) or if you want to see microtuning in a few simple steps that can be learned in real time as you look at it, ie, in 5 minutes or less. 
 
Feel free to pick my brain or chastise me where appropriate. Thanks
Tim
 
.--- On Thu, 6/23/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...m>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Thursday, June 23, 2011, 7:24 AM

Mr. Battaglia, it's only fair to warn you that the recent posts about "perfect" and "truth" tunings mean that we're only one Marcel short of you having to scoop your knobbly moderator's shillelagh from its case velvet lin'd, in order to beat me about the head and shoulders under authority of the Godwin Act.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jun 22, 2011 at 5:44 PM, Tim Reeves <reevest360@...> wrote:
> >
> > sorry to butt in here but I know the answer to the ratio question... it also is the key to understanding far more complex systems...the top number is the number of the harmonic series position, the bottom number is the number of notes in the scale's octave... oh wait you didnt learn it that way did you? There is a better method waiting just for you to discover....
>
> Tim, dude, it's like Chinese water torture with these posts. Please
> reveal what this amazing method is already before I go into cardiac
> arrest from the stress. And if your amazing method doesn't reveal the
> existence of some equivalent to mavila and porcupine temperaments,
> then I'm going to go back to the boring old method.
>
> -Mike
>

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--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:

> So I could go on and on, but I'll spare you that torture. Is all this groundbreaking development?

As far as I can tell you are proposing to write all of your music in the scale consisting of the overtones 10 through 20, reduced to the octave, which would be a personal choice, not a groundbreaking development. But don't let that stop you from sharing any music you may have written using this scale.

Hi genew
 
Keep reading my posts, I don't propose any limits on scale building or composition, just adding my thoughts on how to microtune with little or no effort. Personally, I have ventured into overtones far beyond the 10 to 20 range...how do you think I found the Pythagorean comma "hiding" deep in the NHS?

--- On Thu, 6/23/11, genewardsmith <genewardsmith@sbcglobal.net> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Thursday, June 23, 2011, 6:28 PM

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:

> So I could go on and on, but I'll spare you that torture. Is all this groundbreaking development?

As far as I can tell you are proposing to write all of your music in the scale consisting of the overtones 10 through 20, reduced to the octave, which would be a personal choice, not a groundbreaking development. But don't let that stop you from sharing any music you may have written using this scale.

------------------------------------

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Dear Mr. Lobawad,

Perhaps your allergy to cents is similar to my allergy to using substitute
names. Cents is not a theory for me, but my practice of 3 decades. The
great majority of music we performed, often as premieres, would simply not
have happened without cents notation. It is a misnomer to think 1200/tet
cents notation reinforces standard equal temperament. We could disagree as
well about gay marriage, eating veal, or saying "under god" in the pledge.
But, honestly, I would never have been able to grow as an artist, to be
completely in touch "with larger/deeper musical conceptualization" without
cents. As for use of the word "perfect," how do you feel about the Perfect
Fifth?

Johnny

Maybe you shouldn't thank me just yet, Mr. Reinhard. I think AFMM has
wonderful
performances, and won't pass judgement on claims of pitch accuracy for the
simple reason that my ears, which don't suck if I may be so bold as to
say, hear
pitch consistency in your work that is downright eerie. But, I think that
notating by cent deviation from 12-tET is, artistically, a dreadful idea,
completely out of touch with larger/deeper musical conceptualization, and
am
more than allergic to the idea of any "perfect" or "true" tuning.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> The Stravinsky was my idea to perform in overtone tuning...
> I now imagine doing a performance of Firebird...or the Rite!
> We simply used the actual overtones rather than using ET...
> and basically saved the piece!

We're talking about this recording, right?

http://afmm.org/lied.htm

-Carl

On Thu, Jun 23, 2011 at 1:52 PM, Tim Reeves <reevest360@...> wrote:
>
> Hi Mike,
> Thanks for being real with me.  There is no "secret" other than to use what is there naturally. Most in the tuning group seem to use advanced forms of synthesis to derive divisions of an octave. I appreciate their efforts.  All I'm saying is that  the entire spectrum of possible intervals is available right from the natural harmonic series... without all the mind boggling math.

OK. Well, we've been using the harmonic series as more or less the
basis for everything we're doing, so let's see how you can simplify
things.

> For instance,  most have been taught that the Pythagorean comma occurs by using the closed circle of fifths method. What usually follows in one's study of the comma is rarely explained  to the student adequately, mainly because the math can be so tough, but also because many teachers don't fully understand the subject themselves....   In contrast, my approach shows that the Pythagorean comma occurs naturally in a scale found in the NHS. I treat it as "just another note". and never have to stray far from the original procedure... which follows later in this post.

The Pythagorean comma is also a pretty useless comma, all things
considered, but by virtue of its being 531441/524288, it obviously
occurs in the harmonic series, yes.

> So I could go on and on, but I'll spare you that torture. Is all this groundbreaking development?
> It depends on whether you have studied microtuning for years and still don't quite get it ( not necessarily referring to you, of course) or if you want to see microtuning in a few simple steps that can be learned in real time as you look at it, ie, in 5 minutes or less.

This seems more complicated than what we're doing, unless there's
something I misunderstand. How do you get a meantone major scale from
this, which tempers out 81/80? How about superpyth, which tempers out
64/63? I don't get it.

We've also been using the harmonic series, except instead of using
"integer-limit" as you're doing, we tend to go by prime-limit. That
is, rather than going up to harmonic #4096 or whatever, we look at all
of the harmonics with prime factors that are no greater than n. So the
3-limit would have generating intervals of 2/1 and 3/1, and some
example pitches in this (infinite) set would be 2/1, 3/1, 4/1, 3/2,
9/8, 9/4, 27/16, 8192/6561, 531441/524288, etc. The 5-limit would
throw factors of 5 in there, so you'd get stuff like 5/4, 6/5, 25/16,
128/125, etc in there as well. The 7-limit would give you factors of
7, etc.

You're using integer limit, on the other hand, where you look at all
of the harmonics up to a certain number. Well, that's fine, I just
don't see how it makes anything easier.

-Mike

Yes, Carl. Perhaps it would be helpful to list the harmonics that I am
playing for the Stravinsky "Lied Ohne Name" (1918), in order of appearance:

3 43 3 19 9 43 1 9 1
9 3 43 9 43 3 51 3 43 9
1 9 57 9 57 1 5 9 1 27 1 9 57 1 9
27 1 9 5 1 9 57 1 3 43 19 9 19
9 43 1 9 43 1 3 43 9 43 1 9

Essentially, this is my part, although not specific as to range. But
Stravinsky took care of that.

Johnny Reinhard

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=aNxnGpBpiE_LyOSbSJzRGvK31LzDYTSxJbJcqRqD2vbuJtXxru-1jVNu5VnjSAb
ram1nlXKd2FmaXEiRCa8) , Afmmjr@... wrote:

> The Stravinsky was my idea to perform in overtone tuning...
> I now imagine doing a performance of Firebird...or the Rite!
> We simply used the actual overtones rather than using ET...
> and basically saved the piece!

We're talking about this recording, right?

_http://afmm.org/lied.htm_ (http://afmm.org/lied.htm)

-Carl

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Yes, Carl. Perhaps it would be helpful to list the harmonics that I am
> playing for the Stravinsky "Lied Ohne Name" (1918), in order of appearance:
>
> 3 43 3 19 9 43 1 9 1
> 9 3 43 9 43 3 51 3 43 9
> 1 9 57 9 57 1 5 9 1 27 1 9 57 1 9
> 27 1 9 5 1 9 57 1 3 43 19 9 19
> 9 43 1 9 43 1 3 43 9 43 1 9
>
> Essentially, this is my part, although not specific as to range. But
> Stravinsky took care of that.
>
> Johnny Reinhard

with "do" at 1, that would be

sol, fa, sol, me, re, fa, do, re, do
re, sol, fa, re, fa, sol, le, sol, fa, re
do, re, te, re, te, do, mi, re, do, la, do, re, te, do, re
etc.

It's 12-tET with consistent coloristic intonation, mostly about 2 cents from strict except for fa being a 1/2 comma sharp and the mi a comma flat, but neither of these creates a functional deviation from the mastergrid of 12-tET. I'd have to see the other part, though.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Dear Mr. Lobawad,
>
> Perhaps your allergy to cents is similar to my allergy to using substitute
> names.

I'm not allergic to cents- I think they're a great measurement tool.

Notating by means of cent deviations from 12-tET is what bothers me. Not because it doesn't work as a practical tool.

Cents is not a theory for me, but my practice of 3 decades. The
> great majority of music we performed, often as premieres, would simply not
> have happened without cents notation. It is a misnomer to think 1200/tet
> cents notation reinforces standard equal temperament. We could disagree as
> well about gay marriage, eating veal, or saying "under god" in the pledge.
> But, honestly, I would never have been able to grow as an artist, to be
> completely in touch "with larger/deeper musical conceptualization" without
> cents.

I think your system, while enabling the physical manifestation of many pieces of music, is not conducive to understanding. Why did you not correct me when I earlier incorrectly assumed that you were sharping fa (and by implication adjusting other intervals from traditional Just in the process) in order to mitigate commatic drift? Why did you not answer as to whether your "1" is fixed or movable, and if fixed, where, if moveable, how? There's no understanding your system without knowing these things.

>As for use of the word "perfect," how do you feel about the Perfect
> Fifth?

Hahaha! Good answer! But I have a better riposte: how do you feel about the Perfect Fourth? :-)

So, you're cool with do-sol as 3:2 and la-mi as flat by a good half comma? Nothing wrong with that artistically, but when retuning historical music, that's tinfoil-hat stuff. Look what happens to your typical deceptive cadence to vi or VI (/6 to be typical, but anyway) for example. 12-tET weakens the traditional meaning, but this would wreck it, reducing it to a mere gesture.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> >
> >
> > Yes, Carl. Perhaps it would be helpful to list the harmonics that I am
> > playing for the Stravinsky "Lied Ohne Name" (1918), in order of appearance:
> >
> > 3 43 3 19 9 43 1 9 1
> > 9 3 43 9 43 3 51 3 43 9
> > 1 9 57 9 57 1 5 9 1 27 1 9 57 1 9
> > 27 1 9 5 1 9 57 1 3 43 19 9 19
> > 9 43 1 9 43 1 3 43 9 43 1 9
> >
> > Essentially, this is my part, although not specific as to range. But
> > Stravinsky took care of that.
> >
> > Johnny Reinhard
>
> with "do" at 1, that would be
>
> sol, fa, sol, me, re, fa, do, re, do
> re, sol, fa, re, fa, sol, le, sol, fa, re
> do, re, te, re, te, do, mi, re, do, la, do, re, te, do, re
> etc.
>
> It's 12-tET with consistent coloristic intonation, mostly about 2 cents from strict except for fa being a 1/2 comma sharp and the mi a comma flat, but neither of these creates a functional deviation from the mastergrid of 12-tET. I'd have to see the other part, though.
>

Par. 15 of Eighth Octave Overtone Tuning: A Perfect Tuning by Johnny
Reinhard
While choosing A=440 as the fundamental for generating harmonics might
seem arbitrary in the abstract, it is both resonant in overtones and
technically manageable on woodwinds, and is traditionally an open string on strings.
“A” is more than the first letter of the alphabet. It the first pitch
from which I measure all other musical intervals on my professional model
Püchner bassoon. The symphony orchestra traditionally tunes to the “
harmonically-rich” “A” on the oboe. My bassoon has a comfortable approach to each
of these new notes because they constitute the very fabric of the
instrument’s tone. My bassoon sounds beautiful in overtone tuning, better than in
equal temperament, as if to announce that overtone tuning is its true
identity.

Lobawad: It's 12-tET with consistent coloristic intonation, mostly about
2 cents from strict except for fa being a 1/2 comma sharp and the mi a
comma flat, but neither of these creates a functional deviation from the
mastergrid of 12-tET. I'd have to see the other part, though.

Johnny: I could give you the 2nd bassoon part, but it wouldn't line up as
it would with standard music notation. Others have been screeching about
using the 43/32 as the "perfect" fourth, and you happily dismiss it as
coloristic. That's a good sign to me! Yes, 12-tET is largely a part of the
overtone series, at least half.

Lobawad: I think your system, while enabling the physical manifestation of
many pieces of music, is not conducive to understanding.

Johnny: When Rudolf Rasch reviewed the late Gardner Read's book on
microtonal notation, Gardner was ripped a new one for the same reason. Gardner
telephoned me to try to understand how Rudolf could have been so cruel about
his tireless efforts to present the a collection of the state of the art in
microtonal music in his time. I explained to him that there is a
difference between descriptive notation and prescriptive notation. You appear to
savor the "understanding" factor of descriptive notation. Cents notation is
meant to be prescriptive. It's about the expediency to performance.

Lobawad: Why did you not correct me when I earlier incorrectly assumed that
you were sharping fa (and by implication adjusting other intervals from
traditional Just in the process) in order to mitigate commatic drift? Why did
you not answer as to whether your "1" is fixed or movable, and if fixed,
where, if moveable, how? There's no understanding your system without
knowing these things.

Johnny: Because it is not possible to tell everything at the same time.
If you would like, I would be happy to send the paper to you, with the
priviso that I expect to make a few new edits. Just found a great Schoenberg
quote anticipating the whole enterprise.

Lobawad: So, you're cool with do-sol as 3:2 and la-mi as flat by a good
half comma? Nothing wrong with that artistically, but when retuning
historical music, that's tinfoil-hat stuff. Look what happens to your typical
deceptive cadence to vi or VI (/6 to be typical, but anyway) for example. 12-tET
weakens the traditional meaning, but this would wreck it, reducing it to a
mere gesture.

Johnny: Today I think of the overtone series as the original chord; it is
major and minor and so much more.
My agenda is not to where a tinfoil-hat, it is to create. The Stravinsky,
and a number of other pieces, were meant to make real what the theory only
suggested. It was an opportunity for true experimental music, the kind
where you don't know what the end results will be.

Johnny Reinhard

It would be great to read your paper- as it is, I can't, for example, tell what's relative and what's fixed, which makes for some tremendous differences of course.

As far as tone, the very thing which would make people take seriously whatever you happen to say about bassoon tone, which is your great bassoon tone of course, is paradoxically what would make people take with a grain of salt anything you say about bassoon tone, for you could say that for your tone you wear green underpants in order to facilitate the transduction of Guarnerius waves, and who could really argue otherwise?

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Par. 15 of Eighth Octave Overtone Tuning: A Perfect Tuning by Johnny
> Reinhard
> While choosing A=440 as the fundamental for generating harmonics might
> seem arbitrary in the abstract, it is both resonant in overtones and
> technically manageable on woodwinds, and is traditionally an open string on strings.
> “A” is more than the first letter of the alphabet. It the first pitch
> from which I measure all other musical intervals on my professional model
> Püchner bassoon. The symphony orchestra traditionally tunes to the “
> harmonically-rich” “A” on the oboe. My bassoon has a comfortable approach to each
> of these new notes because they constitute the very fabric of the
> instrument’s tone. My bassoon sounds beautiful in overtone tuning, better than in
> equal temperament, as if to announce that overtone tuning is its true
> identity.
>
>
> Lobawad: It's 12-tET with consistent coloristic intonation, mostly about
> 2 cents from strict except for fa being a 1/2 comma sharp and the mi a
> comma flat, but neither of these creates a functional deviation from the
> mastergrid of 12-tET. I'd have to see the other part, though.
>
> Johnny: I could give you the 2nd bassoon part, but it wouldn't line up as
> it would with standard music notation. Others have been screeching about
> using the 43/32 as the "perfect" fourth, and you happily dismiss it as
> coloristic. That's a good sign to me! Yes, 12-tET is largely a part of the
> overtone series, at least half.
>
>
> Lobawad: I think your system, while enabling the physical manifestation of
> many pieces of music, is not conducive to understanding.
>
> Johnny: When Rudolf Rasch reviewed the late Gardner Read's book on
> microtonal notation, Gardner was ripped a new one for the same reason. Gardner
> telephoned me to try to understand how Rudolf could have been so cruel about
> his tireless efforts to present the a collection of the state of the art in
> microtonal music in his time. I explained to him that there is a
> difference between descriptive notation and prescriptive notation. You appear to
> savor the "understanding" factor of descriptive notation. Cents notation is
> meant to be prescriptive. It's about the expediency to performance.
>
>
> Lobawad: Why did you not correct me when I earlier incorrectly assumed that
> you were sharping fa (and by implication adjusting other intervals from
> traditional Just in the process) in order to mitigate commatic drift? Why did
> you not answer as to whether your "1" is fixed or movable, and if fixed,
> where, if moveable, how? There's no understanding your system without
> knowing these things.
>
>
> Johnny: Because it is not possible to tell everything at the same time.
> If you would like, I would be happy to send the paper to you, with the
> priviso that I expect to make a few new edits. Just found a great Schoenberg
> quote anticipating the whole enterprise.
>
>
> Lobawad: So, you're cool with do-sol as 3:2 and la-mi as flat by a good
> half comma? Nothing wrong with that artistically, but when retuning
> historical music, that's tinfoil-hat stuff. Look what happens to your typical
> deceptive cadence to vi or VI (/6 to be typical, but anyway) for example. 12-tET
> weakens the traditional meaning, but this would wreck it, reducing it to a
> mere gesture.
>
> Johnny: Today I think of the overtone series as the original chord; it is
> major and minor and so much more.
> My agenda is not to where a tinfoil-hat, it is to create. The Stravinsky,
> and a number of other pieces, were meant to make real what the theory only
> suggested. It was an opportunity for true experimental music, the kind
> where you don't know what the end results will be.
>
> Johnny Reinhard
>

Learned so much the other night reading my own archive material. Thanks
to Kyle Gann and Jon Catler, I now understand that La Monte Young's
"Well-Tuned Piano" is in pure overtone tuning....no undertone series. Now I
connect that info to the famous harmonic clouds that are produced by La Monte's
6-hour composition. There is loss of reception when the overtones are
muddied by just intonation undertone intervals (such as the 4/3 or the 6/5).
Doing is believing. So, need a bit more time with the paper. It should be
obvious by now that some things need the proper time to mature, and that
this medium sucks when trying to get across profound and complex music
principles. Love the challenge to verbalize the ineffable, don't you?

Lobawad: It would be great to read your paper- as it is, I can't, for
example, tell
what's relative and what's fixed, which makes for some tremendous
differences of
course.

Johnny: The tuning is fixed, with A=440.

Lobawad: As far as tone, the very thing which would make people take
seriously whatever
you happen to say about bassoon tone, which is your great bassoon tone of
course, is paradoxically what would make people take with a grain of salt
anything you say about bassoon tone, for you could say that for your tone
you
wear green underpants in order to facilitate the transduction of Guarnerius
waves, and who could really argue otherwise?

Johnny: How frustrating that the person that makes the bassoon tone renown
cannot explain how it's done? I've a nice bassoon reed metaphor to share:
using undertones when playing otherwise in overtone tuning is like sanding
the reed against the grain.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Learned so much the other night reading my own archive material. >Thanks
> to Kyle Gann and Jon Catler, I now understand that La Monte >Young's
> "Well-Tuned Piano" is in pure overtone tuning....no undertone >series.
>Now I
> connect that info to the famous harmonic clouds that are produced >by La Monte's
> 6-hour composition. There is loss of reception when the overtones >are
> muddied by just intonation undertone intervals (such as the 4/3 or >the 6/5).

Harmonic/inharmonic or over/undertone are, once we've lifted off from the field of paper, false dichotomies. Even in monophony, if you move from 3/2 to 2/1, you've just played a 4/3.

Whence this silly bifurcation? The most likely source is sadly obvious. The cultural phenomenon of a dichotomy of major and minor is so strong that it was only natural that in days of greater innocence (giving great benefit of doubt to motivations) theorists should seek its source in "nature". So Riemann proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in the 2011 still wasting our time going on as if we've got two distinct things where in actual practice we really have aspects of one.

> Doing is believing.
>So, need a bit more time with the paper. It should be
> obvious by now that some things need the proper time to mature, >and that
> this medium sucks when trying to get across profound and complex >music
> principles. Love the challenge to verbalize the ineffable, don't >you?

Effing the ineffable is a pleasure, but then again effing in general is pleasurable.

>
>
> Lobawad: It would be great to read your paper- as it is, I can't, >for
> example, tell
> what's relative and what's fixed, which makes for some tremendous
> differences of
> course.
>
> Johnny: The tuning is fixed, with A=440.

So you mean octaves of harmonics of A-440, for surely 440Hz isn't the lowest pitch you're playing on the bassoon.

-Cuthbert Lobawad, Lieutenant Janitor of the Mord-Sith

On Fri, Jul 1, 2011 at 4:48 AM, lobawad <lobawad@...> wrote:
>
> Whence this silly bifurcation? The most likely source is sadly obvious. The cultural phenomenon of a dichotomy of major and minor is so strong that it was only natural that in days of greater innocence (giving great benefit of doubt to motivations) theorists should seek its source in "nature". So Riemann proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in the 2011 still wasting our time going on as if we've got two distinct things where in actual practice we really have aspects of one.

Can you elaborate on this? What is minorness, what is majorness, etc?

Keep in mind that if the major/minor dichotomy is "cultural" in
origin, that the word "culture" is actually a code word for "extremely
deep cognitive structure for organizing sound that spontaneously and
mysteriously causes feelings to arise as information fluctuates within
it." It's a great hypothesis, but what does it mean and how does it
work? How does the major/minor duality arise within this structure?
What is the nature of this structure? How can moving around in this
system's phase space cause feelings?

That's what any attribution of phenomena towards "culture" entails.
The cultural argument is no less loaded than the psychoacoustic one
and infinitely more complex. Which is fine, let's not wuss out now
that the going's tough. But it's tough going once culture gets
involved.

-Mike

The adding of the culture dimension is really just an extension of the old
"nature/nurture" argument, culture being the corollary to nurture.
Overtone tuning is clearly in the realm of nature.

I believe that removing the undertone series from overtone only
relationships improves the music reception. Perhaps the true dissonance is in
confusing the two series, overtone (harmonic) and undertone (conceivable through
difference tone patterns), an early form of polymicrotonality. Jon Catler
and I agreed on this the other night for one of our continuing
conversations on the topic. (Should the Microtones band do a big show next year?)

We are all here on the List using cultural definitions, buttressed by
annecdotals in our personal lives. There are different perspectives: Is the
glass half full of half empty? (depends). Sure, the 4/3 exists as the
measurement between the 3rd and 4th harmonics. Good for the interval! However,
it does not exist as a scale note in the overtone series. The power of
harmonics only tuning is self evident when working in it. The paper comes
last.

128 notes in every octave for every instruments (except maybe fretted
guitar) is finally reached. A century ago, a Schoenberg, or most anyone else,
simply could not imagine hearing such a scale, let alone any of the higher
harmonics. It was all paper, until recently.

The sound is totally different in comparison with previously understood
just intonation. So many different interval relationships begging to be
heard.

Johnny

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=Xiv5JzX7UAdHRNKQmeQNjYWNPkerfl84deXPytrqTzLOX8QCuS_RYPXsG7AwDr3
PXFdib4xdUhg5ofWItY3iR1c) , Afmmjr@... wrote:
>
>
> Learned so much the other night reading my own archive material. >Thanks
> to Kyle Gann and Jon Catler, I now understand that La Monte >Young's
> "Well-Tuned Piano" is in pure overtone tuning....no undertone >series.
>Now I
> connect that info to the famous harmonic clouds that are produced >by La
Monte's
> 6-hour composition. There is loss of reception when the overtones >are
> muddied by just intonation undertone intervals (such as the 4/3 or >the
6/5).

Harmonic/inharmonic or over/undertone are, once we've lifted off from the
field
of paper, false dichotomies. Even in monophony, if you move from 3/2 to
2/1,
you've just played a 4/3.

Whence this silly bifurcation? The most likely source is sadly obvious. The
cultural phenomenon of a dichotomy of major and minor is so strong that it
was
only natural that in days of greater innocence (giving great benefit of
doubt
to motivations) theorists should seek its source in "nature". So Riemann
proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in
the
2011 still wasting our time going on as if we've got two distinct things
where
in actual practice we really have aspects of one.

> Doing is believing.
>So, need a bit more time with the paper. It should be
> obvious by now that some things need the proper time to mature, >and that
> this medium sucks when trying to get across profound and complex >music
> principles. Love the challenge to verbalize the ineffable, don't >you?

Effing the ineffable is a pleasure, but then again effing in general is
pleasurable.

>
>
> Lobawad: It would be great to read your paper- as it is, I can't, >for
> example, tell
> what's relative and what's fixed, which makes for some tremendous
> differences of
> course.
>
> Johnny: The tuning is fixed, with A=440.

So you mean octaves of harmonics of A-440, for surely 440Hz isn't the
lowest
pitch you're playing on the bassoon.

-Cuthbert Lobawad, Lieutenant Janitor of the Mord-Sith

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:
>
> Hi Mike,
> Thanks for being real with me.� There is no "secret" other than to use what is there naturally. Most in the tuning group seem to use advanced forms of synthesis to derive divisions of an octave. I appreciate their efforts. �All I'm saying is that� the entire spectrum of possible intervals is available right from the natural harmonic series... without all the mind boggling math.

Of course it is. Nobody's denying this. The entire spectrum of intervals is also available right on the slide of my trombone. Every interval you can possibly think of! (As long as it's in the ~3 octave range of a trombone.)

> For instance, �most have been taught that the Pythagorean�comma occurs by using the closed circle of fifths method. What usually follows in one's study of the comma�is rarely explained� to the student adequately, mainly because the math can be so tough, but also because many teachers don't fully understand the subject themselves....�� In contrast, my approach shows that the Pythagorean comma occurs naturally in a scale found in the NHS. I treat it as "just another note". and never have to stray far from the original procedure... which follows later in this post.

Of course it does. The Pythagorean comma is 531441/524288, so it appears in the harmonic series between harmonics 524288 and 531441. Is it useful to talk about harmonics over 19 octaves above the fundamental (when the range of human hearing is about 10 octaves)? Is it useful to talk about scales with half a million notes in them? For me, no, it is a waste of time. I prefer scales with, say, 7 notes. Maybe 10 or 12. Not half a million.

> �Next I wrote sound statements on my IBM PC Jr and played them back for my mom who was an accomplished singer. She had trouble distinguishing this 8 tone natural scale from the 12 TET� diatonic 7�tone major scale, mainly because the two scales have several intervals in common, with others in close proximity.

I'm not sure I understand what you're saying here. Are you saying your mom really couldn't distinguish between the harmonics 8:9:10:11:12:13:14:15:16, and the diatonic scale, WWHWWWH? If so, either your mom has incredibly bad ear training skills, or you were using some kind of sound that makes it really difficult to tell differences between intervals.

The diatonic scale and the 8-16 harmonic series scale are both great scales (two of my favorites, in fact), but they sound totally different. The harmonic series scale feels like it has just one tonal center to me, but in the diatonic scale it feels like 5 or 6 out of the 7 notes can be made to sound like the tonal center at any given time. The harmonic series has one master note and a hierarchy of slave notes, but the diatonic scale is more of a democracy.

Keenan

hi keenan
 
Thanks for responding to my post,  please read my edit below >>>
 
--- On Fri, 7/1/11, Keenan Pepper <keenanpepper@...> wrote:

From: Keenan Pepper <keenanpepper@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Friday, July 1, 2011, 3:45 PM

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:
>
> Hi Mike,
> Thanks for being real with me.� There is no "secret" other than to use what is there naturally. Most in the tuning group seem to use advanced forms of synthesis to derive divisions of an octave. I appreciate their efforts. �All I'm saying is that� the entire spectrum of possible intervals is available right from the natural harmonic series... without all the mind boggling math.

Of course it is. Nobody's denying this. The entire spectrum of intervals is also available right on the slide of my trombone. Every interval you can possibly think of! (As long as it's in the ~3 octave range of a trombone.)

> For instance, �most have been taught that the Pythagorean�comma occurs by using the closed circle of fifths method. What usually follows in one's study of the comma�is rarely explained� to the student adequately, mainly because the math can be so tough, but also because many teachers don't fully understand the subject themselves....�� In contrast, my approach shows that the Pythagorean comma occurs naturally in a scale found in the NHS. I treat it as "just another note". and never have to stray far from the original procedure... which follows later in this post.

Of course it does. The Pythagorean comma is 531441/524288, so it appears in the harmonic series between harmonics 524288 and 531441
 
>>> let me try to explain my madness...
 
>>> each of the following identify positions of octaves in the nhs...each clearly identifies the number of natural notes in the octave at that point in the nhs
 

>>> 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288
 
>>>...the next number after each of these defines the correct ratio for creating the interval used in the added factor scale at their respective positions...a shortcut is to remember that the octave factor of 2 or 1/2  is also applied to the  added factor ...thus this scale remains constant over the audio spectrum and beyond.
 
>>>check this out
 

>>>as posted before, the top number describes the position in the nhs, the bottom number is the number of notes  in the octave at that point in the nhs The following is data from the natural whole tone scale.
 
>>>  8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8
         A    B     C      D       E     F       G     H     A octave
 
>>> if A has a frequency of 80 then the whole tone factor is 10
 
 
>>> Half tones occur next
 
16/16 17/16 18/16..  .32/16
A            A#       B        A octave
 
>>> here the half tone factor is 5
 
>>>Quarter tones occur next
 
32/32       33/32      34/32      35/32     36/32
    A              Aq t         A#         A#qt         B
 
>>> here the quarter tone factor is 2.5
 
(maybe someone could inject the "correct symbol" for quarter notes....thanks)
 
 
>>> moving into the rocket science level of octaves (haha) the process continues without interuption
 
524288/524288    524289/524288     524290/524288.......531440/524288  531441/524288    531442/524288.......
 
>>> each of these ratios  ( whether found in close proximity to the fundamental or in extreme extensions of the nhs) can be converted into a hertz based interval or given a cent value. Going further,  it is subdivided (or multiplied as the case may be) by the octave factor into the audible octave of your choice and then conveniently given a letter value, but there is no concensus of what to call all of these additional intervals besides A B C D E F G H and their half tone values. It makes sense to continue the microtuning with quarterr, eighth, sixteenth etc  but comming up with symbols is tricky   
 
>>>Recall my previous post that mentioned the "nesting" of all natural intervals to realize that even in a scale with half a million notes, the whole tone steps are still there as are all the other elements of natural microtuning.
 
whew!!!!
 
 
. Is it useful to talk about harmonics over 19 octaves above the fundamental (when the range of human hearing is about 10 octaves)?
 
>>> remember that following the circle of fifths process to the 13th step is already beyond the audio spectrum and from what I've seen ,  this process is used as the "basis" of modern western harmony
 
 Is it useful to talk about scales with half a million notes in them? For me, no, it is a waste of time. I prefer scales with, say, 7 notes. Maybe 10 or 12. Not half a million.
 
>>> hey me, too  I never meant to suggest we should try music with half a million notes in it, just wanted to identify the natural scale where the Pythagorean comma actually occurs   Maybe you'd like to compare the results of my natural microtuning process with the work of someone like Kyle Gann who identified over 700 known intervals 

> �Next I wrote sound statements on my IBM PC Jr and played them back for my mom who was an accomplished singer. She had trouble distinguishing this 8 tone natural scale from the 12 TET� diatonic 7�tone major scale, mainly because the two scales have several intervals in common, with others in close proximity.
> hope the math above gives enough data for you to compare the natural whole tone scale with 12tet

I'm not sure I understand what you're saying here. Are you saying your mom really couldn't distinguish between the harmonics 8:9:10:11:12:13:14:15:16, and the diatonic scale, WWHWWWH? If so, either your mom has incredibly bad ear training skills, or you were using some kind of sound that makes it really difficult to tell differences between intervals.
 
>>> do the math  8 9 10 12 and 16 are the ones she had trouble telling the difference in a very brief listen...some of the others were close for her, while others were way off...
 
 >>>thanks bro
Tim

The diatonic scale and the 8-16 harmonic series scale are both great scales (two of my favorites, in fact), but they sound totally different. The harmonic series scale feels like it has just one tonal center to me, but in the diatonic scale it feels like 5 or 6 out of the 7 notes can be made to sound like the tonal center at any given time. The harmonic series has one master note and a hierarchy of slave notes, but the diatonic scale is more of a democracy.

Keenan

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this is "effing" fantastic to be around you guys... thanks
tim

--- On Fri, 7/1/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@yahoo.com>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Friday, July 1, 2011, 8:48 AM

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> 
> Learned so much the other night reading my own archive material.  >Thanks
> to Kyle Gann and Jon Catler, I now understand  that La Monte >Young's
> "Well-Tuned Piano" is in pure overtone tuning....no  undertone >series.
>Now I
> connect that info to the famous harmonic  clouds that are produced >by La Monte's
> 6-hour composition.  There is loss  of reception when the overtones >are
> muddied by just intonation undertone  intervals (such as the 4/3 or >the 6/5).

Harmonic/inharmonic or over/undertone are, once we've lifted off from the field of paper, false dichotomies. Even in monophony, if you move from 3/2 to 2/1, you've just played a 4/3.

Whence this silly bifurcation? The most likely source is sadly obvious. The cultural phenomenon of a dichotomy of major and minor is so strong that it was only natural that in days of greater innocence  (giving great benefit of doubt to motivations) theorists should seek its source in "nature". So Riemann proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in the 2011 still wasting our time going on as if we've got two distinct things where in actual practice we really have aspects of one.

> Doing is believing. 
>So, need  a bit more time with the paper.  It should be
> obvious by now that some  things need the proper time to mature, >and that
> this medium sucks when trying to  get across profound and complex >music
> principles.  Love the challenge to  verbalize the ineffable, don't >you?

Effing the ineffable is a pleasure, but then again effing in general is pleasurable.

> 
>
> Lobawad: It would be great to read your  paper- as it is, I can't, >for
> example, tell
> what's relative and what's fixed,  which makes for some tremendous
> differences of
> course.
>
> Johnny: The tuning is fixed, with  A=440. 

So you mean octaves of harmonics of A-440, for surely 440Hz isn't the lowest pitch you're playing on the bassoon.

-Cuthbert Lobawad, Lieutenant Janitor of the Mord-Sith

------------------------------------

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  tuning-unsubscribe@yahoogroups.com - leave the group.
  tuning-nomail@yahoogroups.com - turn off mail from the group.
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--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jul 1, 2011 at 4:48 AM, lobawad <lobawad@...> wrote:
> >
> > Whence this silly bifurcation? The most likely source is sadly obvious. The cultural phenomenon of a dichotomy of major and minor is so strong that it was only natural that in days of greater innocence (giving great benefit of doubt to motivations) theorists should seek its source in "nature". So Riemann proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in the 2011 still wasting our time going on as if we've got two distinct things where in actual practice we really have aspects of one.
>
> Can you elaborate on this? What is minorness, what is majorness, etc?
>
> Keep in mind that if the major/minor dichotomy is "cultural" in
> origin, that the word "culture" is actually a code word for "extremely
> deep cognitive structure for organizing sound that spontaneously and
> mysteriously causes feelings to arise as information fluctuates within
> it." It's a great hypothesis, but what does it mean and how does it
> work? How does the major/minor duality arise within this structure?
> What is the nature of this structure? How can moving around in this
> system's phase space cause feelings?
>
> That's what any attribution of phenomena towards "culture" entails.
> The cultural argument is no less loaded than the psychoacoustic one
> and infinitely more complex. Which is fine, let's not wuss out now
> that the going's tough. But it's tough going once culture gets
> involved.
>
> -Mike
>

You've got it backwards- it's not the moderate assumption that in any art form, an organizational and meaningful structure which appears in some cultures but not in others is a cultural rather than "natural" phenomenon that requires elaboration, it's the claim that an organizational and meaningful structure which appears in the art of some cultures but not in others is a "natural" phenomenon that requires a explanation.

The burden of proof lies on the extraordinary claim that the major/minor dichotomy of Western music is "natural". Of course there's a school that makes this claim, going back to Hauptmann in the 19th Century (if I recall correctly, it was Hauptmann who was responsible for such gems as correcting Bach's "mistakes" of lapsing into church modes).

But before we get carried away, let's straighten out a couple of things.

First of all, back to the point I was making, which was harmonic/subharmonic or over/undertone is really a false dichotomy, once we get out of the classroom and onto the streets. Would you maintain that there is a clear dichotomy between the two, and if so, how would you move from 3/2 to 2/1 without playing a 4/3?

Second, let's not conflate a "hard" position position like Hauptmann's (in short, V-I as divine truth) with any and all psychoacoustic explanations of major/minor duality. Unless that's already your position, in which case we might as well end this now, by the authority of the Godwin Act. :-)

Any rational tuning can be described as higher harmonics of a single fundamental. There's even an automagic function in Scala to give you the exact harmonics.

It is certainly not impossible that your instrument, which evolved in an A-440 12-tET world, resonates best at or very near frequencies found on that grid. Downright likely, I'd say. I'll have to read your paper to see what this has to do with Just intonation.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> The adding of the culture dimension is really just an extension of the old
> "nature/nurture" argument, culture being the corollary to nurture.
> Overtone tuning is clearly in the realm of nature.
>
> I believe that removing the undertone series from overtone only
> relationships improves the music reception. Perhaps the true dissonance is in
> confusing the two series, overtone (harmonic) and undertone (conceivable through
> difference tone patterns), an early form of polymicrotonality. Jon Catler
> and I agreed on this the other night for one of our continuing
> conversations on the topic. (Should the Microtones band do a big show next year?)
>
> We are all here on the List using cultural definitions, buttressed by
> annecdotals in our personal lives. There are different perspectives: Is the
> glass half full of half empty? (depends). Sure, the 4/3 exists as the
> measurement between the 3rd and 4th harmonics. Good for the interval! However,
> it does not exist as a scale note in the overtone series. The power of
> harmonics only tuning is self evident when working in it. The paper comes
> last.
>
> 128 notes in every octave for every instruments (except maybe fretted
> guitar) is finally reached. A century ago, a Schoenberg, or most anyone else,
> simply could not imagine hearing such a scale, let alone any of the higher
> harmonics. It was all paper, until recently.
>
> The sound is totally different in comparison with previously understood
> just intonation. So many different interval relationships begging to be
> heard.
>
> Johnny
>
>
>
>
> --- In _tuning@yahoogroups.com_
> (/tuning/post?postID=Xiv5JzX7UAdHRNKQmeQNjYWNPkerfl84deXPytrqTzLOX8QCuS_RYPXsG7AwDr3
> PXFdib4xdUhg5ofWItY3iR1c) , Afmmjr@ wrote:
> >
> >
> > Learned so much the other night reading my own archive material. >Thanks
> > to Kyle Gann and Jon Catler, I now understand that La Monte >Young's
> > "Well-Tuned Piano" is in pure overtone tuning....no undertone >series.
> >Now I
> > connect that info to the famous harmonic clouds that are produced >by La
> Monte's
> > 6-hour composition. There is loss of reception when the overtones >are
> > muddied by just intonation undertone intervals (such as the 4/3 or >the
> 6/5).
>
> Harmonic/inharmonic or over/undertone are, once we've lifted off from the
> field
> of paper, false dichotomies. Even in monophony, if you move from 3/2 to
> 2/1,
> you've just played a 4/3.
>
> Whence this silly bifurcation? The most likely source is sadly obvious. The
> cultural phenomenon of a dichotomy of major and minor is so strong that it
> was
> only natural that in days of greater innocence (giving great benefit of
> doubt
> to motivations) theorists should seek its source in "nature". So Riemann
> proposed a dualism, Partch gave it a Hubbardesque moniker, and here we in
> the
> 2011 still wasting our time going on as if we've got two distinct things
> where
> in actual practice we really have aspects of one.
>
>
> > Doing is believing.
> >So, need a bit more time with the paper. It should be
> > obvious by now that some things need the proper time to mature, >and that
> > this medium sucks when trying to get across profound and complex >music
> > principles. Love the challenge to verbalize the ineffable, don't >you?
>
> Effing the ineffable is a pleasure, but then again effing in general is
> pleasurable.
>
>
> >
> >
> > Lobawad: It would be great to read your paper- as it is, I can't, >for
> > example, tell
> > what's relative and what's fixed, which makes for some tremendous
> > differences of
> > course.
> >
> > Johnny: The tuning is fixed, with A=440.
>
> So you mean octaves of harmonics of A-440, for surely 440Hz isn't the
> lowest
> pitch you're playing on the bassoon.
>
> -Cuthbert Lobawad, Lieutenant Janitor of the Mord-Sith
>

On Fri, Jul 1, 2011 at 9:29 PM, lobawad <lobawad@...> wrote:
>
> You've got it backwards- it's not the moderate assumption that in any art form, an organizational and meaningful structure which appears in some cultures but not in others is a cultural rather than "natural" phenomenon that requires elaboration, it's the claim that an organizational and meaningful structure which appears in the art of some cultures but not in others is a "natural" phenomenon that requires a explanation.

By natural do you mean psychoacoustic?

It is clearly "natural" in some sense in that this behavior, given the
proper repeated application of a "western"-sounding musical stimulus
(whatever that means), spontaneously emerges in human beings all by
itself - which is magical enough to warrant study. It would be nice to
learn how to create other, alternate organizational and meaningful
structures for which analogous percepts to majorness and minorness can
spontaneously arise.

> The burden of proof lies on the extraordinary claim that the major/minor dichotomy of Western music is "natural". Of course there's a school that makes this claim, going back to Hauptmann in the 19th Century (if I recall correctly, it was Hauptmann who was responsible for such gems as correcting Bach's "mistakes" of lapsing into church modes).

All I want is for us to admit what we know and what we don't. It well
may be that your position is correct, I just wanted to open a dialogue
about what, specifically, that entails about musical cognition. It's
not a good idea for someone to play the psychoacoustics card and
handwave away, but one also has to make sure one isn't doing the same
thing with the culture card.

It could very well be that majorness and minorness are culturally
determined, but let's be clear on the precise nature of the claim
being made when we say that something is "cultural." Cultural means
learned, cognitive, etc - it means that a huge bulk of musical
sensation is produced by information fluctuating within a learned
structure. Which is fine, and it may be true. So it should be explored
further.

HOW does culture determine things? What is the mechanism? It's
certainly not from nobles threatening to shoot peasants unless they
smile at major chords and frown at minor chords. There must be some
way that this behavior "naturally" emerges from the meantone cognitive
structure all by itself, for a listener that understands meantone
logic.

1) How do cultures transmit this perspective from person to person?
2) What makes for a coherent and self-consistent perspective?
3) Once we figure out #2, how do we write music that firmly
establishes that perspective for a naive listener?

etc. Perhaps you know - I have no idea. If you have any insights I'm
all ears. I would just like it if we all delved into culture a bit
more.

> First of all, back to the point I was making, which was harmonic/subharmonic or over/undertone is really a false dichotomy, once we get out of the classroom and onto the streets. Would you maintain that there is a clear dichotomy between the two, and if so, how would you move from 3/2 to 2/1 without playing a 4/3?

I don't think I understand the question... I don't think that
undertones and overtones immediately produce different feelings, no. I
think what's important is finding the "root," which is apparently a
learned process and not a psychoacoustically primitive one. I'm trying
to get back to basics these days.

> Second, let's not conflate a "hard" position position like Hauptmann's (in short, V-I as divine truth) with any and all psychoacoustic explanations of major/minor duality. Unless that's already your position, in which case we might as well end this now, by the authority of the Godwin Act. :-)

I just want to figure out how music works.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jul 1, 2011 at 9:29 PM, lobawad <lobawad@...> wrote:
> >
> > You've got it backwards- it's not the moderate assumption that in any art form, an organizational and meaningful structure which appears in some cultures but not in others is a cultural rather than "natural" phenomenon that requires elaboration, it's the claim that an organizational and meaningful structure which appears in the art of some cultures but not in others is a "natural" phenomenon that requires a explanation.
>
> By natural do you mean psychoacoustic?

Mike, remember that I was not talking about my, or your, conceptions of major/minor, "natural" and so on. There's nothing bold or controversial about calling major/minor dichotomies as envisioned by Hauptmann/Riemann, (related Helmholtz etc.) in the 19th Century "cultural phenomena". For example, we need look no further than African-American music to find that the idea of cognizable intervals end at the fifth partial belongs to the realm of things that simply ain't so.

In fact, at the very same time Hauptmann was putting forward his ideas, another theorist, French, whose name I don't remember but can find when I get a chance to go to the library, pointed at that their- and his own- concepts of major/minor and tonality in general were specific to culture, and that other cultures had different concepts. Funny that I don't know offhand the name of this fine, fair thinker.

Speaking of fair, let's be fair to Riemann and Partch- their motivations were idealistic, and ideas more open to broad interpretations than the stances of those upon whose work they built.

> It is clearly "natural" in some sense in that this behavior, given >the
> proper repeated application of a "western"-sounding musical stimulus
> (whatever that means), spontaneously emerges in human beings all by
> itself - which is magical enough to warrant study. It would be nice to
> learn how to create other, alternate organizational and meaningful
> structures for which analogous percepts to majorness and minorness can
> spontaneously arise.

Alternate structures abound, and have for thousands of years.
>
> > The burden of proof lies on the extraordinary claim that the major/minor dichotomy of Western music is "natural". Of course there's a school that makes this claim, going back to Hauptmann in the 19th Century (if I recall correctly, it was Hauptmann who was responsible for such gems as correcting Bach's "mistakes" of lapsing into church modes).
>
> All I want is for us to admit what we know and what we don't.

I don't know about "we", but my experience is that "western" listeners glean "emotional" information from music distinctly removed from major/minor dichotomy, and do so with ease and pleasure.

>It well
> may be that your position is correct, I just wanted to open a >dialogue
> about what, specifically, that entails about musical cognition.

My original point, an absolutely mainstream one, was that we need to take the dichotomy of harmonic/subharmonic, over/undertone, and musical claims based upon it, with a great honkin' chunk of salt.

>It's
> not a good idea for someone to play the psychoacoustics card and
> handwave away, but one also has to make sure one isn't doing the >same
> thing with the culture card.

Absolutely. I don't buy a strong cultural/relativist position at all, and I find contemptible those who do such things as ignore the 2:1 ratio of the octave in their attempts to paint the whole thing as learned and not connected to the harmonic series. If you think I'm making that up, read some recent Parncutt.

>There must be some
> way that this behavior "naturally" emerges from the meantone >cognitive
> structure all by itself, for a listener that understands meantone
> logic.

Now you're off on a tangent. Meantone?

>
> 1) How do cultures transmit this perspective from person to person?
> 2) What makes for a coherent and self-consistent perspective?
> 3) Once we figure out #2, how do we write music that firmly
> establishes that perspective for a naive listener?
>
> etc. Perhaps you know - I have no idea. If you have any insights I'm
> all ears. I would just like it if we all delved into culture a bit
> more.

At this point I'm still concentrating on damage control, first trying to clear some obvious turds from the runway, whether it's the divinity of V-I (Hauptmann) or trying to make like scales are not related to the harmonic series at all (Parncutt).

>
> > First of all, back to the point I was making, which was >harmonic/subharmonic or over/undertone is really a false dichotomy, >once we get out of the classroom and onto the streets. Would you >maintain that there is a clear dichotomy between the two, and if so, >how would you move from 3/2 to 2/1 without playing a 4/3?
>
> I don't think I understand the question... I don't think that
> undertones and overtones immediately produce different feelings, >no.

Even if this were the case (I agree it's not), my point was that in real life we can't separate "overtones" and "undertones" anyway. As I keep saying, the move from one most obvious "o" to another is a "u".

>I
> think what's important is finding the "root," which is apparently a
> learned process and not a psychoacoustically primitive one. I'm trying
> to get back to basics these days.

I would guess that there's some more or less innate perception, or strong tendencies in perception at least. I don't think a 3:2 is likely to be percieved at rooted on 16:13, to use an extreme example.
In studying rootedness, appeals to the harmonic series are clearly fraught with problems, yet I wouldn't go to the extreme of ultimately dismissing them altogether, either.

-Cuthy

"lobawad" <lobawad@...> wrote:

> First of all, back to the point I was making, which was
> harmonic/subharmonic or over/undertone is really a false
> dichotomy, once we get out of the classroom and onto the
> streets. Would you maintain that there is a clear
> dichotomy between the two, and if so, how would you move
> from 3/2 to 2/1 without playing a 4/3?

A single dyad is neither otonal nor utonal. Most chords
will be simpler one way or the other. Most saturated
chords within a given odd limit will be either otonalities
or utonalities. It was reasonable to assume this was a
true dichotomy, but there are exceptions:

http://x31eq.com/ass.htm

Graham

Have you been following this thread? We're not talking specifically about Partchian "o- and utonalities" but about harmonic/subharmonic over/undertone in general (and as the idea has been discussed for going on two hundred years now). We certainly can and do call a 3/2 harmonic and a 4/3 subharmonic (over or under tonal).

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "lobawad" <lobawad@...> wrote:
>
> > First of all, back to the point I was making, which was
> > harmonic/subharmonic or over/undertone is really a false
> > dichotomy, once we get out of the classroom and onto the
> > streets. Would you maintain that there is a clear
> > dichotomy between the two, and if so, how would you move
> > from 3/2 to 2/1 without playing a 4/3?
>
> A single dyad is neither otonal nor utonal. Most chords
> will be simpler one way or the other. Most saturated
> chords within a given odd limit will be either otonalities
> or utonalities. It was reasonable to assume this was a
> true dichotomy, but there are exceptions:
>
> http://x31eq.com/ass.htm
>
>
> Graham
>

"lobawad" <lobawad@...> wrote:
> Have you been following this thread? We're not talking
> specifically about Partchian "o- and utonalities" but
> about harmonic/subharmonic over/undertone in general (and
> as the idea has been discussed for going on two hundred
> years now). We certainly can and do call a 3/2 harmonic
> and a 4/3 subharmonic (over or under tonal).

You can do that, and it's meaningless. The thread seems to
be that you propose something meaningless, and say it's
meaningless. Then you say that the harmonic/subharmonic
distinction is meaningless. That's wrong.

Graham

Dear Lobawad,

We are each talking about what we know. And we each know different
things. Let us share with some flexibility (listening to Mahler in the
background).

Schoenberg says minor is not natural due to its prehistory:

"The minor mode is thus purely synthetic, a product of art, and attempts
to represent it as something given in nature are pointless; its naturalness
is not direct, but, like that of the church modes, indirect. Now it is
true that major and minor have evolved historically, that they represent an
essential simplification over what came before (for they are a sum,
containing everything that appeared in the seven old modes); and it is gtrue that
the dualism presented by major and minor has the power of a symbol suggesting
high forms of order: it reminds us of male and female and delimits the
spheres of expression according to attraction and repulsion."

Schoenberg, Theory of Harmony (1911), p. 95-96.

It is time to reconsider the value of the undertone series. If just
intonation requires its participation, then pure overtone tuning is not just
intonation, by many standards (e.g., vocabulary, resonance, vibrato,
extra-acoustic phenomena such as difference tones and summation tones).

Now who is bifurcating? ;)

Johnny

Have you been following this thread? We're not talking specifically about
Partchian "o- and utonalities" but about harmonic/subharmonic
over/undertone in
general (and as the idea has been discussed for going on two hundred years
now).
We certainly can and do call a 3/2 harmonic and a 4/3 subharmonic (over or
under
tonal).

On Sat, Jul 2, 2011 at 5:31 AM, lobawad <lobawad@...> wrote:
> >
> > By natural do you mean psychoacoustic?
>
> Mike, remember that I was not talking about my, or your, conceptions of major/minor, "natural" and so on. There's nothing bold or controversial about calling major/minor dichotomies as envisioned by Hauptmann/Riemann, (related Helmholtz etc.) in the 19th Century "cultural phenomena". For example, we need look no further than African-American music to find that the idea of cognizable intervals end at the fifth partial belongs to the realm of things that simply ain't so.

I don't know anything about Hauptmann or Riemann's ideas. If they're a
part of the school of thought that says that German common practice
music is superior to all else, then yes, go ahead and Godwin away. I'm
just trying to figure out how music works and thought your statement
was a good chance to open a greater dialogue on specifically how
cultural influences might work, just like Igs' claim about harmonics
32-64 was a good chance for me to open up a greater dialogue on the
role of learning in musical perception.

To me major chords sound "happy" and minor chords sound "sad." There
are examples in which major chords can sound "sad," and minor chords
can sound "happier," but all of the ones I know of can be explained
via modal harmony and by looking at what modes you're borrowing these
defector chords from. The feelings that major and minor chords produce
are responsible for almost the entire gestalt of my musical
experience. Are you saying that you think that these feelings are
culturally determined, then? If so, how do you think it works? Keep in
mind I don't have an opinion either way and I'm currently at the "I
don't know anything about how music works" stage of development with
my ideas.

> In fact, at the very same time Hauptmann was putting forward his ideas, another theorist, French, whose name I don't remember but can find when I get a chance to go to the library, pointed at that their- and his own- concepts of major/minor and tonality in general were specific to culture, and that other cultures had different concepts. Funny that I don't know offhand the name of this fine, fair thinker.

Are you saying that the cliche stereotype of major and minor as being
"happy" and "sad" is a cultural stereotype, or are you saying that
there are cultures for which a major chord might sound darker and
sadder or whatever you want to call it than a minor chord, and that
the feelings themselves are produced by cognition and not
psychoacoustics? If you do think they're produced by cognition, then
you've got Paul Erlich on your side, but I'd like to hear more about
how you think it all works.

> Alternate structures abound, and have for thousands of years.

Major and minor can be said to be "primary colors" of the western
musical system. Can you give an example of an alternate structure that
has different musical primary colors?

> > All I want is for us to admit what we know and what we don't.
>
> I don't know about "we", but my experience is that "western" listeners glean "emotional" information from music distinctly removed from major/minor dichotomy, and do so with ease and pleasure.

I had an interesting experience yesterday where I played a Schumann
composition in 26-equal, then widened it to 19-equal, then 12, then
17, then 22, then 27, then 32, then 37, and then 42 - and then finally
5-equal. I was shocked to find that I could still hear most of the
piece in 5-equal, as though the 5 equal diatonic scale were literally
1 1 0 1 1 1 0. It was quite an interesting experience, and says a lot
about categorical perception. The 5-equal version had a few
"distortions" of perception, but the fact that it was more or less
intelligible at all was beyond ridiculous to me. What do you make of
it?

My current modus operandi is that primary exposure to a psychoacoustic
stimulus (a 5/4, for example) can "burn" an imprint of the experience
into your mind for you to reify in later. So you quickly learn that
the diatonic major third has this ~5/4-ish property, and then all
diatonic major thirds remind you of that, and you fill in the gaps
later. The VF mechanism doesn't actually have to fire for 5-equal so
that you hear 480 cents as 5/4; it only has to be determined by a
different cognitive function that 480 cents is a type of "major third"
in context xyz, and your brain remembers that major thirds are
consonant and rooted and just fills that information in via
reification. What are your thoughts? There has to be some reason why
these intervals sound different from one another, and this is one
possibility.

> My original point, an absolutely mainstream one, was that we need to take the dichotomy of harmonic/subharmonic, over/undertone, and musical claims based upon it, with a great honkin' chunk of salt.

I've never said otherwise. I think I hijacked this thread.

Although I don't think I've ever hidden my disdain for the notion of
"utonality," as a side note I have noticed an interesting pattern
lately - if you're in C major, and you go Fmaj -> Cmaj, it's relaxing.
And if you go Abmaj -> Cmaj it's relaxing, and is kind of like a
5-limit plagal cadence. And if you do the 7-limit version, which is
like D7->C but with the D7 tuned 4:5:6:7 (keeping the C held constant,
so the D is 8/7), it's relaxing. And the 11-limit version is also
relaxing. And if you combine them you get things like Fm6 -> Cmaj,
which is also very relaxing and almost mystical. Try C-E-G-A# ->
E-G#-Cx-F#-A# -> A#-Cx-E#-A# in 19-equal, which should be something
like 4:5:6:7 -> 4:5:7:9:11 -> 4:5:6:8. It sounds like a higher-limit
version of a plagal cadence to me. So there's something to be said for
keeping the root constant and building nice harmonic chords underneath
it, and that's all I can say for now.

> Absolutely. I don't buy a strong cultural/relativist position at all, and I find contemptible those who do such things as ignore the 2:1 ratio of the octave in their attempts to paint the whole thing as learned and not connected to the harmonic series. If you think I'm making that up, read some recent Parncutt.

Parncutt thinks that 2/1 is learned? Can you point me to some recent Parncutt?

> >There must be some
> > way that this behavior "naturally" emerges from the meantone >cognitive
> > structure all by itself, for a listener that understands meantone
> > logic.
>
> Now you're off on a tangent. Meantone?

Meantone would have something to do with western cultural influences,
right? Perhaps I should have said "diatonic" instead, though.

> > I don't think I understand the question... I don't think that
> > undertones and overtones immediately produce different feelings, >no.
>
> Even if this were the case (I agree it's not), my point was that in real life we can't separate "overtones" and "undertones" anyway. As I keep saying, the move from one most obvious "o" to another is a "u".

Your point is that dyads are both utonal and otonal?

> >I think what's important is finding the "root," which is apparently a
> > learned process and not a psychoacoustically primitive one. I'm trying
> > to get back to basics these days.
>
> I would guess that there's some more or less innate perception, or strong tendencies in perception at least. I don't think a 3:2 is likely to be percieved at rooted on 16:13, to use an extreme example.

If you play a bunch of random intervals, people can't figure out what they are.

I came up with a listening test a little while ago - I played the
following dyads:

C-E -> B-D# -> D#-F# -> F#-A -> E-G

and then

C-E -> B-D -> D-F -> F-A -> E-G

I was trying to show that the first example would lead to the percept
that "E" is the root over the last dyad (e.g. that the E-G is part of
E minor) and that in the second example it would lead to the percept
that "C" is the root over the last dyad (e.g. that it's a part of C
major). I sent it to Graham and asked him if he could identify the
root over th elast dyad.

What ended up happening is that Graham heard the opposite results that
I did, which means I guess he heard the first example as being a part
of Clyd#2 and the second one as resolving to E phrygian. Then it
sounded like the opposite of whatever he was trying to get it to sound
like. Then, in an attempt to simplify, I just had it arpeggiate
different chords really fast - Ab-Db -> Db-F -> F-B -> B-E -> E-G, for
example, and had him guess the root. I heard it as Db7#9#11/Ab, and he
heard a bunch of fast mush that went too fast to guess the root, same
with all of my examples, which were made at a quite fast tempo. After
talking with him some time about it I eventually realized that the
problem was that my dyads were too disordered and chaotic for him to
identify by ear without the score, and apparently identifying dyads by
ear is important for imagining the end result chord to figure out what
the root is. Eureka!

To bring it to an even more absurd extreme, can you imagine if we took
a 5-year old with no musical training and played them a bunch of
random arpeggiated modal chords and asked that person to guess the
root? They'd be like uhhh, wtf? So I realized then that root finding
is basically a heuristic process that involves active guessing about
what's going on.

> In studying rootedness, appeals to the harmonic series are clearly fraught with problems, yet I wouldn't go to the extreme of ultimately dismissing them altogether, either.

VF's imply a virtual bass note; that's how they might, in some sense,
be said to "imply" a root. The root is more connected with the bass
note that you're used to people playing under arpeggiated structure
xyz than psychoacoustics. That's what I've come to believe.

-Mike

Mike, please read the this on Riemann to see that the dichotomy of major
and minor is a farce.

_http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf_
(http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf)

Schoenberg showed that minor came to us through church modes.

Dear Lobawad, the true minor third is in the overtone series. Claiming
the perfect fourth exist anyway between higher notes than the fundamental is
like saying a rainbow is part of the sky because it sometimes appears.
Rainbows are resultants, they are not primary. Difference tones exist but
they do not prove a series.

Perhaps utonality is essentially a Partch artifice which worked well for
his music. Perhaps now it is time to move forward, from the fundamental.

Johnny

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Dear Lobawad,
>
> We are each talking about what we know. And we each know different
> things. Let us share with some flexibility (listening to Mahler in the
> background).
>
> Schoenberg says minor is not natural due to its prehistory:
>
> "The minor mode is thus purely synthetic, a product of art, and attempts
> to represent it as something given in nature are pointless; its naturalness
> is not direct, but, like that of the church modes, indirect. Now it is
> true that major and minor have evolved historically, that they represent an
> essential simplification over what came before (for they are a sum,
> containing everything that appeared in the seven old modes); and it is gtrue that
> the dualism presented by major and minor has the power of a symbol suggesting
> high forms of order: it reminds us of male and female and delimits the
> spheres of expression according to attraction and repulsion."
>
> Schoenberg, Theory of Harmony (1911), p. 95-96.

Here you can see that Schoenberg either hadn't the foggiest about the church modes. The church modes were, until the beginning of the last century at least (I have a Roman Catholic instructional book for Gregorian Chant dated 1906), more essentially similar to what we'd call "maqam music" than to anything subsumable by major/minor. The 1948 recording I had of monks in some abbey bore this out. I have no idea what church modes are like nowadays.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Mike, please read the this on Riemann to see that the dichotomy of major
> and minor is a farce.
>
> _http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf_
> (http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf)
>
> Schoenberg showed that minor came to us through church modes.
>
> Dear Lobawad, the true minor third is in the overtone series.

The true minor third is the one that emodies the ineffable I wish to eff, in that time and place.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> Perhaps utonality is essentially a Partch artifice which worked well for
> his music. Perhaps now it is time to move forward, from the fundamental.

Partch pointed out that if you have otonal chords in a scale you will tend to have utonal ones also, whether you want them or not. He thought that since they were there, they might as well be put to use. Utonal chords are also of interest due to the fact that they share common dyads with otonal chords.

Mike, I wasn't thinking about happy/sad, but about a "binary" conceptions of music in general.

You know, I bet that if you determinedly went off major/minor and immersed yourself in "neutral" for, say, a couple of weeks, you'd seriously reevalute.

>
> > My original point, an absolutely mainstream one, was that we need to take the dichotomy of harmonic/subharmonic, over/undertone, and musical claims based upon it, with a great honkin' chunk of salt.
>
> I've never said otherwise. I think I hijacked this thread.

Yeah but that's okay. I wish I had time to respond more. I think you'd have to do the "neutral" immersion first, we'd save a lot of time.

>
> Although I don't think I've ever hidden my disdain for the notion of
> "utonality," as a side note I have noticed an interesting pattern
> lately - if you're in C major, and you go Fmaj -> Cmaj, it's relaxing.
> And if you go Abmaj -> Cmaj it's relaxing, and is kind of like a
> 5-limit plagal cadence. And if you do the 7-limit version, which is
> like D7->C but with the D7 tuned 4:5:6:7 (keeping the C held constant,
> so the D is 8/7), it's relaxing. And the 11-limit version is also
> relaxing. And if you combine them you get things like Fm6 -> Cmaj,
> which is also very relaxing and almost mystical. Try C-E-G-A# ->
> E-G#-Cx-F#-A# -> A#-Cx-E#-A# in 19-equal, which should be something
> like 4:5:6:7 -> 4:5:7:9:11 -> 4:5:6:8. It sounds like a higher-limit
> version of a plagal cadence to me. So there's something to be said for
> keeping the root constant and building nice harmonic chords underneath
> it, and that's all I can say for now.
>
> > Absolutely. I don't buy a strong cultural/relativist position at all, and I find contemptible those who do such things as ignore the 2:1 ratio of the octave in their attempts to paint the whole thing as learned and not connected to the harmonic series. If you think I'm making that up, read some recent Parncutt.
>
> Parncutt thinks that 2/1 is learned? Can you point me to some recent Parncutt?
>
> > >There must be some
> > > way that this behavior "naturally" emerges from the meantone >cognitive
> > > structure all by itself, for a listener that understands meantone
> > > logic.
> >
> > Now you're off on a tangent. Meantone?
>
> Meantone would have something to do with western cultural influences,
> right? Perhaps I should have said "diatonic" instead, though.
>
>
> > > I don't think I understand the question... I don't think that
> > > undertones and overtones immediately produce different feelings, >no.
> >
> > Even if this were the case (I agree it's not), my point was that in real life we can't separate "overtones" and "undertones" anyway. As I keep saying, the move from one most obvious "o" to another is a "u".
>
> Your point is that dyads are both utonal and otonal?
>
> > >I think what's important is finding the "root," which is apparently a
> > > learned process and not a psychoacoustically primitive one. I'm trying
> > > to get back to basics these days.
> >
> > I would guess that there's some more or less innate perception, or strong tendencies in perception at least. I don't think a 3:2 is likely to be percieved at rooted on 16:13, to use an extreme example.
>
> If you play a bunch of random intervals, people can't figure out what they are.
>
> I came up with a listening test a little while ago - I played the
> following dyads:
>
> C-E -> B-D# -> D#-F# -> F#-A -> E-G
>
> and then
>
> C-E -> B-D -> D-F -> F-A -> E-G
>
> I was trying to show that the first example would lead to the percept
> that "E" is the root over the last dyad (e.g. that the E-G is part of
> E minor) and that in the second example it would lead to the percept
> that "C" is the root over the last dyad (e.g. that it's a part of C
> major). I sent it to Graham and asked him if he could identify the
> root over th elast dyad.
>
> What ended up happening is that Graham heard the opposite results that
> I did, which means I guess he heard the first example as being a part
> of Clyd#2 and the second one as resolving to E phrygian. Then it
> sounded like the opposite of whatever he was trying to get it to sound
> like. Then, in an attempt to simplify, I just had it arpeggiate
> different chords really fast - Ab-Db -> Db-F -> F-B -> B-E -> E-G, for
> example, and had him guess the root. I heard it as Db7#9#11/Ab, and he
> heard a bunch of fast mush that went too fast to guess the root, same
> with all of my examples, which were made at a quite fast tempo. After
> talking with him some time about it I eventually realized that the
> problem was that my dyads were too disordered and chaotic for him to
> identify by ear without the score, and apparently identifying dyads by
> ear is important for imagining the end result chord to figure out what
> the root is. Eureka!
>
> To bring it to an even more absurd extreme, can you imagine if we took
> a 5-year old with no musical training and played them a bunch of
> random arpeggiated modal chords and asked that person to guess the
> root? They'd be like uhhh, wtf? So I realized then that root finding
> is basically a heuristic process that involves active guessing about
> what's going on.
>
> > In studying rootedness, appeals to the harmonic series are clearly fraught with problems, yet I wouldn't go to the extreme of ultimately dismissing them altogether, either.
>
> VF's imply a virtual bass note; that's how they might, in some sense,
> be said to "imply" a root. The root is more connected with the bass
> note that you're used to people playing under arpeggiated structure
> xyz than psychoacoustics. That's what I've come to believe.
>
> -Mike
>

On Sun, Jul 3, 2011 at 2:01 PM, lobawad <lobawad@...> wrote:
>
> Mike, I wasn't thinking about happy/sad, but about a "binary" conceptions of music in general.

I've never been one to think about major and minor as being some kind
of yin/yang taoist tradition in the foundations of music. If people
prefer to think in astrological terms like that about music, they can
do whatever they want. There are obviously plenty of colors out there
than those two. But I'm asking if you think that the sounds of those
two chords are culturally determined.

> You know, I bet that if you determinedly went off major/minor and immersed yourself in "neutral" for, say, a couple of weeks, you'd seriously reevalute.

I've been immersed in neutral many times over at this point, but there
are sounds beyond major and minor even in 12-equal.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
>
> > Perhaps utonality is essentially a Partch artifice which worked well for
> > his music. Perhaps now it is time to move forward, from the fundamental.
>
> Partch pointed out that if you have otonal chords in a scale you will tend to have utonal ones also, whether you want them or not. He thought that since they were there, they might as well be put to use. Utonal chords are also of interest due to the fact that they share common dyads with otonal chords.
>

Yes, Partch was refreshingly not allergic to plain old common-sense observations. Although Graham considers it meaningless, it's a simple fact of life that when you've got a system of overtones, you're going to get "undertone" proportions amongst them. Reinhard says it's the overtone relationship to a fundamental that's important. Over a pedal, drone, or resonant frequency of an instrument (which would function something like a pedal), it's not a crazy idea at all, but when octaves of the 43rd and 57th partial are brought into the equation, how can there be any question that we're well into the range of the subjective and probably unfalsifiable?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jul 3, 2011 at 2:01 PM, lobawad <lobawad@...> wrote:
> >
> > Mike, I wasn't thinking about happy/sad, but about a "binary" conceptions of music in general.
>
> I've never been one to think about major and minor as being some kind
> of yin/yang taoist tradition in the foundations of music. If people
> prefer to think in astrological terms like that about music, they can
> do whatever they want. There are obviously plenty of colors out there
> than those two. But I'm asking if you think that the sounds of those
> two chords are culturally determined.

I don't know, and I doubt such things can really be determined at this point. "Nature VS Nurture", which Johnny brought up, wildly missing the point of what I was saying, is patently bogus. Ever seen a human-raised cat try to kill a mouse or lizard? It's a sad and torturous sight, for it's the mommy cat that teaches the baby the proper killing techniques. There's no "versus", the two are intertwined, or part of continuum or something.

>
> > You know, I bet that if you determinedly went off major/minor and immersed yourself in "neutral" for, say, a couple of weeks, you'd seriously reevalute.
>
> I've been immersed in neutral many times over at this point, but there
> are sounds beyond major and minor even in 12-equal.
>
> -Mike
>

Do you find specific "meaning", emotional reactions, etc. in for example "neutral" triads?

On Sun, Jul 3, 2011 at 3:18 PM, lobawad <lobawad@...> wrote:
>
> Yes, Partch was refreshingly not allergic to plain old common-sense observations. Although Graham considers it meaningless, it's a simple fact of life that when you've got a system of overtones, you're going to get "undertone" proportions amongst them.

I think that you and Graham are saying the same thing, which is that
dyads are both utonal and otonal, by virtue of the fact that they can
fit the same way into either a normal otonal harmonic series and an
inverted utonal series, so you can't say that 4/3 is "utonal" any more
than you can say it's "otonal." I'm not sure why you guys seem to
think you're arguing when you appear to be in perfect agreement from
way over here.

-Mike

>"Mike, I wasn't thinking about happy/sad, but about a "binary" conceptions of music in general.

You know, I bet that if you determinedly went off major/minor and
immersed yourself in "neutral" for, say, a couple of weeks, you'd
seriously reevalute. "

   On that note (Mike in particular), try a neutral 1/1 11/9 22/15 as compared to 4:5:6  and 10:12:15.  To me that neutral chord, rather than 1/1 11/9 3/2...is a "true" neutral triad.  And it seems to sound neither happy or sad, nor confused, but instead "confidently melancholy". :-D   Another general comment: even "sad" can actually be more confident than "happy"...try putting overly happy chords in a drum and bass song and they'll sound almost silly...and not confident and steady at all.

>"I've been immersed in neutral many times over at this point, but there

are sounds beyond major and minor even in 12-equal."

   This begs the question of where do you consider suspended, diminished, add2, dominant...chords on this whole happy/sad spectrum...along with neutral?  And, what do you consider neutral?  Again, my guess is most people would say chords like 1/1 11/9 3/2, but I'd say 1 11/9 22/15.

On Sun, Jul 3, 2011 at 3:27 PM, lobawad <lobawad@...> wrote:
>
> > I've never been one to think about major and minor as being some kind
> > of yin/yang taoist tradition in the foundations of music. If people
> > prefer to think in astrological terms like that about music, they can
> > do whatever they want. There are obviously plenty of colors out there
> > than those two. But I'm asking if you think that the sounds of those
> > two chords are culturally determined.
>
> I don't know, and I doubt such things can really be determined at this point. "Nature VS Nurture", which Johnny brought up, wildly missing the point of what I was saying, is patently bogus. Ever seen a human-raised cat try to kill a mouse or lizard? It's a sad and torturous sight, for it's the mommy cat that teaches the baby the proper killing techniques. There's no "versus", the two are intertwined, or part of continuum or something.

I think the continuum is that initial exposure to a psychoacoustic
stimulus burns itself into your brain for categorical perception to
work on later on, and I have some listening tests that I think will
prove it. But we'll wait until later for that, because moving to a new
city is Hard.

> > I've been immersed in neutral many times over at this point, but there
> > are sounds beyond major and minor even in 12-equal.
>
> Do you find specific "meaning", emotional reactions, etc. in for example "neutral" triads?

I find that neutral triads can sound "cloudy" at times and "ambiguous"
at other times. They sometimes sound like flat versions of major or
sharp versions of minor chords. But, I also find that the ideal by
which you're supposed to learn to recognize neutral chords as being
their own gestalt - and have them never sound like sharp minor chords
or flat major chords - is also arbitrary. In fact, the fact that I can
hear shades of major and minor in 7-et is one of my prime reasons for
becoming obsessed with this album:

http://soundcloud.com/knowsur/haneru

-Mike

Dear Lobawad,

L: Yes, Partch was refreshingly not allergic to plain old common-sense
observations.

J: Common sense is not always keen enough. Partch was wrong about JS Bach
being in equal temperament. And he bought into the Riemann idea of the
undertone series. What I am saying is that Partch fully outfits the
undertone series, while I am encouraging the removal of the undertone series notes
in order to let the overtone notes fully resonate. I think there is a big
difference to be gained, akin to La Monte Young's harmonic clouds (caused
by a piano with ONLY overtones). Even La Monte Young and Kyle Gann
believe(d) that The Well-Tuned Piano was in just intonation. If just
intonation requires the undertone series, then TWTP is not just intonation.

L: Although Graham considers it meaningless, it's a simple fact of
life that when you've got a system of overtones, you're going to get
"undertone"
proportions amongst them.

J: Unless I am being dense, you are confusing 2 different things, a
cognitive dissonance. While one can derive undertones and 4/3 relationships
between different tones, they are the results of something else, just like a
rainbow in the sky. IMO, using a 4/3 in the context of overtone tuning is
like sanding a reed against the grain...it cuts down the vibrations.

L: Reinhard says it's the overtone relationship to a fundamental that's
important.

J: True.

L: Over a pedal, drone, or resonant frequency of an instrument (which would
function something like a pedal), it's not a crazy idea at all, but when
octaves of the 43rd and 57th partial are brought into the
equation, how can there be any question that we're well into the range of
the
subjective and probably unfalsifiable? [didn't you mean 'falsifiable'? -
jr]

J: 57th partial is subjective? It's played in almost every musical
situation; it's the minor seventh of the old Star Trek theme -- it's a done deal
already. Come on, it's 999 cents! What conceivable issue could you have
with it? Besides, even self-described just intonation composers have
multiplied ratios to get higher interval functions (Young, Johnston, Catler).

And 43? Dang, we just did 2 concerts devoted to 43. Jon Catler told me a
very interesting opinion. He said he did a 180 because he expected a
dissonance and it was so consonant. My piece started with open strings on the
double bass, each string tuned 512 cents (a 43/32 ratio) apart. Time to
try something new and work with this new interval.

All I am saying is that by using overtone only relationships music is
enriched in a powerful way, based on sound results (pun intended). If you want
to keep sticking to historical ways, as a cultural inheritance, for
example, you are entitled. Just reporting on some new findings.

Johnny

MikeB>"In fact, the fact that I can hear shades of major and minor in 7-et is one of my prime reasons for becoming obsessed with this album:
http://soundcloud.com/knowsur/haneru"

   I'll definitely second that, and especially that song (titled "Haneru") off the album, which sounds especially stunning.  Personally I'm more into the use (scale-wise) of Mohajira's use of neutrals...but Knowsur shows it can still be done very well with 7TET...even when 7TET is generally considered very tricky to compose with.

--- On Sun, 7/3/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Sunday, July 3, 2011, 12:56 PM

On Sun, Jul 3, 2011 at 3:27 PM, lobawad <lobawad@...> wrote:

>

> > I've never been one to think about major and minor as being some kind

> > of yin/yang taoist tradition in the foundations of music. If people

> > prefer to think in astrological terms like that about music, they can

> > do whatever they want. There are obviously plenty of colors out there

> > than those two. But I'm asking if you think that the sounds of those

> > two chords are culturally determined.

>

> I don't know, and I doubt such things can really be determined at this point. "Nature VS Nurture", which Johnny brought up, wildly missing the point of what I was saying, is patently bogus. Ever seen a human-raised cat try to kill a mouse or lizard? It's a sad and torturous sight, for it's the mommy cat that teaches the baby the proper killing techniques. There's no "versus", the two are intertwined, or part of continuum or something.

I think the continuum is that initial exposure to a psychoacoustic

stimulus burns itself into your brain for categorical perception to

work on later on, and I have some listening tests that I think will

prove it. But we'll wait until later for that, because moving to a new

city is Hard.

> > I've been immersed in neutral many times over at this point, but there

> > are sounds beyond major and minor even in 12-equal.

>

> Do you find specific "meaning", emotional reactions, etc. in for example "neutral" triads?

I find that neutral triads can sound "cloudy" at times and "ambiguous"

at other times. They sometimes sound like flat versions of major or

sharp versions of minor chords. But, I also find that the ideal by

which you're supposed to learn to recognize neutral chords as being

their own gestalt - and have them never sound like sharp minor chords

or flat major chords - is also arbitrary. In fact, the fact that I can

hear shades of major and minor in 7-et is one of my prime reasons for

becoming obsessed with this album:

http://soundcloud.com/knowsur/haneru

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>    On that note (Mike in particular), try a neutral 1/1 11/9 22/15 as compared to 4:5:6  and 10:12:15. 

45:55:65. The magic of triangular numbers strikes again!

On Sun, Jul 3, 2011 at 4:06 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >    On that note (Mike in particular), try a neutral 1/1 11/9 22/15 as compared to 4:5:6  and 10:12:15.
>
> 45:55:65. The magic of triangular numbers strikes again!

I think you meant 45:55:66, but hey, I'll take it anyway. 45:55:65 is
actually 9:11:13, which has a different kind of magic, and that magic
is the eternal power of isoharmonic, sync beating chords.

-Mike

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

> I find that neutral triads can sound "cloudy" at times and "ambiguous"
> at other times. They sometimes sound like flat versions of major or
> sharp versions of minor chords. But, I also find that the ideal by
> which you're supposed to learn to recognize neutral chords as being
> their own gestalt - and have them never sound like sharp minor chords
> or flat major chords - is also arbitrary. In fact, the fact that I can
> hear shades of major and minor in 7-et is one of my prime reasons for
> becoming obsessed with this album:
>
> http://soundcloud.com/knowsur/haneru
>
> -Mike
>

I don't know if heard this bit of "hardcore" neutral:

http://soundcloud.com/cameron-bobro/adreamisawound-cbobro

BTW the other day when I was writing out a clean version of the score I remembered that the peice contains something you recently mentioned when you were talking about recognizing 11/9 as 11/9, with an implied root a 9/8 below, and that's the kind of thing that keeps me away from thinking it's all cultural, or not connected to the harmonic series.

Oh, that reminds me- I'll try to find that Parncutt thing for you. No he doesn't say that the octave is completely learned, what he does in a disingenous thing where he simply fails to mention the octave at all
as he brushes off ideas of tuning originating in the harmonic series.

>What I am saying is that Partch fully outfits the
undertone series, while I am encouraging the removal of the undertone series
notes in order to let the overtone notes fully resonate. "

  I don't know exactly how closely related this is...but I've notice even undertone-series-based chords sound strong when at least some dyads in them are low enough in the harmonic series (say, 9-odd-limit or under) to approach overtone series-style ratios.  Some examples include 1 11/9 22/15 with its 6/5 between 22/15 and 11/9 and 1/1 7/6 7/4 with a 3/2 between 7/6 and 7/4.

--- On Sun, 7/3/11, Afmmjr@... <Afmmjr@...> wrote:

From: Afmmjr@... <Afmmjr@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Sunday, July 3, 2011, 1:04 PM

Dear Lobawad,
 
L: Yes, Partch was refreshingly not allergic to plain old
common-sense
observations.
 
J: Common sense is not always keen enough.  Partch was wrong about JS
Bach being in equal temperament.  And he bought into the Riemann idea of
the undertone series.  What I am saying is that Partch fully outfits the
undertone series, while I am encouraging the removal of the undertone series
notes in order to let the overtone notes fully resonate.  I think there is
a big difference to be gained, akin to La Monte Young's harmonic clouds (caused
by a piano with ONLY overtones).  Even La Monte Young and Kyle Gann

believe(d)  that The Well-Tuned Piano was in just intonation.  If
just intonation requires the undertone series, then TWTP is not just
intonation.
 
L: Although Graham considers it meaningless, it's a simple fact of
life
that when you've got a system of overtones, you're going to get
"undertone"
proportions amongst them.
 
J: Unless I am being dense, you are confusing 2 different things, a
cognitive dissonance.  While one can derive undertones and 4/3
relationships between different tones, they are the results of something else,
just like a rainbow in the sky.  IMO, using a 4/3 in the context of
overtone tuning is like sanding a reed against the grain...it cuts down the
vibrations.
 
L: Reinhard says it's the overtone relationship to a fundamental that's
important.
 
J: True.
 
L: Over a pedal, drone, or resonant frequency of an instrument (which would
function something like a pedal), it's not a crazy idea at all, but when octaves
of the 43rd and 57th partial are brought into the
equation, how can there be
any question that we're well into the range of the
subjective and probably
unfalsifiable?   [didn't you mean 'falsifiable'? - jr]

J: 57th partial is subjective?  It's played in almost every musical
situation; it's the minor seventh of the old Star Trek theme -- it's a done deal
already.  Come on, it's 999 cents!  What conceivable issue could
you have with it?  Besides, even self-described just intonation composers
have multiplied ratios to get higher interval functions (Young, Johnston,
Catler).
 
And 43?  Dang, we just did 2 concerts devoted to 43.  Jon Catler
told me a very interesting opinion.  He said he did a 180 because he
expected a dissonance and it was so consonant.  My piece started with open
strings on the double bass, each string tuned 512 cents (a 43/32
ratio) apart.  Time to try something new and work with this new
interval.
 
All I am saying is that by using overtone only relationships music is
enriched in a powerful way, based on sound results (pun intended).  If you
want to keep sticking to historical ways, as a cultural inheritance, for
example, you are entitled.  Just reporting on some new findings.
 
Johnny

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> All I am saying is that by using overtone only relationships music is
> enriched in a powerful way, based on sound results (pun intended). If you want
> to keep sticking to historical ways, as a cultural inheritance, for
> example, you are entitled. Just reporting on some new findings.

If anyone wants to explore this brave new world, that has such scales in't, dwarf scales provide an easy entry route. Here by way of example is the 43-limit patent val dwarf for 19edo:

! over19.scl
Dwarf scale for 43-limit patent val of 19edo
19
!
33/32
17/16
9/8
37/32
19/16
5/4
21/16
43/32
11/8
23/16
3/2
25/16
13/8
27/16
7/4
29/16
15/8
31/16
2/1

On Sun, Jul 3, 2011 at 4:13 PM, lobawad <lobawad@...> wrote:
>
> I don't know if heard this bit of "hardcore" neutral:
>
> http://soundcloud.com/cameron-bobro/adreamisawound-cbobro

I'm hearing more majorness and minorness in all of this, personally.

> BTW the other day when I was writing out a clean version of the score I remembered that the peice contains something you recently mentioned when you were talking about recognizing 11/9 as 11/9, with an implied root a 9/8 below, and that's the kind of thing that keeps me away from thinking it's all cultural, or not connected to the harmonic series.

Yeah, it's really simple. Play an 11/9 with a 9/4 below, and then take
it away, and remember the original sound without the bass note there.
It's not rocket science. These are the things you quickly learn once
you buy an AXiS.

> Oh, that reminds me- I'll try to find that Parncutt thing for you. No he doesn't say that the octave is completely learned, what he does in a disingenous thing where he simply fails to mention the octave at all
> as he brushes off ideas of tuning originating in the harmonic series.

I really do need to get this listening test put out there. I'll try to
focus on it in the next few weeks.

-Mike

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Dear Lobawad,
>
> L: Yes, Partch was refreshingly not allergic to plain old common-sense
> observations.
>
> J: Common sense is not always keen enough. Partch was wrong about JS Bach
> being in equal temperament. And he bought into the Riemann idea of the
> undertone series.

And sometimes common sense is just what's needed. The whole of Genesis, which I consider to be loaded with boloney, is worth it for his cutting of the Gordian knot tied about the theoretical root of the minor triad: pick the one you like.

> What I am saying is that Partch fully outfits the
> undertone series, while I am encouraging the removal of the undertone series notes
> in order to let the overtone notes fully resonate.

But don't you realize that they don't disappear just because you want them to? Or do you realize this and feel that it's the overtone relationship to a particular fundamental that is the main thing? If so, don't you realize that there are countless rational tunings which can be expressed in terms of overtones of a single fundamental?

I >think there is a big
> difference to be gained, akin to La Monte Young's harmonic clouds (caused
> by a piano with ONLY overtones). Even La Monte Young and Kyle Gann
> believe(d) that The Well-Tuned Piano was in just intonation. If >just
> intonation requires the undertone series, then TWTP is not just >intonation.

"Just Intonation" has long been a synonym for "rational tuning".

>
> L: Although Graham considers it meaningless, it's a simple fact of
> life that when you've got a system of overtones, you're going to get
> "undertone"
> proportions amongst them.
>
> J: Unless I am being dense, you are confusing 2 different things, a
> cognitive dissonance. While one can derive undertones and 4/3 relationships
> between different tones, they are the results of something else, just like a
> rainbow in the sky.

Cognitive dissonance isn't the confusing of two different things, and I'm not confusing anything. I'm saying that when you play E-a in your tuning, you're not playing your 43/32 fourth. This means that whatever overtone-derived quality of this 43/32 fourth may be, it's happening in relation to your fundamental, but the fourth from E-a does NOT have this same quality.

>
> L: Reinhard says it's the overtone relationship to a fundamental that's
> important.
>
> J: True.

I understand what you're saying. I don't think you've thought out all the implications. By the way, most of my tuning is based on a phantom fundamental of 13 Hz, has been for years. I've thought about the implications a lot.

>
> L: Over a pedal, drone, or resonant frequency of an instrument (which would
> function something like a pedal), it's not a crazy idea at all, but when
> octaves of the 43rd and 57th partial are brought into the
> equation, how can there be any question that we're well into the range of
> the
> subjective and probably unfalsifiable? [didn't you mean 'falsifiable'? -
> jr]

Unfalsifiable- means can't be scientifically tested. Not that should matter to you, unless you're trying to invoke the name of science.

>
>
> J: 57th partial is subjective? It's played in almost every musical
> situation; it's the minor seventh of the old Star Trek theme -- it's a done deal
> already. Come on, it's 999 cents! What conceivable issue could you have
> with it?

Maybe you should woodshed a bit- the Star Trek seventh is obviously one cent sharper. ;-) I know it's the 12-tET m7, that's why I used it as an example. I think you're confusing the familiarity of it with "sounding good", and as a hardcore microtonalist, bluntly spoken I think it's a joke.

>
> And 43? Dang, we just did 2 concerts devoted to 43. Jon Catler told me a
> very interesting opinion. He said he did a 180 because he expected a
> dissonance and it was so consonant. My piece started with open strings on the
> double bass, each string tuned 512 cents (a 43/32 ratio) apart. Time to
> try something new and work with this new interval.

This one actually interests me, and has for a good long time. Fourths a half-comma sharp happen to show up in my own tetrachordal tunings, so I'm familiar with them, and I really like them.

>
> All I am saying is that by using overtone only relationships music >is
> enriched in a powerful way, based on sound results (pun intended).

I don't doubt highly resonant music can be written this way. As a tuning for older music, honestly I think it's a way to basically play in 12-tET with some little deviations to taste, and pretend it's "microtonal".

>If you want
> to keep sticking to historical ways, as a cultural inheritance, for
> example, you are entitled.

I think that's actually what you're doing, whilst kidding yourself you're not, while I'm doing quite the opposite, which is not hiding that my tunings originate in ancient tetrachords, but using them in a way that is radically unstuck from their history.

>Just reporting on some new findings.

I'd like to hear more stuff like "Dune", whatever tuning scheme you're using.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jul 3, 2011 at 4:13 PM, lobawad <lobawad@...> wrote:
> >
> > I don't know if heard this bit of "hardcore" neutral:
> >
> > http://soundcloud.com/cameron-bobro/adreamisawound-cbobro
>
> I'm hearing more majorness and minorness in all of this, personally.

Interesting- but at any rate, there's a response to your earlier remarks about finding sort of parallels to major/minor. Major/minor is not what's making the "dichotomy" here,(I know that we're in agreement that music doesn't boil down to binaries, but you know what I mean) and in my experience "civilians" like the feeling of options other than major/minor very much.

>
> > BTW the other day when I was writing out a clean version of the score I remembered that the peice contains something you recently mentioned when you were talking about recognizing 11/9 as 11/9, with an implied root a 9/8 below, and that's the kind of thing that keeps me away from thinking it's all cultural, or not connected to the harmonic series.
>
> Yeah, it's really simple. Play an 11/9 with a 9/4 below, and then take
> it away, and remember the original sound without the bass note there.
> It's not rocket science. These are the things you quickly learn once
> you buy an AXiS.

I was referring to how sometimes roots, or things that are rootlike in character, seem to be, in an obvious way, right where they "should" be according to simplistic harmonic-series thinking. So, I assume that that's part of what goes on (but can't be all, as we can find ambiguous or puzzling things as well).

>

Oh, and I sincerely hope that you're not going to tell me that the "true minor third" is 19/16. oh please no....

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> >
> > Mike, please read the this on Riemann to see that the dichotomy of major
> > and minor is a farce.
> >
> > _http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf_
> > (http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf)
> >
> > Schoenberg showed that minor came to us through church modes.
> >
> > Dear Lobawad, the true minor third is in the overtone series.
>
> The true minor third is the one that emodies the ineffable I wish to eff, in that time and place.
>

On Sun, Jul 3, 2011 at 5:48 PM, lobawad <lobawad@...> wrote:
>
> Interesting- but at any rate, there's a response to your earlier remarks about finding sort of parallels to major/minor. Major/minor is not what's making the "dichotomy" here,(I know that we're in agreement that music doesn't boil down to binaries, but you know what I mean) and in my experience "civilians" like the feeling of options other than major/minor very much.

There are options other than major/minor pretty much as soon as you
get away from triads. You might say that modal harmony focuses on
heptadic harmony (although not often with all the notes in the mode
played simultaneously), and there's plenty of difference between
dorian and phrygian alone. sus2 chords could be said to be "either"
major or minor, or perhaps neutral or subminor or supermajor too,
which is something of a zen koan.

> > Yeah, it's really simple. Play an 11/9 with a 9/4 below, and then take
> > it away, and remember the original sound without the bass note there.
> > It's not rocket science. These are the things you quickly learn once
> > you buy an AXiS.
>
> I was referring to how sometimes roots, or things that are rootlike in character, seem to be, in an obvious way, right where they "should" be according to simplistic harmonic-series thinking. So, I assume that that's part of what goes on (but can't be all, as we can find ambiguous or puzzling things as well).

Sure, but if you play 11/9 and you double the bottom note down an
octave or two, and take that away, then the root will sound like it's
the bottom note of the 11/9 again. And if you play 6/5 and you play a
bass note a major third down from the bottom now, the 6/5 sounds like
it's part of a major chord, and if you double the bottom note instead,
it sounds like a minor chord.

I think that the brain simply integrates all of the pitches existing
at a certain point in time - including virtual ones, and including
ones you're imagining - when a pitch briefly flickers into existence
down in the bottom register, your brain just makes note of it as one
of the pitches in the chord and moves on.

I did yet another experiment a while ago that I'll have to post, which
is that I worked with a timbre that was maximally inharmonic - it was
basically 9:11:13:15:17:19:21:etc (not exactly, but that was the gist
of it). My brain heard it as flipping between having a VF that was
equal to the bottom note (meaning as though it were a flat
4:5:6:7:8:9:etc), and a VF a minor third below that, meaning as though
it were a sharp 5:6:7:8:9:10). So I kept hearing two VFs a minor third
apart flipping in and out of existence, and you can imagine what my
perception of the chord was - I heard the lowest two notes of an
arpeggiated "minor" chord flipping back and forth randomly.

There is an integrative mechanism that tracks what notes are played,
even if those notes are "virtual" notes, because psychoacoustically,
all notes are virtual. It takes place on a level after VF processing,
which even if you don't believe my self-reported N=1 sample size
study, is apparent from the fact that we can recognize arpeggiated
chords that produce no VFs at all. Thus ends my report.

-Mike

hi gene
check this out...I see why you might call your scale a dwarf
 
 

HZ

Ratio

A

1

32/32

tonic

1.03125

33/32

33/32

1/4 tone

A#

1.0625

34/32

17/16

1.09375

35/32

B

1.125

36/32

9/8

1.15625

37/32

37/32

1/4 tone

B#

1.1875

38/32

19/16

1.53125

39/32

C

1.25

40/32

5/4

1.28125

41/32

C#

1.3125

42/32

21/16

1.34375

43/32

43/32

1/4 tone

D

1.375

44/32

11/8

1.40625

45/32

D#

1.4375

46/32

23/16

1.46875

47/32

E

1.5

48/32

3/2

1.53125

49/32

E#

1.5625

50/32

25/16

1.59375

51/32

F

1.625

52/32

13/8

1.65625

53/32

F#

1.6875

54/32

27/16

1.71875

55/32

G

1.75

56/32

7/4

1.78125

57/32

G#

1.8125

58/32

29/16

1.84375

59/32

H

1.875

60/32

15/8

1.90625

61/32

H#

1.9375

62/32

31/16

1.96875

63/32

A1

2

64/32

2/1

--- On Sun, 7/3/11, genewardsmith <genewardsmith@...> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Sunday, July 3, 2011, 8:19 PM

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> All I am saying is that by using overtone only relationships music is 
> enriched in a powerful way, based on sound results (pun intended).  If you  want
> to keep sticking to historical ways, as a cultural inheritance, for 
> example, you are entitled.  Just reporting on some new findings.

If anyone wants to explore this brave new world, that has such scales in't, dwarf scales provide an easy entry route. Here by way of example is the 43-limit patent val dwarf for 19edo:

! over19.scl
Dwarf scale for 43-limit patent val of 19edo
19
!
33/32
17/16
9/8
37/32
19/16
5/4
21/16
43/32
11/8
23/16
3/2
25/16
13/8
27/16
7/4
29/16
15/8
31/16
2/1

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johnny I agree~
 
Opening up to the fact that there are many more natural harmonic series (than the 1 2 3 ...version) is just the start   It is up to us how we employ treatments and apply math principles to define our music..... "we may discover but nature invents"
Tim

--- On Sat, 7/2/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Saturday, July 2, 2011, 1:55 AM

Any rational tuning can be described as higher harmonics of a single fundamental. There's even an automagic function in Scala to give you the exact harmonics.

It is certainly not impossible that your instrument, which evolved in an A-440 12-tET world, resonates best at or very near frequencies found on that grid. Downright likely, I'd say. I'll have to read your paper to see what this has to do with Just intonation.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> 
> The adding of the culture dimension is really  just an extension of the old
> "nature/nurture" argument, culture being the  corollary to nurture. 
> Overtone tuning is clearly in the realm of  nature.
> 
> I believe that removing the undertone series  from overtone only
> relationships improves the music reception.  Perhaps the  true dissonance is in
> confusing the two series, overtone (harmonic) and  undertone (conceivable through
> difference tone patterns), an early form of  polymicrotonality.  Jon Catler
> and I agreed on this the other night for one  of our continuing
> conversations on the topic.  (Should the Microtones band  do a big show next year?)
> 
> We are all here on the List using cultural  definitions, buttressed by
> annecdotals in our personal lives.  There are  different perspectives: Is the
> glass half full of half empty?   (depends).  Sure, the 4/3 exists as the
> measurement between the 3rd and 4th  harmonics.  Good for the interval!  However,
> it does not exist as  a scale note in the overtone series.  The power of
> harmonics only  tuning is self evident when working in it.  The paper comes
> last.
> 
> 128 notes in every octave for every  instruments (except maybe fretted
> guitar) is finally reached.  A  century ago, a Schoenberg, or most anyone else,
> simply could not imagine hearing  such a scale, let alone any of the higher
> harmonics.  It was all paper,  until recently.
> 
> The sound is totally different in comparison  with previously understood
> just intonation.  So many different interval  relationships begging to be
> heard.
> 
> Johnny
> 
> 
>
>
> --- In _tuning@yahoogroups.com_
> (/tuning/post?postID=Xiv5JzX7UAdHRNKQmeQNjYWNPkerfl84deXPytrqTzLOX8QCuS_RYPXsG7AwDr3
> PXFdib4xdUhg5ofWItY3iR1c) , Afmmjr@  wrote:
> >
> >
> > Learned so much the other night reading my own  archive material. >Thanks
> > to Kyle Gann and Jon Catler, I now  understand that La Monte >Young's
> > "Well-Tuned Piano" is in pure  overtone tuning....no undertone >series.
> >Now I
> > connect that  info to the famous harmonic clouds that are produced >by  La
> Monte's
> > 6-hour composition. There is loss of reception when the  overtones >are
> > muddied by just intonation undertone intervals (such  as the 4/3 or >the
> 6/5).
>
> Harmonic/inharmonic or over/undertone are,  once we've lifted off from the
> field
> of paper, false dichotomies. Even in  monophony, if you move from 3/2 to
> 2/1,
> you've just played a  4/3.
>
> Whence this silly bifurcation? The most likely source is sadly  obvious. The
> cultural phenomenon of a dichotomy of major and minor is so  strong that it
> was
> only natural that in days of greater innocence (giving  great benefit of
> doubt
> to motivations) theorists should seek its source in  "nature". So Riemann
> proposed a dualism, Partch gave it a Hubbardesque  moniker, and here we in
> the
> 2011 still wasting our time going on as if we've  got two distinct things
> where
> in actual practice we really have aspects of  one.
>
>
> > Doing is believing.
> >So, need a bit more time with  the paper. It should be
> > obvious by now that some things need the proper  time to mature, >and that
> > this medium sucks when trying to get across  profound and complex >music
> > principles. Love the challenge to  verbalize the ineffable, don't >you?
>
> Effing the ineffable is a  pleasure, but then again effing in general  is
> pleasurable.
>
>
> >
> >
> > Lobawad: It would be great to  read your paper- as it is, I can't, >for
> > example, tell
> > what's  relative and what's fixed, which makes for some tremendous
> > differences  of
> > course.
> >
> > Johnny: The tuning is fixed, with  A=440.
>
> So you mean octaves of harmonics of A-440, for surely 440Hz isn't  the
> lowest
> pitch you're playing on the bassoon.
>
> -Cuthbert Lobawad,  Lieutenant Janitor of the Mord-Sith
>

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L: But don't you realize that they don't disappear just because you want
them to?

J: They become secondary phenomena, like a rainbow. Substitute the 43/32
for the 4/3, etc., and let the acoustic ephemera ring out, and there will
be much more of it to experience. Yes, I know the 4/3 still occurs and
that is fine. Just don't forcefit it into the scale. The 8th octave's 128
notes is just fine for seemingly any situation.

L: Or do you realize this and feel that it's the overtone relationship to a
particular fundamental that is the main thing?

J: Of course. I realize this. There are countless possibilities. In
another century we can add the 9th octave of the harmonic series for a
doubling of vocabulary, and more.

L: "Just Intonation" has long been a synonym for "rational tuning".

J: There has been to date little differentiation between just intonation
(with undertone series) and overtone tuning (without an undertone scale).
Extraneous acoustic phenomena occurrences are fine, and I usually love to
encourage them, using rich and resonant churches and cathedrals for the best
venues.

>, just like a
> rainbow in the sky.

L: Cognitive dissonance isn't the confusing of two different things, and
I'm not
confusing anything. I'm saying that when you play E-a in your tuning,
you're not
playing your 43/32 fourth.

J: Yes I am. My scale is reproduced in every octave so it would be a
43/32. For the umpteenth time, there is no 4/3 played. It may only appear
between played pitches.

L: This means that whatever overtone-derived quality of
this 43/32 fourth may be, it's happening in relation to your fundamental,
but
the fourth from E-a does NOT have this same quality.

J: Nope.

>
> L: Reinhard says it's the overtone relationship to a fundamental that's
> important.
>
> J: True.

L: I understand what you're saying. I don't think you've thought out all
the
implications.

J: I have not thought out everything in advance, no. But I can play all
the notes. I can teach them to others and I can make music with them. You
could, too, since they're public domain.

L: By the way, most of my tuning is based on a phantom fundamental of
13 Hz, has been for years. I've thought about the implications a lot.

J: I learned that technique from La Monte Young, using his Saraband for
guitar as a model.

L: Ithink you're confusing the familiarity of it with "sounding good", and
as a
hardcore microtonalist, bluntly spoken I think it's a joke.

J: I think not using an interval because of its familiar usage is
discrimination, unfair and unneccessary.

>If you want
> to keep sticking to historical ways, as a cultural inheritance, for
> example, you are entitled.

L: I think that's actually what you're doing, whilst kidding yourself
you're not,
while I'm doing quite the opposite, which is not hiding that my tunings
originate in ancient tetrachords, but using them in a way that is radically
unstuck from their history.

J: Exactly, we will have to disagree here.

>Just reporting on some new findings.

L: I'd like to hear more stuff like "Dune", whatever tuning scheme you're
using.

J: Thanks, but each piece has its own soundworld. After all, I am a
self-described polymicrotonalist, even with my new found overtone fetish.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jul 3, 2011 at 5:48 PM, lobawad <lobawad@...> wrote:
> >
> > Interesting- but at any rate, there's a response to your earlier remarks about finding sort of parallels to major/minor. Major/minor is not what's making the "dichotomy" here,(I know that we're in agreement that music doesn't boil down to binaries, but you know what I mean) and in my experience "civilians" like the feeling of options other than major/minor very much.
>
> There are options other than major/minor pretty much as soon as you
> get away from triads.

Obviously. But you were more specific, calling for something more "equivalent" to major/minor. Which of these other options offers something that could be cartooned down to a "dichotomy"? Which would not be major/minor, but would be something you'd mistake for major/minor? You say you hear major/minor in the piece I linked to, but the piece isn't based on major/minor.

I suspect that you conflate major/minor signalling with "accessible" "emotional/meaning" signalling, and that's why you're hearing something that isn't major/minor as major/minor.

>You might say that modal harmony focuses on
> heptadic harmony (although not often with all the notes in the mode
> played simultaneously), and there's plenty of difference between
> dorian and phrygian alone.

Historically, before the modes were commonly confused with modal scales, the mood of a mode was also expressed through stereotyped figures, as happens in "maqam music". I don't think you were aware of this, but you did, not long ago, express this same concept in the realm of modal harmony- something like "signifying progressions".

Hang on- is this not your scale?

0: 1/1 0.000 unison, perfect prime
1: 129/128 13.473
2: 65/64 26.841 13th-partial chroma
3: 131/128 40.108
4: 33/32 53.273 undecimal comma, al-Farabi's 1/4-tone
5: 133/128 66.339
6: 67/64 79.307
7: 135/128 92.179 major chroma, major limma
8: 17/16 104.955 17th harmonic
9: 137/128 117.638
10: 69/64 130.229
11: 139/128 142.729
12: 35/32 155.140 septimal neutral second
13: 141/128 167.462
14: 71/64 179.697
15: 143/128 191.846
16: 9/8 203.910 major whole tone
17: 145/128 215.891
18: 73/64 227.789
19: 147/128 239.607
20: 37/32 251.344 37th harmonic
21: 149/128 263.002
22: 75/64 274.582 classic augmented second
23: 151/128 286.086
24: 19/16 297.513 19th harmonic
25: 153/128 308.865
26: 77/64 320.144
27: 155/128 331.349
28: 39/32 342.483 39th harmonic, Zalzal wosta of Ibn Sina
29: 157/128 353.545
30: 79/64 364.537
31: 159/128 375.460
32: 5/4 386.314 major third
33: 161/128 397.100
34: 81/64 407.820 Pythagorean major third
35: 163/128 418.474
36: 41/32 429.062
37: 165/128 439.587
38: 83/64 450.047
39: 167/128 460.445
40: 21/16 470.781 narrow fourth
41: 169/128 481.055
42: 85/64 491.269
43: 171/128 501.423
44: 43/32 511.518
45: 173/128 521.554
46: 87/64 531.532
47: 175/128 541.453
48: 11/8 551.318 undecimal semi-augmented fourth
49: 177/128 561.127
50: 89/64 570.880
51: 179/128 580.579
52: 45/32 590.224 diatonic tritone
53: 181/128 599.815
54: 91/64 609.354
55: 183/128 618.840
56: 23/16 628.274 23rd harmonic
57: 185/128 637.658
58: 93/64 646.991
59: 187/128 656.273
60: 47/32 665.507
61: 189/128 674.691
62: 95/64 683.827
63: 191/128 692.915
64: 3/2 701.955 perfect fifth
65: 193/128 710.948
66: 97/64 719.895
67: 195/128 728.796
68: 49/32 737.652
69: 197/128 746.462
70: 99/64 755.228
71: 199/128 763.950
72: 25/16 772.627 classic augmented fifth
73: 201/128 781.262
74: 101/64 789.854
75: 203/128 798.403
76: 51/32 806.910
77: 205/128 815.376
78: 103/64 823.801
79: 207/128 832.184
80: 13/8 840.528 tridecimal neutral sixth
81: 209/128 848.831
82: 105/64 857.095 septimal neutral sixth
83: 211/128 865.319
84: 53/32 873.505
85: 213/128 881.652
86: 107/64 889.760
87: 215/128 897.831
88: 27/16 905.865 Pythagorean major sixth
89: 217/128 913.861
90: 109/64 921.821
91: 219/128 929.744
92: 55/32 937.632
93: 221/128 945.483
94: 111/64 953.299
95: 223/128 961.080
96: 7/4 968.826 harmonic seventh
97: 225/128 976.537 augmented sixth
98: 113/64 984.215
99: 227/128 991.858
100: 57/32 999.468
101: 229/128 1007.045
102: 115/64 1014.588
103: 231/128 1022.099
104: 29/16 1029.577 29th harmonic
105: 233/128 1037.023
106: 117/64 1044.438
107: 235/128 1051.820
108: 59/32 1059.172
109: 237/128 1066.492
110: 119/64 1073.781
111: 239/128 1081.040
112: 15/8 1088.269 classic major seventh
113: 241/128 1095.467
114: 121/64 1102.636 two (undecimal semi-augmented fourth)
115: 243/128 1109.775 Pythagorean major seventh
116: 61/32 1116.885
117: 245/128 1123.966
118: 123/64 1131.017
119: 247/128 1138.041
120: 31/16 1145.036 31st harmonic
121: 249/128 1152.002
122: 125/64 1158.941 classic augmented seventh, octave - minor diesis
123: 251/128 1165.852
124: 63/32 1172.736 octave - septimal comma
125: 253/128 1179.592
126: 127/64 1186.422
127: 255/128 1193.224
128: 2/1 1200.000 octave

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
>
> L: But don't you realize that they don't disappear just because you want
> them to?
>
> J: They become secondary phenomena, like a rainbow. Substitute the 43/32
> for the 4/3, etc., and let the acoustic ephemera ring out, and there will
> be much more of it to experience. Yes, I know the 4/3 still occurs and
> that is fine. Just don't forcefit it into the scale. The 8th octave's 128
> notes is just fine for seemingly any situation.
>
> L: Or do you realize this and feel that it's the overtone relationship to a
> particular fundamental that is the main thing?
>
> J: Of course. I realize this. There are countless possibilities. In
> another century we can add the 9th octave of the harmonic series for a
> doubling of vocabulary, and more.
>
>
> L: "Just Intonation" has long been a synonym for "rational tuning".
>
> J: There has been to date little differentiation between just intonation
> (with undertone series) and overtone tuning (without an undertone scale).
> Extraneous acoustic phenomena occurrences are fine, and I usually love to
> encourage them, using rich and resonant churches and cathedrals for the best
> venues.
>
> >, just like a
> > rainbow in the sky.
>
> L: Cognitive dissonance isn't the confusing of two different things, and
> I'm not
> confusing anything. I'm saying that when you play E-a in your tuning,
> you're not
> playing your 43/32 fourth.
>
> J: Yes I am. My scale is reproduced in every octave so it would be a
> 43/32. For the umpteenth time, there is no 4/3 played. It may only appear
> between played pitches.
>
>
> L: This means that whatever overtone-derived quality of
> this 43/32 fourth may be, it's happening in relation to your fundamental,
> but
> the fourth from E-a does NOT have this same quality.
>
> J: Nope.
>
> >
> > L: Reinhard says it's the overtone relationship to a fundamental that's
> > important.
> >
> > J: True.
>
> L: I understand what you're saying. I don't think you've thought out all
> the
> implications.
>
> J: I have not thought out everything in advance, no. But I can play all
> the notes. I can teach them to others and I can make music with them. You
> could, too, since they're public domain.
>
>
> L: By the way, most of my tuning is based on a phantom fundamental of
> 13 Hz, has been for years. I've thought about the implications a lot.
>
> J: I learned that technique from La Monte Young, using his Saraband for
> guitar as a model.
>
>
> L: Ithink you're confusing the familiarity of it with "sounding good", and
> as a
> hardcore microtonalist, bluntly spoken I think it's a joke.
>
> J: I think not using an interval because of its familiar usage is
> discrimination, unfair and unneccessary.
>
>
> >If you want
> > to keep sticking to historical ways, as a cultural inheritance, for
> > example, you are entitled.
>
> L: I think that's actually what you're doing, whilst kidding yourself
> you're not,
> while I'm doing quite the opposite, which is not hiding that my tunings
> originate in ancient tetrachords, but using them in a way that is radically
> unstuck from their history.
>
> J: Exactly, we will have to disagree here.
>
> >Just reporting on some new findings.
>
> L: I'd like to hear more stuff like "Dune", whatever tuning scheme you're
> using.
>
> J: Thanks, but each piece has its own soundworld. After all, I am a
> self-described polymicrotonalist, even with my new found overtone fetish.
>

Afmmjr@... wrote:
> Mike, please read the this on Riemann to see that the
> dichotomy of major and minor is a farce.
>
> _http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf_
> (http://catdir.loc.gov/catdir/samples/cam033/2002031364.pdf)

There's little about reality in that paper. It's too post
modern to admit that reality even exists. Choice quote:

"What is more, since the scientific prestige of Helmholtz’s
work automatically put him ‘in the right’ . . ."

On page 8, we have "For while the objections to har-
monic dualism during Riemann’s lifetime were in principle
as obvious as they are now . . ." On page 15, we finally
get a definition of "harmonic dualism". That gets beaten
about until page 17, when ". . . harmonic dualism, taken at
its basic level, is the postulate of theoretical
equivalence between the major and minor systems. There is
little controversy about this point." So harmonic dualism
is essentially correct, but let's define it so that it
becomes wrong, or argue about it regardless.

If we turn to reality, we can say that undertones don't
really exist, and nobody other than Riemann ever seemed to
think they did. That doesn't make a dualistic approach of
major and minor a farce. We know that major and minor
triads have the same intervals. Plomp and Levelt, and
later theorists who were interested in the reality of human
perception, produced models of sensory consonance that are
purely dyadic and so naturally dualistic. A diatonic scale
with major triads will also have minor triads with a
5-limit tuning following their major counterparts.

In reality, we also know that virtual pitch recognition
favors major over minor. But music theory should say the
same thing. Minor keys involve movable pitches to give
more major triads. You won't find that argument in the
cited PDF though.

Another reason to consider utonalities is that traditional
scales can arise from equal divisions of a string or pipe.
Utonal scales are proven melodically. They have the same
constituent intervals as otonal scales. A utonality will
have pitches closer together at the bottom than the top,
whereas an otonal scale will be the other way round.
Combining the otonal and utonal gives you balance --
between high and low and melody and harmony. That was
Partch's insight and in his time it was a good one. It
saved him from the trap of retuning the major scale to fix
the major triads.

You can say that reality prefers the otonal to the utonal.
Most of us would agree -- higher-limit utonal chords don't
work nearly as well as their otonal counterparts. But
reality, as it applies to human perception, still runs into
difficulty in the 32 to 64 range.

I'm now going to consume huge quantities of vitamin C
on the grounds that the scientific prestige of Pauling's
work automatically puts him 'in the right'. Don't worry, I
won't take the tablets out of their scare quotes.

Graham

Naturally!!!!!  See how easy this is? The shortcut is to use the added factor not the ratio, but the ratio reveals the hz and cent values easily.  See how the whole tone, half tone, quarter tone values are "nested"? This is a very good primer for microtuning with completely natural scales.
 
Tim

--- On Mon, 7/4/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 7:54 AM

Hang on- is this not your scale?

0:          1/1               0.000  unison, perfect prime
  1:        129/128            13.473
  2:         65/64             26.841  13th-partial chroma
  3:        131/128            40.108
  4:         33/32             53.273  undecimal comma, al-Farabi's 1/4-tone
  5:        133/128            66.339
  6:         67/64             79.307
  7:        135/128            92.179  major chroma, major limma
  8:         17/16            104.955  17th harmonic
  9:        137/128           117.638
10:         69/64            130.229
11:        139/128           142.729
12:         35/32            155.140  septimal neutral second
13:        141/128           167.462
14:         71/64            179.697
15:        143/128           191.846
16:          9/8             203.910  major whole tone
17:        145/128           215.891
18:         73/64            227.789
19:        147/128           239.607
20:         37/32            251.344  37th harmonic
21:        149/128           263.002
22:         75/64            274.582  classic augmented second
23:        151/128           286.086
24:         19/16            297.513  19th harmonic
25:        153/128           308.865
26:         77/64            320.144
27:        155/128           331.349
28:         39/32            342.483  39th harmonic, Zalzal wosta of Ibn Sina
29:        157/128           353.545
30:         79/64            364.537
31:        159/128           375.460
32:          5/4             386.314  major third
33:        161/128           397.100
34:         81/64            407.820  Pythagorean major third
35:        163/128           418.474
36:         41/32            429.062
37:        165/128           439.587
38:         83/64            450.047
39:        167/128           460.445
40:         21/16            470.781  narrow fourth
41:        169/128           481.055
42:         85/64            491.269
43:        171/128           501.423
44:         43/32            511.518
45:        173/128           521.554
46:         87/64            531.532
47:        175/128           541.453
48:         11/8             551.318  undecimal semi-augmented fourth
49:        177/128           561.127
50:         89/64            570.880
51:        179/128           580.579
52:         45/32            590.224  diatonic tritone
53:        181/128           599.815
54:         91/64            609.354
55:        183/128           618.840
56:         23/16            628.274  23rd harmonic
57:        185/128           637.658
58:         93/64            646.991
59:        187/128           656.273
60:         47/32            665.507
61:        189/128           674.691
62:         95/64            683.827
63:        191/128           692.915
64:          3/2             701.955  perfect fifth
65:        193/128           710.948
66:         97/64            719.895
67:        195/128           728.796
68:         49/32            737.652
69:        197/128           746.462
70:         99/64            755.228
71:        199/128           763.950
72:         25/16            772.627  classic augmented fifth
73:        201/128           781.262
74:        101/64            789.854
75:        203/128           798.403
76:         51/32            806.910
77:        205/128           815.376
78:        103/64            823.801
79:        207/128           832.184
80:         13/8             840.528  tridecimal neutral sixth
81:        209/128           848.831
82:        105/64            857.095  septimal neutral sixth
83:        211/128           865.319
84:         53/32            873.505
85:        213/128           881.652
86:        107/64            889.760
87:        215/128           897.831
88:         27/16            905.865  Pythagorean major sixth
89:        217/128           913.861
90:        109/64            921.821
91:        219/128           929.744
92:         55/32            937.632
93:        221/128           945.483
94:        111/64            953.299
95:        223/128           961.080
96:          7/4             968.826  harmonic seventh
97:        225/128           976.537  augmented sixth
98:        113/64            984.215
99:        227/128           991.858
100:        57/32            999.468
101:       229/128          1007.045
102:       115/64           1014.588
103:       231/128          1022.099
104:        29/16           1029.577  29th harmonic
105:       233/128          1037.023
106:       117/64           1044.438
107:       235/128          1051.820
108:        59/32           1059.172
109:       237/128          1066.492
110:       119/64           1073.781
111:       239/128          1081.040
112:        15/8            1088.269  classic major seventh
113:       241/128          1095.467
114:       121/64           1102.636  two (undecimal semi-augmented fourth)
115:       243/128          1109.775  Pythagorean major seventh
116:        61/32           1116.885
117:       245/128          1123.966
118:       123/64           1131.017
119:       247/128          1138.041
120:        31/16           1145.036  31st harmonic
121:       249/128          1152.002
122:       125/64           1158.941  classic augmented seventh, octave - minor diesis
123:       251/128          1165.852
124:        63/32           1172.736  octave - septimal comma
125:       253/128          1179.592
126:       127/64           1186.422
127:       255/128          1193.224
128:         2/1            1200.000  octave

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> 
> 
> L: But don't you realize that they don't  disappear just because you want
> them to?
>
> J:  They become secondary phenomena, like a  rainbow.  Substitute the 43/32
> for the 4/3, etc., and let the acoustic  ephemera ring out, and there will
> be much more of it to experience.  Yes, I  know the 4/3 still occurs and
> that is fine.  Just don't forcefit it into  the scale.  The 8th octave's 128
> notes is just fine for seemingly any  situation.
> 
> L: Or do you realize this and feel that it's the  overtone relationship to a
> particular fundamental that is the main thing?
> 
> J: Of course.  I realize this.  There  are countless possibilities.  In
> another century we can add the 9th octave  of the harmonic series for a
> doubling of vocabulary, and more.
> 
>
> L:  "Just Intonation" has long been a  synonym for "rational tuning".
>
> J: There has been to date little differentiation  between just intonation
> (with undertone series) and overtone tuning (without an  undertone scale). 
> Extraneous acoustic phenomena occurrences are fine, and  I usually love to
> encourage them, using rich and resonant churches and  cathedrals for the best
> venues.
>
> >, just like a
> > rainbow in the  sky.
>
> L: Cognitive dissonance isn't the confusing of  two different things, and
> I'm not
> confusing anything. I'm saying that when  you play E-a in your tuning,
> you're not
> playing your 43/32 fourth.
> 
> J: Yes I am.  My scale is reproduced in  every octave so it would be a
> 43/32.  For the umpteenth time, there is no  4/3 played.  It may only appear
> between played pitches.
> 
> 
> L: This means that whatever overtone-derived  quality of
> this 43/32 fourth may be, it's happening in relation to your  fundamental,
> but
> the fourth from E-a does NOT have this same  quality.
>
> J: Nope. 
>
> >
> > L: Reinhard says it's the  overtone relationship to a fundamental that's
> > important.
> >
> >  J: True.
>
> L: I understand what you're saying. I don't think you've thought  out all
> the
> implications.
> 
> J: I have not thought out everything in advance,  no.  But I can play all
> the notes.  I can teach them to others and I  can make music with them.  You
> could, too, since they're public  domain.
> 
> 
> L: By the way, most of my tuning is based on a  phantom fundamental of
> 13 Hz, has been for years. I've thought about the  implications a lot.
>
> J: I learned that technique from La Monte Young,  using his Saraband for
> guitar as a model. 
>
>
> L: Ithink you're  confusing the familiarity of it with "sounding good", and
> as a
> hardcore  microtonalist, bluntly spoken I think it's a joke.
>
> J: I think not using  an interval because of its familiar usage is
> discrimination, unfair and  unneccessary.
>
>
> >If you want
> > to keep sticking to historical  ways, as a cultural inheritance, for
> > example, you are  entitled.
>
> L: I think that's actually what you're doing, whilst kidding  yourself
> you're not,
> while I'm doing quite the opposite, which is not hiding  that my tunings
> originate in ancient tetrachords, but using them in a way  that is radically
> unstuck from their history.
> 
> J: Exactly, we will have to disagree  here.
>
> >Just reporting on some new findings.
>
> L: I'd like to hear  more stuff like "Dune", whatever tuning scheme you're
> using.
>
> J: Thanks, but each piece has its own  soundworld.  After all, I am a
> self-described polymicrotonalist, even with  my new found overtone fetish.
>

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Thanks, Tim. Of course this should be obvious, but it has somehow been
hidden for various reasons, none of them having to do with sound. I have
come up with different names for the intervals, and a notation (to include
cents) I will be happen to share. Guess there is no rush to give out the
bassoon fingerings. I look forward to sharing at Jacob Barton's microtonal
camp taking place his summer in West Virginia.

Mr. Lobawad, you might consider renumbering so that 1/1 is the number "1"
and not "0" as in music we count on the one. The hard sciences start on
the zero.

Johnny

Naturally!!!!! See how easy this is? The shortcut is to use the added
factor not the ratio, but the ratio reveals the hz and cent values easily. See
how the whole tone, half tone, quarter tone values are "nested"? This is a
very good primer for microtuning with completely natural scales.

Tim

--- On Mon, 7/4/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 7:54 AM

Hang on- is this not your scale?

0: 1/1 0.000 unison, perfect prime
1: 129/128 13.473

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

>
> Mr. Lobawad, you might consider renumbering so that 1/1 is the number "1"
> and not "0" as in music we count on the one. The hard sciences start on
> the zero.
>
> Johnny

Musical set theory is a hard science? Anyway, that's just how Scala lists it, obviously I also use "1" at the "1" in ratio calculations too. In other musical uses, people sometimes use "0".

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> Mr. Lobawad, you might consider renumbering so that 1/1 is the number "1"
> and not "0" as in music we count on the one. The hard sciences start on
> the zero.

The log of one is zero in both music theory and science.

Oh, and you haven't responded as to whether you consider 19/16 as the "true" minor third.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
>
> >
> > Mr. Lobawad, you might consider renumbering so that 1/1 is the number "1"
> > and not "0" as in music we count on the one. The hard sciences start on
> > the zero.
> >
> > Johnny
>
>
> Musical set theory is a hard science? Anyway, that's just how Scala lists it, obviously I also use "1" at the "1" in ratio calculations too. In other musical uses, people sometimes use "0".
>

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:
> ... Opening up to the fact that there are many more natural harmonic series (than the 1 2 3 ...version) is just the start ...

Tim,
I'm a bit confused by this - could you explain or give an example, please?

Steve.

Ok Steve, check this out, you may eventually find where all those strange ratios come from...
 
(1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc
 
Same as before, you will see natural microtuning occur in every series with nested values throughout each system/   Of course you will see sharing of ratios with standard nhs tuning iin many places...that allows you to modulate from one series to another.
 
how do you like me now?
Tim
July 4,2011   Happy birthday America
 
--- On Mon, 7/4/11, martinsj013 <martinsj@...> wrote:

From: martinsj013 <martinsj@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 9:26 PM

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:
> ... Opening up to the fact that there are many more natural harmonic series (than the 1 2 3 ...version) is just the start ...

Tim,
I'm a bit confused by this - could you explain or give an example, please?

Steve.

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Should be careful to call this a series and not an harmonic series.

On 5 Jul 2011, at 02:54, Tim Reeves wrote:

> Ok Steve, check this out, you may eventually find where all those > strange ratios come from...
>
> (1/3 2/3) 3/3 4/3 5/3 6/3 = 6/6 7/6 8/6 9/6 10/6 11/6 > 12/6 = 12/12 13/12 14/12 15/12 16/12 17/12 18/12 19/12 > 20/12 21/12 22/12 23/12 24/12 = 24/24 etc

>>>Why's that? it follows the same logic and process as the common nhs, ie,  3 is the base (or basis) for whole tone values, and the top number clearly defines the harmonic at that point in the numeric series. To call this another nhs may seem arbitrary, but I would tend to call it natural synthesis.
 
Thanks
Tim >>>

--- On Tue, 7/5/11, Steve Parker <steve@pinkrat.co.uk> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 8:26 AM

Should be careful to call this a series and not an harmonic series.

On 5 Jul 2011, at 02:54, Tim Reeves wrote:

Ok Steve, check this out, you may eventually find where all those strange ratios come from...
 
(1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc

Dear Gene,

Music starts with 1, physics starts with 0. I was taught that at Columbia
University by Prof. Steven Feld, an ethnomusicologist.

The music emphasis is as follows: We count measures starting with "1" for
the first measure we are counting. Additionally, it is hard for a
musician to consider that the 1/1 = 0 sound. Check and see what the musicians
have done, they count the first note as 1 for every scale. (An exception
might be Carrillo who used 0-95 for his 96 notes).

Johnny

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=D4ix_BGv8rS0s01dPtSB5mCXxrAyyZWLkSUUG4uQpnYXx9NzMN9JVxWlpMr4Ge_
ZGDmWibn0UAeAdavk3Q) , Afmmjr@... wrote:

> Mr. Lobawad, you might consider renumbering so that 1/1 is the number
"1"
> and not "0" as in music we count on the one. The hard sciences start on
> the zero.

The log of one is zero in both music theory and science.

>>>  i i i i i....(Lucy!!!!)     as per ricky and lucy tuning i guess
 
like i said earlier this morning, every great musician needs a rocket scientist!
 
tim >>>

--- On Tue, 7/5/11, Afmmjr@... <Afmmjr@aol.com> wrote:

From: Afmmjr@... <Afmmjr@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 1:39 PM

Dear Gene,
 
Music starts with 1, physics starts with 0. I was taught that at Columbia University by Prof. Steven Feld, an ethnomusicologist.
 
The music emphasis is as follows:  We count measures starting with "1" for the first measure we are counting.  Additionally, it is hard for a musician to consider that the 1/1 = 0 sound.  Check and see what the musicians have done, they count the first note as 1 for every scale.  (An exception might be Carrillo who used 0-95 for his 96 notes).
 
Johnny

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> Mr. Lobawad, you might consider renumbering so that 1/1 is the number "1"
> and not "0" as in music we count on the one. The hard sciences start on
> the zero.

The log of one is zero in both music theory and science.

as do the cent values

--- On Mon, 7/4/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 8:58 PM

Oh, and you haven't responded as to whether you consider 19/16 as the "true" minor third.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> 
> > 
> > Mr. Lobawad, you might consider renumbering so that  1/1 is the number "1"
> > and not "0" as in music we count on the one.   The hard sciences start on
> > the zero.
> > 
> > Johnny
>
>
> Musical set theory is a hard science? Anyway, that's just how Scala lists it, obviously I also use "1" at the "1" in ratio calculations too. In other musical uses, people sometimes use "0".
>

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In musical set theory, sets start with "0", not "1".

When measuring intervals by cents, we start from 0, not 1.

String players, in practice, effectively work from "zero", the open string, and have for millenia. First finger is first finger (fret), not open string. In fact, some fretted string instruments which try to avoid intonational inconsistencies caused by varying string heights and lengths due to vagaries at the nut slots have an extra fret (technically probably a bridge) over which the open strings are strung. Guess what it's called? A "zero fret".

"Music" and "physics" is not a dichotomy. You display gross ignorance of, or woeful failure to comprehend, the history of music- especially the history of "microtonal" music- when you make such statements. Stop with these hysterical black-and-white perceptions, child.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Dear Gene,
>
> Music starts with 1, physics starts with 0. I was taught that at Columbia
> University by Prof. Steven Feld, an ethnomusicologist.

>
> The music emphasis is as follows: We count measures starting with "1" for
> the first measure we are counting. Additionally, it is hard for a
> musician to consider that the 1/1 = 0 sound. Check and see what the musicians
> have done, they count the first note as 1 for every scale. (An exception
> might be Carrillo who used 0-95 for his 96 notes).
>
> Johnny
>
>
>
> --- In _tuning@yahoogroups.com_
> (/tuning/post?postID=D4ix_BGv8rS0s01dPtSB5mCXxrAyyZWLkSUUG4uQpnYXx9NzMN9JVxWlpMr4Ge_
> ZGDmWibn0UAeAdavk3Q) , Afmmjr@ wrote:
>
> > Mr. Lobawad, you might consider renumbering so that 1/1 is the number
> "1"
> > and not "0" as in music we count on the one. The hard sciences start on
> > the zero.
>
> The log of one is zero in both music theory and science.
>

So we should abandon the physical basis for the HS of pipes and strings?

Steve P.

On 5 Jul 2011, at 14:24, Tim Reeves wrote:

> Why's that? it follows the same logic and process as the common nhs, > ie, 3 is the base (or basis) for whole tone values, and the top > number clearly defines the harmonic at that point in the numeric > series. To call this another nhs may seem arbitrary, but I would > tend to call it natural synthesis.

On 5 Jul 2011, at 14:39, Afmmjr@... wrote:

> An exception might be Carrillo who used 0-95 for his 96 notes)

and MIDI......

Steve P.

yes midi how could we forget...gotta get out my tx81z
 
tim

--- On Tue, 7/5/11, Steve Parker <steve@...> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 3:18 PM

On 5 Jul 2011, at 14:39, Afmmjr@... wrote:

An exception might be Carrillo who used 0-95 for his 96 notes)

and MIDI......

Steve P.

how could we...it is physical..On the other hand, synths allow for so much more and pure theory is unlimited.
Tim

--- On Tue, 7/5/11, Steve Parker <steve@...> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 3:17 PM

So we should abandon the physical basis for the HS of pipes and strings?

Steve P.

On 5 Jul 2011, at 14:24, Tim Reeves wrote:

Why's that? it follows the same logic and process as the common nhs, ie,  3 is the base (or basis) for whole tone values, and the top number clearly defines the harmonic at that point in the numeric series. To call this another nhs may seem arbitrary, but I would tend to call it natural synthesis.

On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@...> wrote:
>
> Ok Steve, check this out, you may eventually find where all those strange ratios come from...
>
> (1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc
>
> Same as before, you will see natural microtuning occur in every series with nested values throughout each system/   Of course you will see sharing of ratios with standard nhs tuning iin many places...that allows you to modulate from one series to another.
>
> how do you like me now?

That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
omitted, and transposed.

-Mike

Mike
 
That may very well be the case, still working on it to see what's up in applying  the process. Do you think there is a difference when it is applied to all primes or do you suspect that they all can be reduced to values of 1
 
Anyway, I find this very interesting.
Thanks
Tim
 
--- On Tue, 7/5/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 5:57 PM

On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@...> wrote:
>
> Ok Steve, check this out, you may eventually find where all those strange ratios come from...
>
> (1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc
>
> Same as before, you will see natural microtuning occur in every series with nested values throughout each system/   Of course you will see sharing of ratios with standard nhs tuning iin many places...that allows you to modulate from one series to another.
>
> how do you like me now?

That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
omitted, and transposed.

-Mike

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LOBAWAD,

I asked you why you need to be condescending when you contacted me off
list, and you are behaving worse. Music is older than theory and technology.
The classics:
The English horn is not English.
The French horn is not French.
The German B natural is an H.
And many musicians feeling the 1/1 pull on them equate it with 1 and not 0,
perhaps indicating counting numbers and not integers. Calling me names is
a stupid response. And I think we're done here.

Johnny

In musical set theory, sets start with "0", not "1".

When measuring intervals by cents, we start from 0, not 1.

String players, in practice, effectively work from "zero", the open
string, and
have for millenia. First finger is first finger (fret), not open string. In
fact, some fretted string instruments which try to avoid intonational
inconsistencies caused by varying string heights and lengths due to
vagaries at
the nut slots have an extra fret (technically probably a bridge) over
which the
open strings are strung. Guess what it's called? A "zero fret".

"Music" and "physics" is not a dichotomy. You display gross ignorance of,
or
woeful failure to comprehend, the history of music- especially the history
of
"microtonal" music- when you make such statements. Stop with these
hysterical
black-and-white perceptions, child.

Johnny,
 
I can't even imagine calling anyone on this group "child"  You have identified H and it does have a historic basis that not everyone here seems to get... i got your back bro, look at this comparative study:
 
C  D  E  F  G  A  B  B#  C is something I recall seeing along the way, anyway check this out
A  B  C  D  E  F  G  H    A = natural whole tone scale, probably just the way Pythagoras saw it because it occurs in the first glance at the natural harmonic series....after all, why would he  want to go to extremes of complicated processes to "find" a logical musical scale when this hits you in the face right from the start?
Tim

--- On Tue, 7/5/11, Afmmjr@... <Afmmjr@...> wrote:

From: Afmmjr@... <Afmmjr@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 6:51 PM

LOBAWAD,
 
I asked you why you need to be condescending when you contacted me off list, and you are behaving worse.   Music is older than theory and technology.  The classics:
The English horn is not English.
The French horn is not French.
The German B natural is an H.
And many musicians feeling the 1/1 pull on them equate it with 1 and not 0, perhaps indicating counting numbers and not integers.  Calling me names is a stupid response.  And I think we're done here.
 
Johnny
 
 

 
In musical set theory, sets start with "0", not "1".

When measuring intervals by cents, we start from 0, not 1.

String players, in practice, effectively work from "zero", the open string, and
have for millenia. First finger is first finger (fret), not open string. In
fact, some fretted string instruments which try to avoid intonational
inconsistencies caused by varying string heights and lengths due to vagaries at
the nut slots have an extra fret (technically probably a bridge) over which the
open strings are strung. Guess what it's called? A "zero fret".

"Music" and "physics" is not a dichotomy. You display gross ignorance of, or
woeful failure to comprehend, the history of music- especially the history of
"microtonal" music- when you make such statements. Stop with these hysterical
black-and-white perceptions, child.

Mike
 
I have had time to come to my senses on this. Please look at the following and tell me how you equate your statement with my post.

Hz

Hz

1

6/6

6

6/1

1.166666667

7/6

7

7/1

1.333333333

8/6

8

8/1

1.5

9/6

9

9/1

1.666666667

10/6

10

10/1

1.833333333

11/6

11

11/1

2

12/6

12

12/1

My claim of more than one nhs doesn't mean that this is a new invention of a number series
ie 1 2 3  but is in fact an extension of a process, (the one I use to define natural scales),  that will yield an infinity of musical scales and interval values. 
 
This might explain the difference in our reasoning:
 
In describing a ratio for musical purposes  I state that when you have a ratio such as 9/8 or m/n, the top number or m = the number value of the harmonic in the sequence
 and the bottom number, or  n = the number of notes in the octave at that point in the series.
 
So, if I tried to apply this reasoning to the scale you reduced down to, there would be 1 note in the octave...all I see here is a simple numeric series, not a similar or equal musical scale .. Maybe you could elaborate and I could see your point.
Thanks
Tim
 
--- On Tue, 7/5/11, Tim Reeves <reevest360@...> wrote:

From: Tim Reeves <reevest360@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 6:43 PM

Mike
 
That may very well be the case, still working on it to see what's up in applying  the process. Do you think there is a difference when it is applied to all primes or do you suspect that they all can be reduced to values of 1
 
Anyway, I find this very interesting.
Thanks
Tim
 
--- On Tue, 7/5/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 5:57 PM

On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@...> wrote:
>
> Ok Steve, check this out, you may eventually find where all those strange ratios come from...
>
> (1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc
>
> Same as before, you will see natural microtuning occur in every series with nested values throughout each system/   Of course you will see sharing of ratios with standard nhs tuning iin many places...that allows you to modulate from one series to another.
>
> how do you like me now?

That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
omitted, and transposed.

-Mike

------------------------------------

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Can you at all justify the word 'harmonic' in this? We really should
reserve that word for the infinite series 1 + 1/2 + 1/3 +1/4 +
1/5 . . . . . which describes the overtones of a vibrating string's
fundamental.
I'm not sure that the word 'series' applies either.

Microtonal music theory is DITW if anyone can call anything anything..

Steve P.

On 6 Jul 2011, at 17:51, Tim Reeves wrote:

>
> Mike
>
> I have had time to come to my senses on this. Please look at the
> following and tell me how you equate your statement with my post.
> Hz
>
> Hz
>
> 1
>
> 6/6
>
> 6
>
> 6/1
>
> 1.166666667
>
> 7/6
>
> 7
>
> 7/1
>
> 1.333333333
>
> 8/6
>
> 8
>
> 8/1
>
> 1.5
>
> 9/6
>
> 9
>
> 9/1
>
> 1.666666667
>
> 10/6
>
> 10
>
> 10/1
>
> 1.833333333
>
> 11/6
>
> 11
>
> 11/1
>
> 2
>
> 12/6
>
> 12
>
> 12/1
>
>
> My claim of more than one nhs doesn't mean that this is a new
> invention of a number series
> ie 1 2 3 but is in fact an extension of a process, (the one I use
> to define natural scales), that will yield an infinity of musical
> scales and interval values.
>
> This might explain the difference in our reasoning:
>
> In describing a ratio for musical purposes I state that when you
> have a ratio such as 9/8 or m/n, the top number or m = the number
> value of the harmonic in the sequence
> and the bottom number, or n = the number of notes in the octave at
> that point in the series.
>
> So, if I tried to apply this reasoning to the scale you reduced down
> to, there would be 1 note in the octave...all I see here is a simple
> numeric series, not a similar or equal musical scale .. Maybe you
> could elaborate and I could see your point.
> Thanks
> Tim
>
> --- On Tue, 7/5/11, Tim Reeves <reevest360@...> wrote:
>
> From: Tim Reeves <reevest360@yahoo.com>
> Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64
> program
> To: tuning@yahoogroups.com
> Date: Tuesday, July 5, 2011, 6:43 PM
>
>
>
> Mike
>
> That may very well be the case, still working on it to see what's up
> in applying the process. Do you think there is a difference when it
> is applied to all primes or do you suspect that they all can be
> reduced to values of 1
>
> Anyway, I find this very interesting.
> Thanks
> Tim
>
> --- On Tue, 7/5/11, Mike Battaglia <battaglia01@gmail.com> wrote:
>
> From: Mike Battaglia <battaglia01@...>
> Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64
> program
> To: tuning@yahoogroups.com
> Date: Tuesday, July 5, 2011, 5:57 PM
>
> On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@...>
> wrote:
> >
> > Ok Steve, check this out, you may eventually find where all those
> strange ratios come from...
> >
> > (1/3 2/3) 3/3 4/3 5/3 6/3 = 6/6 7/6 8/6 9/6 10/6
> 11/6 12/6 = 12/12 13/12 14/12 15/12 16/12 17/12 18/12 19/12
> 20/12 21/12 22/12 23/12 24/12 = 24/24 etc
> >
> > Same as before, you will see natural microtuning occur in every> series with nested values throughout each system/ Of course you
> will see sharing of ratios with standard nhs tuning iin many
> places...that allows you to modulate from one series to another.
> >
> > how do you like me now?
>
> That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
> 12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
> omitted, and transposed.
>
> -Mike
>
>
> ------------------------------------
>
> 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.
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> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>
>
>
>

Tim

Are you familiar with
https://sites.google.com/site/240edo/arithmeticrationaldivisionsofoctave ?

DanN

On Wed, Jul 6, 2011 at 12:32 PM, Steve Parker <steve@...> wrote:

> **
>
>
> Can you at all justify the word 'harmonic' in this? We really should
> reserve that word for the infinite series 1 + 1/2 + 1/3 +1/4 + 1/5 . . . . .
> which describes the overtones of a vibrating string's fundamental.
> I'm not sure that the word 'series' applies either.
>
> Microtonal music theory is DITW if anyone can call anything anything..
>
> Steve P.
>
> On 6 Jul 2011, at 17:51, Tim Reeves wrote:
>
>
> Mike
>
> I have had time to come to my senses on this. Please look at the following
> and tell me how you equate your statement with my post.
>
> Hz
>
> Hz
>
> 1
>
> 6/6
>
> 6
>
> 6/1
>
> 1.166666667
>
> 7/6
>
> 7
>
> 7/1
>
> 1.333333333
>
> 8/6
>
> 8
>
> 8/1
>
> 1.5
>
> 9/6
>
> 9
>
> 9/1
>
> 1.666666667
>
> 10/6
>
> 10
>
> 10/1
>
> 1.833333333
>
> 11/6
>
> 11
>
> 11/1
>
> 2
>
> 12/6
>
> 12
>
> 12/1
>
> My claim of more than one nhs doesn't mean that this is a new invention of
> a number series
> ie 1 2 3 but is in fact an extension of a process, (the one I use to
> define natural scales), that will yield an infinity of musical scales and
> interval values.
>
> This might explain the difference in our reasoning:
>
> In describing a ratio for musical purposes I state that when you have a
> ratio such as 9/8 or m/n, the top number or m = the number value of the
> harmonic in the sequence
> and the bottom number, or n = the number of notes in the octave at that
> point in the series.
>
> So, if I tried to apply this reasoning to the scale you reduced down to,
> there would be 1 note in the octave...all I see here is a simple numeric
> series, not a similar or equal musical scale .. Maybe you could elaborate
> and I could see your point.
> Thanks
> Tim
>
> --- On *Tue, 7/5/11, Tim Reeves <reevest360@...>* wrote:
>
>
> From: Tim Reeves <reevest360@...>
> Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64
> program
> To: tuning@yahoogroups.com
> Date: Tuesday, July 5, 2011, 6:43 PM
>
>
>
> Mike
>
> That may very well be the case, still working on it to see what's up
> in applying the process. Do you think there is a difference when it is
> applied to all primes or do you suspect that they all can be reduced to
> values of 1
>
> Anyway, I find this very interesting.
> Thanks
> Tim
>
> --- On *Tue, 7/5/11, Mike Battaglia <battaglia01@...>* wrote:
>
>
> From: Mike Battaglia <battaglia01@...>
> Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64
> program
> To: tuning@yahoogroups.com
> Date: Tuesday, July 5, 2011, 5:57 PM
>
> On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@...<http://us.mc1202.mail.yahoo.com/mc/compose?to=reevest360@...>>
> wrote:
> >
> > Ok Steve, check this out, you may eventually find where all those strange
> ratios come from...
> >
> > (1/3 2/3) 3/3 4/3 5/3 6/3 = 6/6 7/6 8/6 9/6 10/6 11/6
> 12/6 = 12/12 13/12 14/12 15/12 16/12 17/12 18/12 19/12 20/12 21/12
> 22/12 23/12 24/12 = 24/24 etc
> >
> > Same as before, you will see natural microtuning occur in every series
> with nested values throughout each system/ Of course you will see sharing
> of ratios with standard nhs tuning iin many places...that allows you to
> modulate from one series to another.
> >
> > how do you like me now?
>
> That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
> 12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
> omitted, and transposed.
>
> -Mike
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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> - receive general help information.
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>
>
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>
>
>
>
>
>
>

On Wed, Jul 6, 2011 at 12:51 PM, Tim Reeves <reevest360@...> wrote:
>
> This might explain the difference in our reasoning:
>
> In describing a ratio for musical purposes  I state that when you have a ratio such as 9/8 or m/n, the top number or m = the number value of the harmonic in the sequence
>  and the bottom number, or  n = the number of notes in the octave at that point in the series.

These ratios signify different just intervals. That's all. 5/4 is 386
cents, 3/2 is 702 cents, 4/3 is 498 cents. You get a 5/4 by looking at
the difference between the fifth and fourth harmonics in a harmonic
series. 6/6 7/6 8/6 9/6 10/6 is not a different harmonic series than
6/1 7/1 8/1 9/1 10/1, because all of this is relative.

> So, if I tried to apply this reasoning to the scale you reduced down to, there would be 1 note in the octave...all I see here is a simple numeric series, not a similar or equal musical scale .. Maybe you could elaborate and I could see your point.

So what happens if I want to talk about the interval that is an octave
plus a major third? I'd get 5/2.

Musical scales are not only derived from the harmonic series. The fact
that you have chosen to explore subsets of the harmonic series for
scale construction is great, but it's not the only way to go.

-Mike

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> In musical set theory, sets start with "0", not "1".
>
> When measuring intervals by cents, we start from 0, not 1.
>
> String players, in practice, effectively work from "zero", the open string, and have for millenia. First finger is first finger (fret), not open string. In fact, some fretted string instruments which try to avoid intonational inconsistencies caused by varying string heights and lengths due to vagaries at the nut slots have an extra fret (technically probably a bridge) over which the open strings are strung. Guess what it's called? A "zero fret".
>
> "Music" and "physics" is not a dichotomy. You display gross ignorance of, or woeful failure to comprehend, the history of music- especially the history of "microtonal" music- when you make such statements. Stop with these hysterical black-and-white perceptions, child.

1 is the first natural number. It represents a unity, as opposed to 0 which represents a lack of something or a null operator. Any number multiplied by 1 is itself, and therefore retains identity. When classifying different intervals on the piano (major third, perfect fifth, minor tenth, etc) the unison falls under class 1. There is no 0 class on the piano, and there never has been. When playing a C major scale, the first note you press is the tonic. All common practice theory uses 1 to designate the beginning of a scale, no exceptions.

See? I can handwave just as well as you.

--- In tuning@yahoogroups.com, "domeofatonement" <domeofatonement@...> wrote:

> 1 is the first natural number. It represents a unity, as opposed to 0 which represents a lack of something or a null operator.

There's no agreement that 1 is the first natural number; sometimes the phrase is used to include 0. The reason for this is that 0 is a cardinal number; it counts the number of elements in a set, and is the smallest cardinal.

>
> 1 is the first natural number. It represents a unity, as opposed to 0 which
> represents a lack of something or a null operator.
>

What does a unity have to do with anything?

> Any number multiplied by 1 is itself, and therefore retains identity.
>

Logarithmic degrees are additive, not multiplicative.

> When classifying different intervals on the piano (major third, perfect
> fifth, minor tenth, etc) the unison falls under class 1. There is no 0 class
> on the piano, and there never has been.
>

There is and there has been.

> When playing a C major scale, the first note you press is the tonic.
>

The ascending, anyway. That's the best argument so far, but if you hold down
tonic and play the scale the zero-centered represents all the intervals.

> All common practice theory uses 1 to designate the beginning of a scale, no
> exceptions.
>

That's not really true, and that's the entire reason for this discussion in
the first place.

>"1 is the first natural number. It represents a unity, as opposed to 0
which represents a lack of something or a null operator. Any number
multiplied by 1 is itself, and therefore retains identity."

   General comment...it appalls me to see how much effort this list is putting into arguing whether we should use 0 or 1 to denote sets, scale steps/notes, etc.  It's like dealing with people who argue of the first element in an array should be denoted as 0 or 1...or if a null terminated string should have an actual character with a value of null at the end that has to be manually inputted vs. having the programming language handle that automatically.

  In the end, it seems you're just rephrasing the same concept and getting the same end result regardless.  If anything, 1 IE the "automated option" seems slightly easier to use, though that certainly doesn't make the other option incorrect for those who prefer to use it.

   If I call a unison 1 instead of 0...does it sound any different?  If a call an octave 2/1 vs. 1200 cents, does it sound any different?  What's the point in how these actually apply to, ahem, making music sound better?

  And so on and so forth.  At what point do these arguments translate to how things sound to people, from this current day onward?  Say you give me a scale generation system...how would 0 act differently in generating that system than 1?  If someone says "it should be done this way because that was what has been done historically..." what are the reasons behind these historical usages that can also help us today?

--- On Wed, 7/6/11, domeofatonement <domeofatonement@...> wrote:

From: domeofatonement <domeofatonement@...>
Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Wednesday, July 6, 2011, 3:22 PM

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

>

> In musical set theory, sets start with "0", not "1".

>

> When measuring intervals by cents, we start from 0, not 1.

>

> String players, in practice, effectively work from "zero", the open string, and have for millenia. First finger is first finger (fret), not open string. In fact, some fretted string instruments which try to avoid intonational inconsistencies caused by varying string heights and lengths due to vagaries at the nut slots have an extra fret (technically probably a bridge) over which the open strings are strung. Guess what it's called? A "zero fret".

>

> "Music" and "physics" is not a dichotomy. You display gross ignorance of, or woeful failure to comprehend, the history of music- especially the history of "microtonal" music- when you make such statements. Stop with these hysterical black-and-white perceptions, child.

1 is the first natural number. It represents a unity, as opposed to 0 which represents a lack of something or a null operator. Any number multiplied by 1 is itself, and therefore retains identity. When classifying different intervals on the piano (major third, perfect fifth, minor tenth, etc) the unison falls under class 1. There is no 0 class on the piano, and there never has been. When playing a C major scale, the first note you press is the tonic. All common practice theory uses 1 to designate the beginning of a scale, no exceptions.

See? I can handwave just as well as you.

I hold no opinion in this particular debate, as I see the merits of both sides, but I'd like to pose a thought experiment (and break it down in detail even though it will probably be fairly self-evident, so feel free to skim) to demonstrate the relevance and importance of the debate itself.

Consider a pentatonic scale of some kind -- any kind. Now suppose you are going to map it to the black keys of a MIDI keyboard (certainly a plausible scenario). Now, even though the ACTUAL PITCHES produced will not be affected, consider the ways your compositions or improvisations might be influenced by putting one of the pitches on the C#/Db key as opposed to the F#/Gb key. Thinking of that pitch as the base of the scale, the third pitch of the scale would then be either above or below the physical gap in the keys. Of course, putting that base pitch on any of the three remaining keys instead would have a similar influence, each of its own distinctive character.

Conceptually, it should make no difference -- but how many compositions are written completely without ever laying hands on an instrument? How easy is it to get a feel for a new scale without *feeling* it physically, up and down, stepwise and skipwise, intervals and chords, at the speed of thought? The physical manifestation of a scale on an instrument means the nature of the instrument is going to influence your perception of it. Even if the distance in cents from C#/Db to D#/Eb was the same as the distance from D#/Eb to F#/Gb, the latter could easily *feel* wider, and thereby influence the way you use those two intervals.

Therefore, I could easily see conceptualizing the diatonic scale (for example) as pitch classes 0-6 versus 1-7 having an impact on a musician's work, even if objectively they refer to the same things.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"1 is the first natural number. It represents a unity, as opposed to 0
> which represents a lack of something or a null operator. Any number
> multiplied by 1 is itself, and therefore retains identity."
>
>    General comment...it appalls me to see how much effort this list is putting into arguing whether we should use 0 or 1 to denote sets, scale steps/notes, etc.  It's like dealing with people who argue of the first element in an array should be denoted as 0 or 1...or if a null terminated string should have an actual character with a value of null at the end that has to be manually inputted vs. having the programming language handle that automatically.
>
>   In the end, it seems you're just rephrasing the same concept and getting the same end result regardless.  If anything, 1 IE the "automated option" seems slightly easier to use, though that certainly doesn't make the other option incorrect for those who prefer to use it.
>
>
>    If I call a unison 1 instead of 0...does it sound any different?  If a call an octave 2/1 vs. 1200 cents, does it sound any different?  What's the point in how these actually apply to, ahem, making music sound better?
>
>   And so on and so forth.  At what point do these arguments translate to how things sound to people, from this current day onward?  Say you give me a scale generation system...how would 0 act differently in generating that system than 1?  If someone says "it should be done this way because that was what has been done historically..." what are the reasons behind these historical usages that can also help us today?
>
>
>
>
>
>
> --- On Wed, 7/6/11, domeofatonement <domeofatonement@...> wrote:
>
> From: domeofatonement <domeofatonement@...>
> Subject: [tuning] Re: Clarification of my comments on Igs' 32-64 program
> To: tuning@yahoogroups.com
> Date: Wednesday, July 6, 2011, 3:22 PM
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>  
>
>
>
>
>
>
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> >
>
> > In musical set theory, sets start with "0", not "1".
>
> >
>
> > When measuring intervals by cents, we start from 0, not 1.
>
> >
>
> > String players, in practice, effectively work from "zero", the open string, and have for millenia. First finger is first finger (fret), not open string. In fact, some fretted string instruments which try to avoid intonational inconsistencies caused by varying string heights and lengths due to vagaries at the nut slots have an extra fret (technically probably a bridge) over which the open strings are strung. Guess what it's called? A "zero fret".
>
> >
>
> > "Music" and "physics" is not a dichotomy. You display gross ignorance of, or woeful failure to comprehend, the history of music- especially the history of "microtonal" music- when you make such statements. Stop with these hysterical black-and-white perceptions, child.
>
>
>
> 1 is the first natural number. It represents a unity, as opposed to 0 which represents a lack of something or a null operator. Any number multiplied by 1 is itself, and therefore retains identity. When classifying different intervals on the piano (major third, perfect fifth, minor tenth, etc) the unison falls under class 1. There is no 0 class on the piano, and there never has been. When playing a C major scale, the first note you press is the tonic. All common practice theory uses 1 to designate the beginning of a scale, no exceptions.
>
>
>
> See? I can handwave just as well as you.
>

On Wed, Jul 6, 2011 at 9:16 PM, Michael <djtrancendance@...> wrote:
>
> >"1 is the first natural number. It represents a unity, as opposed to 0 which represents a lack of something or a null operator. Any number multiplied by 1 is itself, and therefore retains identity."
>
>    General comment...it appalls me to see how much effort this list is putting into arguing whether we should use 0 or 1 to denote sets, scale steps/notes, etc.  It's like dealing with people who argue of the first element in an array should be denoted as 0 or 1...or if a null terminated string should have an actual character with a value of null at the end that has to be manually inputted vs. having the programming language handle that automatically.

Seriously. Are we going to start arguing about if red is more
masculine than blue next? I can't believe this discussion is actually
occurring.

-Mike

On Wed, Jul 6, 2011 at 10:59 PM, Jay Random <cortaigne@...> wrote:
>
> Conceptually, it should make no difference -- but how many compositions are written completely without ever laying hands on an instrument? How easy is it to get a feel for a new scale without *feeling* it physically, up and down, stepwise and skipwise, intervals and chords, at the speed of thought? The physical manifestation of a scale on an instrument means the nature of the instrument is going to influence your perception of it. Even if the distance in cents from C#/Db to D#/Eb was the same as the distance from D#/Eb to F#/Gb, the latter could easily *feel* wider, and thereby influence the way you use those two intervals.
>
> Therefore, I could easily see conceptualizing the diatonic scale (for example) as pitch classes 0-6 versus 1-7 having an impact on a musician's work, even if objectively they refer to the same things.

If we're talking about the cognitive benefits of referring to a scale
as starting from 1 vs starting from 0, that's at least more
substantive of a discussion than whether 0 or 1 is more natural.

Either way, my opinion is - the convention is to start from 1, so
that's what it should be. It is not the 0 chord, it is the I chord. If
we want to explore different systems just for the hell of it, great.
But it really doesn't matter how easy or how hard it is to think of
something, because musicians are not normal people. They will spend
years learning to figure things out no matter how hard they are. This
forum is living proof of it. So at the end of the day, it doesn't
really matter.

Frankly, the entire numbering system is completely broken even in
12-equal other than meantone - b6 and #5 are the same thing, and when
you get into the octatonic scale or the augmented scale, they're
really the same thing. People end up working it out nonetheless.

-Mike

>"If we're talking about the cognitive benefits of referring to a scale as starting from 1 vs starting from 0, that's at least more substantive of a discussion than whether 0 or 1 is more natural."

   It seems like a pretty lousy conundrum....but I think it has already been solved.

  Starting from 0 makes the note an octave ABOVE -12 (for a 12-tone scale) while the note an octave above is also 12...this is easy, because 0 is the center of the number line).

   However, when it comes to actual frequency ratios that represent these notes...the octave 2/1 certainly is not 2 times 0/1...making 0 very hard to digest in analyzing fractional relationships.

--------------------

  What would make sense here, to me, is a logarithmic system that started at zero but, when then logarithm was taken in fractional form, made 0 represent a 1/1 IE (x^0 = 1).

  Oh wait...we already have one of those, the traditional cent (although, as we've debated before, something like a 72EDO or 19EDO cent could also work this way).  The
only thing (perhaps sadly) is that many musicians don't think of notes by root and difference/gaps in cents, but as the "xth step of the scale".  They think C#-D as "1-2" or "2-3" and not "100-200")

>"Even if the distance in cents from C#/Db to D#/Eb was the same as the
distance from D#/Eb to F#/Gb, the latter could easily *feel* wider, and
thereby influence the way you use those two intervals."

   Very true...but I'd suggest representing cents as a distance from the middle C, rather than from the root of a scale and then taking the actual root/register, rather than just the numbered interval o the scale, as a factor in how the scale sounds.  That way your C#-D# gap and D#-F# gaps having different registers/root would show up numerically.
 

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"If we're talking about the cognitive benefits of referring to a scale as starting from 1 vs starting from 0, that's at least more substantive of a discussion than whether 0 or 1 is more natural."
>
>    It seems like a pretty lousy conundrum....but I think it has already been solved.

If you really want the point of view which makes th most cognative/conceptual sense, I vote for this:

http://xenharmonic.wikispaces.com/Periodic+scale

But of course making the most sense from a mathematical point of view is hardly the only consideration.

Hi Mike
 
>>>Thanks for taxing my brain, this is a good workout and causes me to reflect on theory I haven't even considered for over 15 years. I have some real studying to get back to. Our conversation has to be very fluid, moving back and forth between the natural and physical and then to conceptual or strictly theoretical. Sometimes the line blurs. there will be areas of "understood movements" where we don't even explain where we are coming from. That is cool and certainly part of the process.
 
It is true that music is relative (on a universal basis).  Harmony, ie the full spectrum of tonality from consonance to dissonance, is relative to the sharing of math properties between one set or scale and another. This proves itself as you compare one scale with another...also one process or treatment and another. It doesn't do much good to argue over the validity of one procedure over another, because, like you said it is all relative ...so, we do need to be open to any system for the reason of comparative study, if for no other.
 
Strict interpretation of systems like equal temperament or just intonation may yield fixed results, but  doesn't even begin to touch on all the other data that is available. The same can be said for the interpretation of natural scales derived from the nhs. Complete music study screams out that we should be open minded.
 
Going from math that includes addition, subtraction, multiplication and division,  moving into algebra, geometry, and trigonometry, doesn't even come close to the world of calculus and advanced physics. It is mind blowing to think that there are imaginary sets and numbers in music study, the same can be said for imaginary processes and treatments applied on all levels.
 
That said, I would like to say that I am open to the concept that the letter values we commonly associate with music do indeed  have multiple values when we apply them to multiple systems...

(A ) B C in 12tet does not have the same value as ( A) B C in a Base 11 natural scale.  Also ratios in one system do take on other interval values in multiple systems.  I've already shown how what is commonly known as a "major scale step" can become a "quarter tone value" when applied in another tuning system. 
 
See what I mean about being open minded?  For instance, by being open minded,  I can accept your position that multiple base natural scales are a subset of the broader picture of the nhs   WIth an understanding of both lineal and exponetial scales in my musical background, I do agree that there isn't just one way to go in this whole thing.
 
Thanks again
Tim

--- On Wed, 7/6/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Wednesday, July 6, 2011, 6:47 PM

On Wed, Jul 6, 2011 at 12:51 PM, Tim Reeves <reevest360@...> wrote:
>
> This might explain the difference in our reasoning:
>
> In describing a ratio for musical purposes  I state that when you have a ratio such as 9/8 or m/n, the top number or m = the number value of the harmonic in the sequence
>  and the bottom number, or  n = the number of notes in the octave at that point in the series.

These ratios signify different just intervals. That's all. 5/4 is 386
cents, 3/2 is 702 cents, 4/3 is 498 cents. You get a 5/4 by looking at
the difference between the fifth and fourth harmonics in a harmonic
series. 6/6 7/6 8/6 9/6 10/6 is not a different harmonic series than
6/1 7/1 8/1 9/1 10/1, because all of this is relative.

> So, if I tried to apply this reasoning to the scale you reduced down to, there would be 1 note in the octave...all I see here is a simple numeric series, not a similar or equal musical scale .. Maybe you could elaborate and I could see your point.

So what happens if I want to talk about the interval that is an octave
plus a major third? I'd get 5/2.

Musical scales are not only derived from the harmonic series. The fact
that you have chosen to explore subsets of the harmonic series for
scale construction is great, but it's not the only way to go.

-Mike

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I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.
Is it safe to return to the list now?;-)

If so, maybe we can get on much better without his tyranny, and some of the other microtonalists who share my intolerance of his "authority" will return.

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can found at:

http://www.lullabies.co.uk

Yes I am familiar with what I saw,  though, not the exact study or source..Looks like we are not alone in this universe of study, but it has been difficult to find people who travel this road until David Doty pointed me to this tuning group.  I really like this and would love to follow threads all the time but it is very time consuming ...after all, I do need to get back to actually composing etc 
 
It would be great if a moderator could pick out the most significant posts and file them on a separate page that could be reviewed on a daily , weekly or monthly basis. I have saved several hundred posts for review already and think this is a fantastic source of info and conversation.
 
Thanks to all
Tim
--- On Wed, 7/6/11, Daniel Nielsen <nielsed@...> wrote:

From: Daniel Nielsen <nielsed@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Wednesday, July 6, 2011, 6:04 PM

Tim

Are you familiar with https://sites.google.com/site/240edo/arithmeticrationaldivisionsofoctave ?

DanN

On Wed, Jul 6, 2011 at 12:32 PM, Steve Parker <steve@...> wrote:

Can you at all justify the word 'harmonic' in this? We really should reserve that word for the infinite series 1 + 1/2 + 1/3 +1/4 + 1/5 . . . . .  which describes the overtones of a vibrating string's fundamental.
I'm not sure that the word 'series' applies either.

Microtonal music theory is DITW if anyone can call anything anything..

Steve P.

On 6 Jul 2011, at 17:51, Tim Reeves wrote:

Mike
 
I have had time to come to my senses on this. Please look at the following and tell me how you equate your statement with my post.

Hz

Hz

1

6/6

6

6/1

1.166666667

7/6

7

7/1

1.333333333

8/6

8

8/1

1.5

9/6

9

9/1

1.666666667

10/6

10

10/1

1.833333333

11/6

11

11/1

2

12/6

12

12/1

My claim of more than one nhs doesn't mean that this is a new invention of a number series
ie 1 2 3  but is in fact an extension of a process, (the one I use to define natural scales),  that will yield an infinity of musical scales and interval values. 
 
This might explain the difference in our reasoning:
 
In describing a ratio for musical purposes  I state that when you have a ratio such as 9/8 or m/n, the top number or m = the number value of the harmonic in the sequence
 and the bottom number, or  n = the number of notes in the octave at that point in the series.
 
So, if I tried to apply this reasoning to the scale you reduced down to, there would be 1 note in the octave...all I see here is a simple numeric series, not a similar or equal musical scale .. Maybe you could elaborate and I could see your point.
Thanks
Tim
 
--- On Tue, 7/5/11, Tim Reeves <reevest360@...> wrote:

From: Tim Reeves <reevest360@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 6:43 PM

Mike
 
That may very well be the case, still working on it to see what's up in applying  the process. Do you think there is a difference when it is applied to all primes or do you suspect that they all can be reduced to values of 1
 
Anyway, I find this very interesting.
Thanks
Tim
 
--- On Tue, 7/5/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Tuesday, July 5, 2011, 5:57 PM

On Mon, Jul 4, 2011 at 9:54 PM, Tim Reeves <reevest360@yahoo.com> wrote:
>
> Ok Steve, check this out, you may eventually find where all those strange ratios come from...
>
> (1/3  2/3)   3/3  4/3  5/3  6/3  =   6/6  7/6  8/6  9/6  10/6  11/6  12/6  = 12/12  13/12  14/12  15/12 16/12  17/12  18/12  19/12  20/12  21/12  22/12 23/12  24/12 = 24/24 etc
>
> Same as before, you will see natural microtuning occur in every series with nested values throughout each system/   Of course you will see sharing of ratios with standard nhs tuning iin many places...that allows you to modulate from one series to another.
>
> how do you like me now?

That's still just a normal harmonic series. 6/6 7/6 8/6 9/6 10/6 11/6
12/6 is the same as 6/1 7/1 8/1 9/1 10/1 11/1 12/1, with harmonics 1-6
omitted, and transposed.

-Mike

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Hello Mr Lucy
 
It is an honor to have you in our midst!!!!  Of course you are welcome as far as I am concerned. Feel free to contact me anytime...wowwwww!
 
Tim

--- On Thu, 7/7/11, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: [tuning] Has Lumma now gone altogether?
To: tuning@yahoogroups.com
Date: Thursday, July 7, 2011, 11:33 AM

I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.
Is it safe to return to the list now?;-)

If so, maybe we can get on much better without his tyranny, and some of the other microtonalists who share my intolerance of his "authority" will return.

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can found at:

http://www.lullabies.co.uk

Charles>"I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.Is it safe to return to the list now?;-)"
  

  To Carl's credit...I haven't often found him acting like tyrant for the most part at least for the past couple of months, if not more...minus an occasional "it is because it is" viewpoint against Mike B.
    There have been a few nasty off-topic comments about Marcel (when he's not even on the list) but, other than that, things have been surprisingly mature on here (if not overly exciting) lately.  Perhaps some people have learned that cracking a whip and name-calling on other people is not a good way to convince them to admire or even vaguely respect their opinions.  Anyhow, point is...the list is shaping up, in many ways, and we need you and other people tired of the gossip and the name-calling back on it. :-)

--- On Thu, 7/7/11, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: [tuning] Has Lumma now gone altogether?
To: tuning@yahoogroups.com
Date: Thursday, July 7, 2011, 4:33 AM

I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.Is it safe to return to the list now?;-)

If so, maybe we can get on much better without his tyranny, and some of the other microtonalists who share my intolerance of his "authority" will return.

Charles Lucylucy@...
-- Promoting global harmony through LucyTuning --
For more information on LucyTuning go to:
http://www.lucytune.com
LucyTuned Lullabies (from around the world) can found at:
http://www.lullabies.co.uk

On Thu, Jul 7, 2011 at 11:34 AM, Tim Reeves <reevest360@...> wrote:
>
> It is true that music is relative (on a universal basis).  Harmony, ie the full spectrum of tonality from consonance to dissonance, is relative to the sharing of math properties between one set or scale and another. This proves itself as you compare one scale with another...also one process or treatment and another. It doesn't do much good to argue over the validity of one procedure over another, because, like you said it is all relative ...so, we do need to be open to any system for the reason of comparative study, if for no other.

You can think of things however you'd like - if you prefer to think of
7/4 as being a single note in a 4-note scale, you are free to do so.
However, we need to communicate, and around here, the convention that
has been used since I've joined, and in the decade and a half prior,
and in all of the music theory literature I've ever seen on the
subject, is that 7/4 just signifies an interval. So it's confusing if
you now want to impose an alternate terminology. And even so, if you
want something like 7/4 to signify a scale, how are we supposed to
refer to JI intervals?

> Strict interpretation of systems like equal temperament or just intonation may yield fixed results, but  doesn't even begin to touch on all the other data that is available. The same can be said for the interpretation of natural scales derived from the nhs. Complete music study screams out that we should be open minded.

We're not all about equal temperaments or JI. Most of the research on
this list has to do with temperaments in between those. Paul Erlich's
A Middle Path paper would be a good read:
http://sethares.engr.wisc.edu/paperspdf/Erlich-MiddlePath.pdf

> Going from math that includes addition, subtraction, multiplication and division,  moving into algebra, geometry, and trigonometry, doesn't even come close to the world of calculus and advanced physics. It is mind blowing to think that there are imaginary sets and numbers in music study, the same can be said for imaginary processes and treatments applied on all levels.

Let's not forget multilinear algebra and group theory. Perhaps it'll
help you understand the state of the union if you can see the
wavelength we're on:

http://xenharmonic.wikispaces.com/Mathematical+Theory

> That said, I would like to say that I am open to the concept that the letter values we commonly associate with music do indeed  have multiple values when we apply them to multiple systems...
> (A ) B C in 12tet does not have the same value as ( A) B C in a Base 11 natural scale.  Also ratios in one system do take on other interval values in multiple systems.  I've already shown how what is commonly known as a "major scale step" can become a "quarter tone value" when applied in another tuning system.
>
> See what I mean about being open minded?  For instance, by being open minded,  I can accept your position that multiple base natural scales are a subset of the broader picture of the nhs   WIth an understanding of both lineal and exponetial scales in my musical background, I do agree that there isn't just one way to go in this whole thing.

You would probably be interested in one of these phi-based
faux-harmonic series. Check out 1:1+phi:1+2*phi:1+3*phi:etc.

-Mike

On Thu, Jul 7, 2011 at 7:33 AM, Charles Lucy <lucy@...> wrote:
>
> I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.
>
> Is it safe to return to the list now?;-)
>
> If so, maybe we can get on much better without his tyranny, and some of the other microtonalists who share my intolerance of his "authority" will return.

Carl and his tyranny are both still here. However, I'm even more of a
tyrant than Carl is - I think everyone here can testify that I
tyrannize the population of this list often and without restraint. So
you better keep your guard up.

You are welcome back at any time, but the word "pi" has been banned
from these forums. Even mentioning it is grounds for an immediate ban.
It's true. OK, relax, I'm just joking.

Mike Battaglia
Tyrannical Moderator.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> General comment...it appalls me to see how much effort this list is putting into arguing whether we should use 0 or 1 to denote sets, scale steps/notes, etc.  It's like dealing with people who argue of the first element in an array should be denoted as 0 or 1...or if a null terminated string should have an actual character with a value of null at the end that has to be manually inputted vs. having the programming language handle that automatically.

I guess people missed the hint of sarcasm in my last message.

I totally agree, that regardless if you call it 0 or 1, 2/1 or 1200, etc... both describe the same thing. The true difference lies in whether you choose to look at it from a melodic/logarithmic perspective or a harmonic/arithmetic perspective.

-Ryan

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

> If we're talking about the cognitive benefits of referring to a scale
> as starting from 1 vs starting from 0, that's at least more
> substantive of a discussion than whether 0 or 1 is more natural.

The original "argument", if it could be dignified with such a description, was not about what is natural, better, etc. Look back to the beginning and you'll see that it was simply I correcting the false
blanket statement that musicians count from 1 and physicists from 0.

There are several places in which musicians count from 0 (and I'm sure physicists count from 1 in some places too, LOL). A 12-tET major triad described in cents is 0-400-700, not 1- 401-701. Set theory (as it is called, it's better to distinguish it as musical set theory to avoid confusion)counts from zero. And so on.

The statement was simply... false.

There is no need for foggy speculation- there are long, strong functioning of traditions of where and when musicians count from 1 (most cases) or 0 (some cases). In all cases, as far as I know, the most reasonable method is used. Gene could probably argue thoughtfully otherwise, and I'm looking forward to reading his proposals, but only sheer ignorance is fuelling most of the speculation.

Everyone is eventually going to check the facts on this and see that I'm simply stating the way things are. So, the passions of internet sophistry are going to demand taking another tack. The most predictable one is to create yet more fictitious dichotomies- in this case, the first thing for an internet bullshit artist would be to seperate "musicians" from "theorists". This would cross Ornette Coleman, Wagner, Rimsky-Korsakov, etc. off the list of "musicians", but that's not going to deter the less thoughtful.

Cuthaliciously yours,
da Lob

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> Gene could probably argue thoughtfully otherwise, and I'm looking forward to reading his proposals, but only sheer ignorance is fuelling most of the speculation.

I already gave my point of view, which is that if you are interested in conceptual usefulness, viewing scales as quasiperiodic functions (in the mathematician's sense of that word) is the approach which makes the theory easiest. That doesn't mean musicians have to think that way, but I'd recommend it to scale theorists.

On Thu, Jul 7, 2011 at 7:15 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> > Gene could probably argue thoughtfully otherwise, and I'm looking forward to reading his proposals, but only sheer ignorance is fuelling most of the speculation.
>
> I already gave my point of view, which is that if you are interested in conceptual usefulness, viewing scales as quasiperiodic functions (in the mathematician's sense of that word) is the approach which makes the theory easiest. That doesn't mean musicians have to think that way, but I'd recommend it to scale theorists.

OK, I said this, and you said they weren't quasiperiodic functions.
Now they are. And from all of the definitions on this page:

http://en.wikipedia.org/wiki/Quasiperiodic_function

It looks like they should be fully periodic functions, not quasiperiodic. No?

-Mike

Hi Mike
 
Thank you for the links to work with...the terminology update for me will certainly help in communicating with the group... I'm definitely into learning new concepts so I'll keep reading.
 
As far as the methods I have been using, I can imagine it isn't easy to get where I'm heading in a snap shot that can be posted here...so I really want to complete an exhaustive study that will better represent those ideas..  
 
BTW It is encouraging to know that there are people like you that are pursuing musical knowledge on a higher level  and using it in their daily lives.
 
Thanks
Tim
--- On Thu, 7/7/11, Mike Battaglia <battaglia01@...m> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Clarification of my comments on Igs' 32-64 program
To: tuning@yahoogroups.com
Date: Thursday, July 7, 2011, 6:01 PM

On Thu, Jul 7, 2011 at 11:34 AM, Tim Reeves <reevest360@...> wrote:
>
> It is true that music is relative (on a universal basis).  Harmony, ie the full spectrum of tonality from consonance to dissonance, is relative to the sharing of math properties between one set or scale and another. This proves itself as you compare one scale with another...also one process or treatment and another. It doesn't do much good to argue over the validity of one procedure over another, because, like you said it is all relative ...so, we do need to be open to any system for the reason of comparative study, if for no other.

You can think of things however you'd like - if you prefer to think of
7/4 as being a single note in a 4-note scale, you are free to do so.
However, we need to communicate, and around here, the convention that
has been used since I've joined, and in the decade and a half prior,
and in all of the music theory literature I've ever seen on the
subject, is that 7/4 just signifies an interval. So it's confusing if
you now want to impose an alternate terminology. And even so, if you
want something like 7/4 to signify a scale, how are we supposed to
refer to JI intervals?

> Strict interpretation of systems like equal temperament or just intonation may yield fixed results, but  doesn't even begin to touch on all the other data that is available. The same can be said for the interpretation of natural scales derived from the nhs. Complete music study screams out that we should be open minded.

We're not all about equal temperaments or JI. Most of the research on
this list has to do with temperaments in between those. Paul Erlich's
A Middle Path paper would be a good read:
http://sethares.engr.wisc.edu/paperspdf/Erlich-MiddlePath.pdf

> Going from math that includes addition, subtraction, multiplication and division,  moving into algebra, geometry, and trigonometry, doesn't even come close to the world of calculus and advanced physics. It is mind blowing to think that there are imaginary sets and numbers in music study, the same can be said for imaginary processes and treatments applied on all levels.

Let's not forget multilinear algebra and group theory. Perhaps it'll
help you understand the state of the union if you can see the
wavelength we're on:

http://xenharmonic.wikispaces.com/Mathematical+Theory

> That said, I would like to say that I am open to the concept that the letter values we commonly associate with music do indeed  have multiple values when we apply them to multiple systems...
> (A ) B C in 12tet does not have the same value as ( A) B C in a Base 11 natural scale.  Also ratios in one system do take on other interval values in multiple systems.  I've already shown how what is commonly known as a "major scale step" can become a "quarter tone value" when applied in another tuning system.
>
> See what I mean about being open minded?  For instance, by being open minded,  I can accept your position that multiple base natural scales are a subset of the broader picture of the nhs   WIth an understanding of both lineal and exponetial scales in my musical background, I do agree that there isn't just one way to go in this whole thing.

You would probably be interested in one of these phi-based
faux-harmonic series. Check out 1:1+phi:1+2*phi:1+3*phi:etc.

-Mike

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LOL wow what a group...I love it!

--- On Thu, 7/7/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Has Lumma now gone altogether?
To: tuning@yahoogroups.com
Date: Thursday, July 7, 2011, 5:43 PM

On Thu, Jul 7, 2011 at 7:33 AM, Charles Lucy <lucy@...> wrote:
>
> I have had a quick look at the recent posts here, and notice that Lumma seems to have disappeared.
>
> Is it safe to return to the list now?;-)
>
> If so, maybe we can get on much better without his tyranny, and some of the other microtonalists who share my intolerance of his "authority" will return.

Carl and his tyranny are both still here. However, I'm even more of a
tyrant than Carl is - I think everyone here can testify that I
tyrannize the population of this list often and without restraint. So
you better keep your guard up.

You are welcome back at any time, but the word "pi" has been banned
from these forums. Even mentioning it is grounds for an immediate ban.
It's true. OK, relax, I'm just joking.

Mike Battaglia
Tyrannical Moderator.

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

> OK, I said this, and you said they weren't quasiperiodic functions.
> Now they are.

I think you've gotten what happened confused.

And from all of the definitions on this page:
>
> http://en.wikipedia.org/wiki/Quasiperiodic_function
>
> It looks like they should be fully periodic functions, not quasiperiodic. No?

No. They fit the definition you see there perfectly, so I don't see what the problem is.

2011/7/7 genewardsmith <genewardsmith@...>:
>
> I think you've gotten what happened confused.
>
>  And from all of the definitions on this page:
>>
>> http://en.wikipedia.org/wiki/Quasiperiodic_function
>>
>> It looks like they should be fully periodic functions, not quasiperiodic. No?
>
> No. They fit the definition you see there perfectly, so I don't see what the problem is.

OK, I see what's going on. The derivative of the function should be
periodic, right?

-Mike

In the immortal words of Laurence Welk:

And a 0
And a 1
And a 0, 1, 2, 3....

On Fri, Jul 8, 2011 at 9:43 AM, <Afmmjr@...> wrote:

> **
>
>
> **
> In the immortal words of Laurence Welk:
>
> And a 0
> And a 1
> And a 0, 1, 2, 3....
>

When reading a .scl file, defining as one is basically like saying "a 2, and
a 3, and a 2,3,4,5".

I think the real point is that pitch perception is (basically) logarithmic,
so centering at 1 doesn't describe the log-linear perceptual relationship
terribly well; although, unlike some other logarithmic perceptions (like
weight judgement), there is no clear logical baseline point at which pitch
is nonexistent.

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

> OK, I see what's going on. The derivative of the function should be
> periodic, right?

Assuming it has a derivative and you are considering the simplest kind of quasiperiodic function, the arithmetic kind. But of course scales don't have derivatives.

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:

> I think the real point is that pitch perception is (basically) logarithmic,
> so centering at 1 doesn't describe the log-linear perceptual relationship
> terribly well; although, unlike some other logarithmic perceptions (like
> weight judgement), there is no clear logical baseline point at which pitch
> is nonexistent.

Starting at 0 is also what fits to the regular mapping paradigm. Traditional interval names can be viewed as based on <7 11 16|, except that you add 1 after applying the val. So, you map 1 to 0, add 1, and call it a unison. You map 6/5 or 5/4 to 2, add 1, and call it a third. You map 3/2 to 4, add 1, and call it a fifth. And so forth.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Starting at 0 is also what fits to the regular mapping paradigm. Traditional interval names can be viewed as based on <7 11 16|, except that you add 1 after applying the val. So, you map 1 to 0, add 1, and call it a unison. You map 6/5 or 5/4 to 2, add 1, and call it a third. You map 3/2 to 4, add 1, and call it a fifth. And so forth.

You can also extend this to higher limits, but unfortunately you need to decide if you are going to use the patent val naming system which fits to dominant or the 7d naming system which accords with meantone. The patent val system calls 7/6, 6/5, 5/4 and 9/7 all thirds, which would make many people happy, and 7/4 a seventh. The 7d/meantone system says that 7/6 is a second, 9/7 a fourth and 7/4 is a sixth. Both, of course, fit the peculiar arithmetic of traditional nomenclature, where 3+3=5, because we added a 1.

now that is funny

--- On Fri, 7/8/11, Daniel Nielsen <nielsed@...> wrote:

From: Daniel Nielsen <nielsed@...>
Subject: Re: [tuning] Re: The Physics of Music?! :-(
To: tuning@yahoogroups.com
Date: Friday, July 8, 2011, 3:09 PM

On Fri, Jul 8, 2011 at 9:43 AM, <Afmmjr@...> wrote:

In the immortal words of Laurence Welk:
 
And a 0
And a 1
And a 0, 1, 2, 3....

When reading a .scl file, defining as one is basically like saying "a 2, and a 3, and a 2,3,4,5".

I think the real point is that pitch perception is (basically) logarithmic, so centering at 1 doesn't describe the log-linear perceptual relationship terribly well; although, unlike some other logarithmic perceptions (like weight judgement), there is no clear logical baseline point at which pitch is nonexistent.