Yahoo Tuning Groups Ultimate Backup makemicromusic Replacement tuning for 12 Equal

Finding a tuning is one thing. Getting the entire western world to embrace it is quite another. There are plenty of better alternatives to 12-TET, the question is "are they better *enough* to spark a continent-spanning paradigm shift?" The "problem" is that 12-TET is "good enough" for the regular 5-limit harmonies and that it also provides a "good enough" framework for ensembles that tend toward a sort of "adaptive JI" paradigm (barbershop quartets, string ensembles, etc.), and ALSO that the massive musical infrastructures that exist (commercially-produced instruments, tuners, theory books, musical education programs, etc.) are ALL based on a 12-TET paradigm. If we can't get Westerners to abandon fossil fuel in the face of global ecological collapse, how on EARTH can we expect them to abandon the 12-TET infrastructure for the sake of a new tuning?

Just like getting people to adopt alternative fuels, the only option is to start small and slowly build an infrastructure in one locale at a time. Trouble is, there's vastly more alternative tunings to 12-TET (even assuming a single set of harmonic goals) than there are alternative fuels. So everyone trying to build an infrastructure is in competition with everyone else doing the same, instead of cooperating. So instead of amassing an army to overthrow the military dictator, we've got a bunch of would-be dictators fighting with each other over the right to lead the revolution. And plenty of others who don't want to bother with full-scale revolution (since any revolutionary regime is going to be as totalitarian as the old one) and are content to wage their own solo guerilla war in their own little locale.

-Igs

--- In MakeMicroMusic@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Chris said: "The likelihood of the entire western world embracing any microtonal tuning as a *replacement* to 12 equal I feel is slim to none."
>
> I disagree. I set out to find such a *replacement* tuning in 1995 and after fifteen years hard work I think I have found it: Blue Temperament. I really don't think I can do any better. My reasonings are outlined in my book. Chris said in a post to Michael about my system: "The method is easy to understand and hard to argue against."
>
> Chris composed a number of tunes using my Blue Just and Blue Temperament tunings and if anyone is interested there are links to five of them on my web site:
>
> www.johnsmusic7.com
>
> Here's Blue Temperament again if anyone wants to try it...
>
> 0.0, 121.6, 200.7, 313.5, 388.4, 501.2, 580.4, 702.0, 816.9, 889.4, 1012.5, 1085.1, 1200.0
>
> John.
>

🔗john777music <jfos777@...>

Igs,

I sent you an email offlist a day or two ago, did you get it? The one thing that is going to promote my tuning is my book. If the book catches on then my tuning should catch on. As Chris said about my system: "The method is easy to understand and hard to argue against." Give me your postal address offlist and I'll send you a free copy and you can judge for yourself.

This applies to others on MMM or the Tuning List, email me your postal address and I'll post you a copy of my book. All I ask in return is that you post a review of the book.

John.

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Finding a tuning is one thing. Getting the entire western world to embrace it is quite another. There are plenty of better alternatives to 12-TET, the question is "are they better *enough* to spark a continent-spanning paradigm shift?" The "problem" is that 12-TET is "good enough" for the regular 5-limit harmonies and that it also provides a "good enough" framework for ensembles that tend toward a sort of "adaptive JI" paradigm (barbershop quartets, string ensembles, etc.), and ALSO that the massive musical infrastructures that exist (commercially-produced instruments, tuners, theory books, musical education programs, etc.) are ALL based on a 12-TET paradigm. If we can't get Westerners to abandon fossil fuel in the face of global ecological collapse, how on EARTH can we expect them to abandon the 12-TET infrastructure for the sake of a new tuning?
>
> Just like getting people to adopt alternative fuels, the only option is to start small and slowly build an infrastructure in one locale at a time. Trouble is, there's vastly more alternative tunings to 12-TET (even assuming a single set of harmonic goals) than there are alternative fuels. So everyone trying to build an infrastructure is in competition with everyone else doing the same, instead of cooperating. So instead of amassing an army to overthrow the military dictator, we've got a bunch of would-be dictators fighting with each other over the right to lead the revolution. And plenty of others who don't want to bother with full-scale revolution (since any revolutionary regime is going to be as totalitarian as the old one) and are content to wage their own solo guerilla war in their own little locale.
>
> -Igs
>
> --- In MakeMicroMusic@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Chris said: "The likelihood of the entire western world embracing any microtonal tuning as a *replacement* to 12 equal I feel is slim to none."
> >
> > I disagree. I set out to find such a *replacement* tuning in 1995 and after fifteen years hard work I think I have found it: Blue Temperament. I really don't think I can do any better. My reasonings are outlined in my book. Chris said in a post to Michael about my system: "The method is easy to understand and hard to argue against."
> >
> > Chris composed a number of tunes using my Blue Just and Blue Temperament tunings and if anyone is interested there are links to five of them on my web site:
> >
> > www.johnsmusic7.com
> >
> > Here's Blue Temperament again if anyone wants to try it...
> >
> > 0.0, 121.6, 200.7, 313.5, 388.4, 501.2, 580.4, 702.0, 816.9, 889.4, 1012.5, 1085.1, 1200.0
> >
> > John.
> >
>

🔗Chris Vaisvil <chrisvaisvil@...>

John,

The context of "The method is easy to understand and hard to argue against."
was a statement to Michael was a suggestion he try to use your methodology
to develop tunings. It was not an endorsement of the superiority of your
tuning, and I prefer your Blue JI over your Blue temperament actually.

Your tunings are nice, but so is Charles Lucy's and a number of other
meantone tunings. I'm not sure though why people suggest meantone tunings to
be a better solution to 12 equal when 12 equal came *from* meantone tunings.
There was obviously deficiencies in the mind of composers / instrument
designers / performers / tune smiths with meantone tunings that caused the
evolution to 12 equal. Most of us here are familiar with a number of the
reasons for that evolution.

Thanks,

Chris

On Thu, Feb 3, 2011 at 5:51 PM, john777music <jfos777@...> wrote:

>
>
> Chris said: "The likelihood of the entire western world embracing any
> microtonal tuning as a *replacement* to 12 equal I feel is slim to none."
>
> I disagree. I set out to find such a *replacement* tuning in 1995 and after
> fifteen years hard work I think I have found it: Blue Temperament. I really
> don't think I can do any better. My reasonings are outlined in my book.
> Chris said in a post to Michael about my system: "The method is easy to
> understand and hard to argue against."
>
> Chris composed a number of tunes using my Blue Just and Blue Temperament
> tunings and if anyone is interested there are links to five of them on my
> web site:
>
> www.johnsmusic7.com
>
> Here's Blue Temperament again if anyone wants to try it...
>
> 0.0, 121.6, 200.7, 313.5, 388.4, 501.2, 580.4, 702.0, 816.9, 889.4, 1012.5,
> 1085.1, 1200.0
>
> John.
>
>
>

[Non-text portions of this message have been removed]

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:
> Finding a tuning is one thing. Getting the entire
> western world to embrace it is quite another. There are
> plenty of better alternatives to 12-TET, the question is
> "are they better *enough* to spark a continent-spanning
> paradigm shift?" The "problem" is that 12-TET is "good
<snip>

There's a historicist fallacy here: the idea that a new
monoculture has to replace the old monoculture you don't
like. Whether you look at technologies or ecosystems it's
more likely that a new niche opens up. The larger an
ecosystem, the more niches it can sustain. The global
music scene (and yes, let's be global) is bigger than it's
ever been before. There are more musicians and listeners
in contact with each other than one tuning system can
sustain. There are more instruments capable of systematic
retuning than ever before.

Some people are going to want more complex harmonies.
(Evolution tends towards higher complexity only in that
more niches open up to support complexity. Most life
forms are single celled.) Those people may want extended
meantone, magic, orwell, schismatic, miracle, and so on.
Others will want more simplicity, hence semaphore,
slendric, mohajira, meantone diatonics, or whatever. Some
people want weird tunings that break the rules. The
paradigm shift is to see that all these tunings are valid
and don't have to be in competition with one another.

> Just like getting people to adopt alternative fuels, the
> only option is to start small and slowly build an
> infrastructure in one locale at a time. Trouble is,
> there's vastly more alternative tunings to 12-TET (even
> assuming a single set of harmonic goals) than there are
> alternative fuels. So everyone trying to build an
> infrastructure is in competition with everyone else doing
> the same, instead of cooperating. So instead of amassing
> an army to overthrow the military dictator, we've got a
> bunch of would-be dictators fighting with each other over
> the right to lead the revolution. And plenty of others
> who don't want to bother with full-scale revolution
> (since any revolutionary regime is going to be as
> totalitarian as the old one) and are content to wage
> their own solo guerilla war in their own little locale.

That's a very aggressive analogy. Different nations and
cultures can live at peace with each other. We don't all
need to be fighting the Empire.

There is a need for strong theories, so that cross-cultural
meetings don't end up standardizing on the thing
everybody knows. This is what I believe happens with a lot
of world music today. Supposedly western (but really
Japanese) keyboards can adapt to ethnic scales. You can
build rules of harmony around them. Orchestras can adapt
to the authentic tunings of mouth organs or bagpipes.

Graham

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 4, 2011 at 4:37 AM, Graham Breed <gbreed@...> wrote:
>
> Some people are going to want more complex harmonies.
> (Evolution tends towards higher complexity only in that
> more niches open up to support complexity. Most life
> forms are single celled.) Those people may want extended
> meantone, magic, orwell, schismatic, miracle, and so on.
> Others will want more simplicity, hence semaphore,
> slendric, mohajira, meantone diatonics, or whatever. Some
> people want weird tunings that break the rules. The
> paradigm shift is to see that all these tunings are valid
> and don't have to be in competition with one another.

I just sent a message to Carl and Igs offlist about this, but I might
as well post it here as well. Not only do I think that these tunings
are all valid and don't have to be competition with one another, but I
think that it should be embraced that some form of fragmented
"diatonic" hearing applies to a lot of other tunings as well, e.g.
something like Blackwood. Not only is this valid to admit, but it's
probably the most likely way to get people into something like
11-limit harmony anyway, since it resembles a simple extension of how
they've already adapted to hear.

People have been admitting that the octatonic scale resembles near-MOS
meantone harmony for almost a century now. They've been using it as a
musical feature, rather than assuming that there's some other way to
hear the octatonic scale that is somehow "more valid." Well, there is
also another way to hear the octatonic scale, but there's also the
meantone near-near-MOS way as well. And they both coexist in 12-equal,
and you can morph between both of them and use the octatonic scale
over certain types of dominant 7 chords, which people have been doing
for nearly 100 years now.

I think that a good ear training exercise is to try and hear fragments
of as many regular temperaments in other regular temperaments as
possible, so that you can really morph fluidly between tuning systems.
Not only should we accept that blackwood resembles in some way a
symmetrical "diatonic" scale, we should also be looking for
resemblances between magic and miracle and mohajira and semaphore, as
well, or whatever.

I wish I could get some decent synth working in 22-et...

-Mike

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> I just sent a message to Carl and Igs offlist about this,
> but I might as well post it here as well. Not only do I
> think that these tunings are all valid and don't have to
> be competition with one another, but I think that it
> should be embraced that some form of fragmented
> "diatonic" hearing applies to a lot of other tunings as
> well, e.g. something like Blackwood. Not only is this
> valid to admit, but it's probably the most likely way to
> get people into something like 11-limit harmony anyway,
> since it resembles a simple extension of how they've
> already adapted to hear.

When I was working on Hardy songs, I wanted to know if it
was possible to think outside of diatonic melodies. When
you think up a tune in your head, the theory is that it'll
imply a diatonic scale. So I was worried that I'd be
forcing alien harmonies onto a meantone core.

In "When I Set Out for Lyonnesse" I chose the tune freely
from miracle temperament. (At least, the Blackjack+3
tuning on my keyboard.) At one point I thought it was
sounding so stable that I must have brought a diatonic
scale in by the back door. Because I was using decimal
notation, the pitches weren't being measured relative to a
diatonic, and I had to work out how close it was. The
result -- nowhere near. I'd been picking out neutral
intervals. You can find the score and MP3 on my website if
you want to check what I was doing. (Record it properly if
you like!)

> People have been admitting that the octatonic scale
> resembles near-MOS meantone harmony for almost a century
> now. They've been using it as a musical feature, rather
> than assuming that there's some other way to hear the
> octatonic scale that is somehow "more valid." Well, there
> is also another way to hear the octatonic scale, but
> there's also the meantone near-near-MOS way as well. And
> they both coexist in 12-equal, and you can morph between
> both of them and use the octatonic scale over certain
> types of dominant 7 chords, which people have been doing
> for nearly 100 years now.

I used to use a meantone octatonic for 7-limit harmony.
It's on my "Blues Scales" page of 7-limit scales.

> I think that a good ear training exercise is to try and
> hear fragments of as many regular temperaments in other
> regular temperaments as possible, so that you can really
> morph fluidly between tuning systems. Not only should we
> accept that blackwood resembles in some way a symmetrical
> "diatonic" scale, we should also be looking for
> resemblances between magic and miracle and mohajira and
> semaphore, as well, or whatever.

The common ground of Magic and Miracle is 9-limit harmony.
I recorded a Fleetwood Mac cover once using both tunings
simultaneously to prove that it can be done.

> I wish I could get some decent synth working in 22-et...

What's holding you back?

Graham

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 4, 2011 at 6:08 AM, Graham Breed <gbreed@...> wrote:
>
> When I was working on Hardy songs, I wanted to know if it
> was possible to think outside of diatonic melodies. When
> you think up a tune in your head, the theory is that it'll
> imply a diatonic scale. So I was worried that I'd be
> forcing alien harmonies onto a meantone core.

I was thinking more the other way, where you allow yourself to project
isolated fragments of the meantone core onto the alien structure.

> In "When I Set Out for Lyonnesse" I chose the tune freely
> from miracle temperament. (At least, the Blackjack+3
> tuning on my keyboard.) At one point I thought it was
> sounding so stable that I must have brought a diatonic
> scale in by the back door. Because I was using decimal
> notation, the pitches weren't being measured relative to a
> diatonic, and I had to work out how close it was. The
> result -- nowhere near. I'd been picking out neutral
> intervals. You can find the score and MP3 on my website if
> you want to check what I was doing. (Record it properly if
> you like!)

Longer response posted on tuning; perhaps this entire situation is
best modeled as a feature space, which is a hot topic in DSP these
days. Perhaps some tenets of language processing mapped onto an
adaptable feature space, or set of feature spaces, would be best here.

But for example, you often resolve notes upward and downward in the
Hardy piece by something resembling a half step, aka you're using a
leading tone. Whether or not leading tones work because of some
psychoacoustic thing, or because we have cognitively learned that this
is a trigger to start analyzing this note differently from the last,
or whether the two are really the same, is besides the point - it
works, and you end up hearing a stable pattern in the scale that you
probably recognize the diatonic scale as also sharing.

You also arpeggiate chords that sound like diatonic structures I know,
and those are recognizable. Sometimes the structures diverge in a
noticeable way, and that sounds interesting: it sounds to me, in the
beginning of this, you're playing a distorted version of meantone E,
G, F#, A#, but then you go D-F#-G-A, F#, A. Except the A# in the first
line and the A in the second line sound like they might actually the
same note, except they're just barely not, which is an interesting
pun. So now I'm hearing this as some kind of weird, fragmented,
detuned meantone structure in which E-G-F#-A# forms a consistent
chunk, and D-F#-G-A-F#-A forms a consistent chunk, but they don't
relate to each other in a meantone-consistent way in that the
difference between A# and A is way smaller than my meantone machine
predicted.

Either way, I think - why run away from this? If you accept this, then
you're hearing how it's similar to meantone (hearing the note names
laid out as I mentioned before), and how it's different (noticing that
A and A# ended up at almost the same spot), which is just another way
of saying you're hearing how meantone and your miracle-based scale in
general relate to one another. After enough listens, one will grasp
the at first counterintuitive weirdness of that small semitone between
A and A#, and now you're starting to form a new paradigm that relates
the two other paradigms. I'm not sure it's really optional, either,
since I don't think that hearing the meantone similarities will ever
really go away, so you can either fight with yourself about it or do
this. Maybe I'm wrong, just my current thoughts.

Well, at least that's my current theory. I don't really claim to know
how it works, but I do know that there's nothing wrong with accepting
when classical conditioning does occur.

> I used to use a meantone octatonic for 7-limit harmony.
> It's on my "Blues Scales" page of 7-limit scales.

I like the 8-note 29-tet version. A different take on the blues. To
me, the full blues scale gamut is a particular SPM mode but in
12-equal - 2 1 1 1 1 1 2 1 1 1. All notes except the b1 and the b6.
Pretty much sums up the blues to me. My main problem with it is that
in 22-equal, the fifth of the V chord is a step off, but in 12-equal
this works out to 3/2.

> > I think that a good ear training exercise is to try and
> > hear fragments of as many regular temperaments in other
> > regular temperaments as possible, so that you can really
> > morph fluidly between tuning systems. Not only should we
> > accept that blackwood resembles in some way a symmetrical
> > "diatonic" scale, we should also be looking for
> > resemblances between magic and miracle and mohajira and
> > semaphore, as well, or whatever.
>
> The common ground of Magic and Miracle is 9-limit harmony.
> I recorded a Fleetwood Mac cover once using both tunings
> simultaneously to prove that it can be done.

Whoa, do you have this uploaded somewhere? What song did you do?

> > I wish I could get some decent synth working in 22-et...
>
> What's holding you back?

I'm having problems getting the release trails to work in EastWest. I
release a note, and then - kapwing! The pitch bend suddenly shuts off,
and the note jumps back over to its nearest 12-tet neighbor as it
decays. This sounds like bullets ricocheting off the walls. It also
ends up affecting the most xenharmonic intervals the most.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> I was thinking more the other way, where you allow
> yourself to project isolated fragments of the meantone
> core onto the alien structure.

Yes, I know. I said you don't have to do that.

> > In "When I Set Out for Lyonnesse" I chose the tune
> > freely from miracle temperament. (At least, the
> > Blackjack+3 tuning on my keyboard.) At one point I
> > thought it was sounding so stable that I must have
> > brought a diatonic scale in by the back door. Because I
> > was using decimal notation, the pitches weren't being
> > measured relative to a diatonic, and I had to work out
> > how close it was. The result -- nowhere near. I'd been
> > picking out neutral intervals. You can find the score
> > and MP3 on my website if you want to check what I was
> > doing. (Record it properly if you like!)

There is a sense of a diatonic scale, in that only 7 of the
10 degrees of the decimal scale are used. Each degree can
be raised or lowered by a quomma (between a comma and a
quartertone). I was wrong about it keeping to
Blackjack+3. I must have used my Ztar, although I
remember working the melody out on a remapped Halberstadt.

> Longer response posted on tuning; perhaps this entire
> situation is best modeled as a feature space, which is a
> hot topic in DSP these days. Perhaps some tenets of
> language processing mapped onto an adaptable feature
> space, or set of feature spaces, would be best here.

It's based on the decimal scale. To understand it properly
you need to follow that.

> But for example, you often resolve notes upward and
> downward in the Hardy piece by something resembling a
> half step, aka you're using a leading tone. Whether or
> not leading tones work because of some psychoacoustic
> thing, or because we have cognitively learned that this
> is a trigger to start analyzing this note differently
> from the last, or whether the two are really the same, is
> besides the point - it works, and you end up hearing a
> stable pattern in the scale that you probably recognize
> the diatonic scale as also sharing.

The decimal scale's built out of semitones: secors,
approximating 16:15 or 15:14. So you don't need diatonic
logic to explain them. Reduced secors, equivalent to 21:20
I think, are allowed in decimal counterpoint. Quommas
shouldn't be used as direct intervals, but they can be
indirect, and you spotted one below. Double quommas,
equivalent to 25:24, wouldn't come about in strict decimal
counterpoint, but you spotted one here.

> You also arpeggiate chords that sound like diatonic
> structures I know, and those are recognizable. Sometimes
> the structures diverge in a noticeable way, and that
> sounds interesting: it sounds to me, in the beginning of
> this, you're playing a distorted version of meantone E,
> G, F#, A#, but then you go D-F#-G-A, F#, A. Except the A#
> in the first line and the A in the second line sound like
> they might actually the same note, except they're just
> barely not, which is an interesting pun. So now I'm
> hearing this as some kind of weird, fragmented, detuned
> meantone structure in which E-G-F#-A# forms a consistent
> chunk, and D-F#-G-A-F#-A forms a consistent chunk, but
> they don't relate to each other in a meantone-consistent
> way in that the difference between A# and A is way
> smaller than my meantone machine predicted.

Bleagh! There's a mistake in the PDF scores that I'll have
to fix. Fortunately, I have the original pencil and paper
one here to check.

Those things at the start can count as arpeggios because
they're over a constant note in the bass. The first is
above a C, so it's 4:5:6:7 with the F# as an additional
7:5. (Certainly not an 11:8 -- I wasn't very 11-limit with
my miracle harmony.) The two rough As are a quomma apart.
Other notes are a quomma off in the other direction between
these two bars, and that probably was deliberate. The root
moves up by a neutral third. Ah yes, compare bars 1 and 4
-- all notes have been shifted by a quomma but not all in
the same direction.

You're hearing it as meantone but it's really 7-limit
harmony. The quomma shifts are also written as different
versions of the same note in decimal notation. You can
interpret any interval relative to meantone if you want.

> Either way, I think - why run away from this? If you
> accept this, then you're hearing how it's similar to
> meantone (hearing the note names laid out as I mentioned
> before), and how it's different (noticing that A and A#
> ended up at almost the same spot), which is just another
> way of saying you're hearing how meantone and your
> miracle-based scale in general relate to one another.
> After enough listens, one will grasp the at first
> counterintuitive weirdness of that small semitone between
> A and A#, and now you're starting to form a new paradigm
> that relates the two other paradigms. I'm not sure it's
> really optional, either, since I don't think that hearing
> the meantone similarities will ever really go away, so
> you can either fight with yourself about it or do this.
> Maybe I'm wrong, just my current thoughts.

I don't hear it relative to Meantone. I wrote it using
decimal counterpoint and 7-limit harmony. I'd spent
enough time with Miracle to get the decimal scale
internalized. If you spend enough time listening to a body
of miracle music you'll stop hearing the meantone.

> > I used to use a meantone octatonic for 7-limit harmony.
> > It's on my "Blues Scales" page of 7-limit scales.
>
> I like the 8-note 29-tet version. A different take on the
> blues. To me, the full blues scale gamut is a particular
> SPM mode but in 12-equal - 2 1 1 1 1 1 2 1 1 1. All notes
> except the b1 and the b6. Pretty much sums up the blues
> to me. My main problem with it is that in 22-equal, the
> fifth of the V chord is a step off, but in 12-equal this
> works out to 3/2.

What I put on that page are scales inspired by a particular
theory of the blues pentatonic. They aren't intended to be
unusually appropriate for the blues.

> > The common ground of Magic and Miracle is 9-limit
> > harmony. I recorded a Fleetwood Mac cover once using
> > both tunings simultaneously to prove that it can be
> > done.
>
> Whoa, do you have this uploaded somewhere? What song did
> you do?

It's You Make Loving Fun, and the two temperament classes
are named in the lyrics.

Graham

🔗Graham Breed <gbreed@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 4, 2011 at 2:13 PM, Graham Breed <gbreed@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > I was thinking more the other way, where you allow
> > yourself to project isolated fragments of the meantone
> > core onto the alien structure.
>
> Yes, I know. I said you don't have to do that.

But sometimes it's hard to discern which fragments are really
"meantone" and which ones are just basic musical features that also
happen to be a part of meantone.

Maybe it's just a personal realization: I have been trying to "get
away" from diatonic hearing, so that I can hear these tunings from the
perspective of a person who had hypothetically grown up in "miracle"
culture or something. But instead, now I'm asking myself, why should I
try to "get away" from it at all? Bilingual people surely have an
extra layer of perception in how they can compare and relate different
languages to one another, and in that they have a better understanding
of how language works at all. Sometimes words in one language sound
similar to words in another language, although the meaning might be
different, and classical conditioning reminds you of that sometimes.
How is that any different than what's going on here?

I don't think I'll ever need to forget "diatonic hearing" entirely to
develop new, additional forms of hearing as well, and perhaps I'll
always hear resemblances in those two forms of hearing. Sometimes I
hear resemblances to 11-limit harmony in 12-equal as well, but I never
had much of a negative complex against that one. I don't know, just my
current thoughts.

> There is a sense of a diatonic scale, in that only 7 of the
> 10 degrees of the decimal scale are used. Each degree can
> be raised or lowered by a quomma (between a comma and a
> quartertone). I was wrong about it keeping to
> Blackjack+3. I must have used my Ztar, although I
> remember working the melody out on a remapped Halberstadt.

Out of curiosity, what keyboards do you have?

> The decimal scale's built out of semitones: secors,
> approximating 16:15 or 15:14. So you don't need diatonic
> logic to explain them.

Maybe "chromatic" language is more apt for something like that. I
meant that I'll hear things that resemble things I already know.
Movement by half step or something like that.

> Reduced secors, equivalent to 21:20
> I think, are allowed in decimal counterpoint. Quommas
> shouldn't be used as direct intervals, but they can be
> indirect, and you spotted one below. Double quommas,
> equivalent to 25:24, wouldn't come about in strict decimal
> counterpoint, but you spotted one here.

Aha.

> Those things at the start can count as arpeggios because
> they're over a constant note in the bass. The first is
> above a C, so it's 4:5:6:7 with the F# as an additional
> 7:5.

Is that really 7 on top? It sounded a bit sharp to me. But now that
you say what it is, the 12-tet-ized version of it is crystal clear in
my head. Sometimes it diverges noticeably from any 12-tet imprint, and
I think that moments when that happens are really interesting. As I
listen to it more and more I will no doubt come to a better mental
structure to categorize the divergences. Since theoretically we
already know they're categorized by being a part of this decimal
structure, I assume all this means is that I'll just come to a better
symbolic representation for decimal.

But I'll probably still hear some 12-tet features in there too, and my
question is, what's wrong with this? Perhaps if I had never listened
to 12-tet, I'd still hear those same features, but I wouldn't ever
know that they were "12-tet" features at all.

> Ah yes, compare bars 1 and 4
> -- all notes have been shifted by a quomma but not all in
> the same direction.

I think this is another mistake in the score, at bar 4 I just hear
what you have listed as bar 5, and then at bar 5 I hear bar 5 played
again.

> You're hearing it as meantone but it's really 7-limit
> harmony. The quomma shifts are also written as different
> versions of the same note in decimal notation. You can
> interpret any interval relative to meantone if you want.

I'm just saying that, since I don't think hearing relations between
things and meantone will ever go away, I might as well just embrace it
and then try to hear as many relationships between different
temperaments as possible. Rather than trying to not hear things as
meantone, I should not only be okay with accepting that that
interpretation will sometimes arise, but also try to hear orwell and
miracle in everything too, and lemba and magic and so on.

> I don't hear it relative to Meantone. I wrote it using
> decimal counterpoint and 7-limit harmony. I'd spent
> enough time with Miracle to get the decimal scale
> internalized. If you spend enough time listening to a body
> of miracle music you'll stop hearing the meantone.

What body of miracle music shall I listen to? I've listened to your
decimal counterpoint stuff before, but wasn't sure exactly what it was
I was hearing. I still can't really get into miracle, it always sounds
sort of sinister and ominous to me.

-Mike

🔗Graham Breed <gbreed@...>

On 5 February 2011 10:34, Mike Battaglia <battaglia01@...> wrote:

> But sometimes it's hard to discern which fragments are really
> "meantone" and which ones are just basic musical features that also
> happen to be a part of meantone.

That's why you need exposure to non-meantone harmony.

> Maybe it's just a personal realization: I have been trying to "get
> away" from diatonic hearing, so that I can hear these tunings from the
> perspective of a person who had hypothetically grown up in "miracle"
> culture or something. But instead, now I'm asking myself, why should I
> try to "get away" from it at all? Bilingual people surely have an
> extra layer of perception in how they can compare and relate different
> languages to one another, and in that they have a better understanding
> of how language works at all. Sometimes words in one language sound
> similar to words in another language, although the meaning might be
> different, and classical conditioning reminds you of that sometimes.
> How is that any different than what's going on here?

If you learn another language, you have to think in terms of that
language. Translating in your head slows you down. If you want
meantone, it's much simpler to stick with meantone.

> I don't think I'll ever need to forget "diatonic hearing" entirely to
> develop new, additional forms of hearing as well, and perhaps I'll
> always hear resemblances in those two forms of hearing. Sometimes I
> hear resemblances to 11-limit harmony in 12-equal as well, but I never
> had much of a negative complex against that one. I don't know, just my
> current thoughts.

You don't need to forget one language when you learn another. You can
even use similarities between words to help you communicate. 7-limit
tunings will have common features to help you the same as Romance
languages. Many features of a genre are independent of the tuning,
like you find English words all over the world. But you need to think
in terms of the language you're speaking. Most people are very good
at that, if only between dialects. Are you one of the rare people who
speaks perfect standard English with your family and friends?

>> There is a sense of a diatonic scale, in that only 7 of the
>> 10 degrees of the decimal scale are used. Each degree can
>> be raised or lowered by a quomma (between a comma and a
>> quartertone). I was wrong about it keeping to
>> Blackjack+3. I must have used my Ztar, although I
>> remember working the melody out on a remapped Halberstadt.
>
> Out of curiosity, what keyboards do you have?

I have a Ztar and a few conventional MIDI keyboards. I used to have a
rebuilt DX21 but I threw it away when I moved house. All I have
access to right now is a Casio with a USB socket.

>> The decimal scale's built out of semitones: secors,
>> approximating 16:15 or 15:14. So you don't need diatonic
>> logic to explain them.
>
> Maybe "chromatic" language is more apt for something like that. I
> meant that I'll hear things that resemble things I already know.
> Movement by half step or something like that.

It's a kind of chromatic, yes. You can build diatonics out of it.

>> Reduced secors, equivalent to 21:20
>> I think, are allowed in decimal counterpoint. Quommas
>> shouldn't be used as direct intervals, but they can be
>> indirect, and you spotted one below. Double quommas,
>> equivalent to 25:24, wouldn't come about in strict decimal
>> counterpoint, but you spotted one here.
>
> Aha.

Actually, what you spotted was a single quomma, but I saw doubles in the score.

>> Those things at the start can count as arpeggios because
>> they're over a constant note in the bass. The first is
>> above a C, so it's 4:5:6:7 with the F# as an additional
>> 7:5.
>
> Is that really 7 on top? It sounded a bit sharp to me. But now that
> you say what it is, the 12-tet-ized version of it is crystal clear in
> my head. Sometimes it diverges noticeably from any 12-tet imprint, and
> I think that moments when that happens are really interesting. As I
> listen to it more and more I will no doubt come to a better mental
> structure to categorize the divergences. Since theoretically we
> already know they're categorized by being a part of this decimal
> structure, I assume all this means is that I'll just come to a better
> symbolic representation for decimal.

It's a miracle tempered 7 relative to the 1 in the bass.

You can listen to it relative to 12-tet if you like. It happens not
to be the way I wrote it or the way I hear it. Magic comma pumps may
be more interesting if you want to relate them to traditional harmony.
Every chord is familiar (maybe with the harmonic seventh) and they're
all related by pure 5-limit intervals, but the whole thing doesn't add
up in meantone. It's a shame I didn't finish the piece with the
tritone puns as well.

> But I'll probably still hear some 12-tet features in there too, and my
> question is, what's wrong with this? Perhaps if I had never listened
> to 12-tet, I'd still hear those same features, but I wouldn't ever
> know that they were "12-tet" features at all.

It's a different way of listening, and for my Miracle pieces not an
authentic one. If it works for you, all the better. Different
listeners are going to interpret the same music in different ways.

>> Ah yes, compare bars 1 and 4
>> -- all notes have been shifted by a quomma but not all in
>> the same direction.
>
> I think this is another mistake in the score, at bar 4 I just hear
> what you have listed as bar 5, and then at bar 5 I hear bar 5 played
> again.

I think the score's right. If anything's wrong it's the rendering.
But those bars should be the same tune with quomma inflections. The
bass has moved by a neutral third so they can't be the same and in
tune.

> I'm just saying that, since I don't think hearing relations between
> things and meantone will ever go away, I might as well just embrace it
> and then try to hear as many relationships between different
> temperaments as possible. Rather than trying to not hear things as
> meantone, I should not only be okay with accepting that that
> interpretation will sometimes arise, but also try to hear orwell and
> miracle in everything too, and lemba and magic and so on.

Do you speak German? After a while the word "Grossvater" stops being
funny and you have to consciously remember what the monolinguals are
giggling about.

>> I don't hear it relative to Meantone. I wrote it using
>> decimal counterpoint and 7-limit harmony. I'd spent
>> enough time with Miracle to get the decimal scale
>> internalized. If you spend enough time listening to a body
>> of miracle music you'll stop hearing the meantone.
>
> What body of miracle music shall I listen to? I've listened to your
> decimal counterpoint stuff before, but wasn't sure exactly what it was
> I was hearing. I still can't really get into miracle, it always sounds
> sort of sinister and ominous to me.

You'll have to write it! I did my bit.

The decimal counterpoint exercises are adapted from Fux. I translated
each cantus firmus into the decimal scale, and allowed quomma shifts
to get the harmony right. Then I wrote the counterpoint to follow
Fux's rules with 7-limit consonances allowed and some melodic rules to
distinguish steps from leaps. The result is that you should be able
to hear independent melodies moving in harmony and dissonances
resolving when they arise.

Graham

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Igs>"If we can't get Westerners to abandon fossil fuel in the face of global
ecological collapse, how on EARTH can we expect them to abandon the 12-TET
infrastructure for the sake of a new tuning?"

Interesting example, but fossil fuels have one huge/different limiting
factor: range. American's don't want to switch to electric cars because the
best ones only have 100 miles range, and more like 60 with some of the
stop-and-go traffic during rush hour. Electricity (for travel) is not a mature
technology because the batteries powering it are not capable enough for many
realistic travel situations...microtonality in most ways is: we have
equivalently capable (or better) scales/chords...and even instruments to play
them with.

Three main barriers exists in my mind
A) Competitively priced instruments with microtonal capability
B) The issue of getting other people in your "band" to use microtonal
instruments
C) Getting listeners to accept the typical "informality"/non-compliance of the
tunings to Pythagorean-like "common practice" intervals
D) Good theory documentation (not everyone is going to want to learn prime
factorized vectors and yadayada to understand this new type of music)

Now for ELECTRONIC music, particularly of NON-(NEO)CLASSICAL genre, I don't
even consider A, B,. and C to be an issue. I've found electronic musicians far
less interested in formality than classical ones and a lot more tolerant of
"noise".
Also, well priced microtonal capable softsynths are all over the place, all
members of any electronica group can easily use them, and using non-standard
intervals (just like typical electronica use of weird timbres) are not
issues. It seems electronica lacks ONLY D and most other genres lack A,B,C,
and D. But, like Neil said, A and B would likely come automatically if there
were just one pop star who did microtonal music and companies like Yamaha
started mass-producing microtonal acoustic instruments and C would come when
people who liked the artist started saying "hey these weird intervals are
actually pretty hip".

>"Trouble is, there's vastly more alternative tunings to 12-TET (even assuming a
>single set of harmonic goals) than there are alternative fuels. So everyone
>trying to build an infrastructure is in competition with everyone else doing
>the same, instead of cooperating. "

Agreed. Personally, I just wish we were able to pick a top 5 or so scales
and start popularizing those. And, just as importantly, state the scales in
cents or fractions rather than some funky mapping or MOS notation 99% of
musicians won't understand (as we often do on this list). Personally 19TET,
31TET, and Blackwood seem like easy enough targets...perhaps the best test would
be for someone like you to compose a bunch of songs in each of them and see
which songs people like best.

>"So instead of amassing an army to overthrow the military dictator, we've got a
>bunch of would-be dictators fighting with each other over the right to lead the
>revolution. "
Well, can we at least agree that the easiest path is a scale system that
extends the diatonic scale (IE lets musicians do what they've always done plus
add something new if/when they want)?

[Non-text portions of this message have been removed]

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

Igs wrote:

>>If we can't get Westerners to abandon fossil fuel in the face of global
>>ecological collapse, how on EARTH can we expect them to abandon the
>>12-TET infrastructure for the sake of a new tuning?
>
> Interesting example,

Indeed... Gene and I were just discussing it on facebook. Also, no
"global ecological collapse" is threatened.

>but fossil fuels have one huge/different limiting factor: range.
>American's don't want to switch to electric cars because the
>best ones only have 100 miles range, and more like 60 with some of the
>stop-and-go traffic during rush hour.

Actually, the best ones have 300 miles range, and it is not commonly
appreciated that there will be no gasoline-powered passenger cars
left in the U.S. in ten years. The astute investor is planning on
what to do with all the prime real estate now occupied by gas stations.

>Electricity (for travel) is not a mature technology because the
>batteries powering it are not capable enough for many realistic travel
>situations...microtonality in most ways is: we have equivalently
>capable (or better) scales/chords...and even instruments to play
>them with.

This is only true in the case of aircraft and heavy trucks. And,
we do NOT have better microtonal keyboards, and the prototypes aren't
as far along as those of electric cars.

>B) The issue of getting other people in your "band" to use microtonal
>instruments

Critical mass of microtonal musicians seems to be the biggest
hold-up.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

Mike wrote:

>> Indeed... Gene and I were just discussing it on facebook. Also, no
>> "global ecological collapse" is threatened.
>
>Not a fan of man-made climate change, are you?

Consensus estimates of its effects over the next century are nowhere
near "global eco-collapse". Projections generally call for net
positive economic effects in the next 50 years, and net negative ones
in the following 50, on the order of 1-2% world GDP. Notably, the
poorest 1B people will be hit negatively the whole time (mostly by
drought). As for biodiversity, ocean acidification may be the biggest
problem, though plain old overfishing seems at least as bad. Likewise
on land, regular habitat loss seems a bigger threat. Of course there
is considerable uncertainty in all of it and since it would be
economically beneficial to reduce CO2 emissions anyway, it makes no
sense not to.

>> Critical mass of microtonal musicians seems to be the biggest
>> hold-up.
>
>Which itself is held up by getting people to get out of the cliche
>mindset that "they have enough trouble with just the 12 normal notes."

That's exactly what my guitarist friend told me years ago when
I tried to turn him to the dark side.

>It would help if some kind of revolutionary book on the subject were
>written that didn't involve lots of calculus.

Does any existing microtonal book involve calculus?

-Carl

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 7, 2011 at 4:47 PM, Carl Lumma <carl@...> wrote:
> >
> >Not a fan of man-made climate change, are you?
>
> Consensus estimates of its effects over the next century are nowhere
> near "global eco-collapse". Projections generally call for net
> positive economic effects in the next 50 years, and net negative ones
> in the following 50, on the order of 1-2% world GDP. Notably, the
> poorest 1B people will be hit negatively the whole time (mostly by
> drought). As for biodiversity, ocean acidification may be the biggest
> problem, though plain old overfishing seems at least as bad. Likewise
> on land, regular habitat loss seems a bigger threat. Of course there
> is considerable uncertainty in all of it and since it would be
> economically beneficial to reduce CO2 emissions anyway, it makes no
> sense not to.

This is really interesting. Can you point me to some good resources to
read on this stuff? I have recently become really interested in this
entire field of study and the SNR here has been just a bit too low
lately. Maybe respond offlist.

> >> Critical mass of microtonal musicians seems to be the biggest
> >> hold-up.
> >
> >Which itself is held up by getting people to get out of the cliche
> >mindset that "they have enough trouble with just the 12 normal notes."
>
> That's exactly what my guitarist friend told me years ago when
> I tried to turn him to the dark side.

That's what every musician I've ever tried to turn to the dark side
has ever said. I finally made a breakthrough with my friend Tivon,
who's playing a gig with Ari Hoenig at Small's tonight (yeeeeah!), and
told him if he'd just learn 24-TET, I'd analyze it as a
2.3.5.11.13.17.19 subgroup temperament and figure out some good MOS's
and stuff to do. I didn't say it quite like that.

> >It would help if some kind of revolutionary book on the subject were
> >written that didn't involve lots of calculus.
>
> Does any existing microtonal book involve calculus?

LOL, you know what I mean.

-Mike

🔗Carl Lumma <carl@...>

Michael wrote:
>Carl>"Actually, the best ones have 300 miles rang"
> Then why does Nissan stink so badly as to only release a 100 mile range
>electric car?

Because they're idiots? But anyway, at the moment they can't
build the Leaf fast enough.

>With 300 miles range (and assuming it doesn't cost over $20K),
>I'd already have one....who makes it?)

Sorry, like anything else, this starts for people with deep pockets.
The Roadster has been shipping with a 250 mi. range since 2007.
Preorders for the S started in 2009 -- their line is tooling up now
just up the road from me. $50K for the 160mi range model, extra for
the 300mi. range and fast charger for your garage. But you'll get
more for your money than you will with BMW or Mercedes, which plenty
of people already happily buy. This is for a 0th generation product.

>>And, we do NOT have better microtonal keyboards, and the prototypes
>>aren't as far along as those of electric cars."
> Really? I've seen just about everything up to 31TET or so pop
>up far as keyboards

Oh yeah? Which keyboards are those?

There are only 3 explicitly microtonal keyboards available today,
all of them built to order and none specifically 31. The C-Thru
and Opal stuff is micro-usable, but not explicitly so. None of
them hold a candle to a good grand piano.

>and guitars...

Yes, guitars are there. Have been for some time.

-Carl

🔗Carl Lumma <carl@...>

Mike wrote:

>> >Not a fan of man-made climate change, are you?
>>
>> Consensus estimates of its effects over the next century are nowhere
>> near "global eco-collapse". Projections generally call for net
>> positive economic effects in the next 50 years, and net negative ones
>> in the following 50, on the order of 1-2% world GDP. Notably, the
>> poorest 1B people will be hit negatively the whole time (mostly by
>> drought). As for biodiversity, ocean acidification may be the biggest
>> problem, though plain old overfishing seems at least as bad. Likewise
>> on land, regular habitat loss seems a bigger threat. Of course there
>> is considerable uncertainty in all of it and since it would be
>> economically beneficial to reduce CO2 emissions anyway, it makes no
>> sense not to.
>
>This is really interesting. Can you point me to some good resources to
>read on this stuff? I have recently become really interested in this
>entire field of study and the SNR here has been just a bit too low
>lately. Maybe respond offlist.

Wikipedia is a good place to start.

>> >Which itself is held up by getting people to get out of the cliche
>> >mindset that "they have enough trouble with just the 12 normal notes."
>>
>> That's exactly what my guitarist friend told me years ago when
>> I tried to turn him to the dark side.
>
>That's what every musician I've ever tried to turn to the dark side
>has ever said. I finally made a breakthrough with my friend Tivon,
>who's playing a gig with Ari Hoenig at Small's tonight (yeeeeah!),

w00t!

-Carl

🔗Michael <djtrancendance@...>

Carl>"Does any existing microtonal book involve calculus?"

Not exactly...but vectors, matrices, and factorizations used seem akin in
difficulty to calculus. I mean how many people do you know who don't have
math-related degrees in college who know how to multiply, not to mention rotate
a matrix? Ditto for even prime factorizations...they don't teach those as
standard in high school or even college across all majors... So many of us on
the list have computer science and/or math backgrounds...go figure. Ok, with
exception of Igs the Philosophy major...but he's rebellious enough to figure out
anything... :-D

________________________________
From: Carl Lumma <carl@...>
To: MakeMicroMusic@yahoogroups.com
Sent: Mon, February 7, 2011 3:47:44 PM
Subject: Re: [MMM] 12 equal and fossil fuels :-D

Mike wrote:

>> Indeed... Gene and I were just discussing it on facebook. Also, no
>> "global ecological collapse" is threatened.
>
>Not a fan of man-made climate change, are you?

That's exactly what my guitarist friend told me years ago when
I tried to turn him to the dark side.

>It would help if some kind of revolutionary book on the subject were
>written that didn't involve lots of calculus.

Does any existing microtonal book involve calculus?

-Carl

[Non-text portions of this message have been removed]

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 7, 2011 at 5:06 PM, Michael <djtrancendance@...> wrote:
>
> Not exactly...but vectors, matrices, and factorizations used seem akin in
> difficulty to calculus. I mean how many people do you know who don't have
> math-related degrees in college who know how to multiply, not to mention rotate
> a matrix? Ditto for even prime factorizations...they don't teach those as
> standard in high school or even college across all majors... So many of us on
> the list have computer science and/or math backgrounds...go figure. Ok, with
> exception of Igs the Philosophy major...but he's rebellious enough to figure out
> anything... :-D

I don't think a revolutionary microtonal music book has been written
at all. I think the last revolutionary music theory book to come out
was probably the Lydian Chromatic Concept, and compared to the
Renaissance that's taken place around here it's kind of laughable how
primitive it really is.

But there were tons of musicians who dug the entire concept, which had
certainly been around for long before that, but was never communicated
effectively. This same archetype of musician still exists today, and
probably doesn't understand higher-dimensional vector spaces.

Someone (all eyes on Carl) should probably find a way to extract the
relevant message here and phrase it in such a way that people can
understand. Someone with a particular knack for understanding almost
all sides of the research that's been done, and who has an ability to
explain it for people who don't know lots of math (so Carl). I vote
for the title being "A Brief History of Music." I also think that
whoever does this (Carl) will probably make a good amount of money
from such a book, if there's substance to the material (which there
is) and if it's presented readably.

There is a huge market of "thinking musicians" out there who buy Kenny
Werner's "Effortless Mastery" book. And of these people, everyone
knows that our tuning system is somewhat arbitrary. They also know
that, when you play with quarter tones, it sounds dissonant and
irritating. So a book in which someone comes along (Carl) and reveals
the big pattern underneath, can still go into depth when warranted,
admits we don't have all of the answers yet, and simply points the way
forward - and encourages musicians to explore for themselves and gives
them the tools to do so - would probably sell a ()#@$*)(*#$()load of
copies.

I'm not sure who might be a good candidate to write this kind of a
book though (Rick Ballan?).

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

I'll weigh in with this book idea.

I've seen tons of stuff in 12 equal that lists every scale known to man and
a few extraterrestials as well.

Frankly I've never found that too useful. Sticking to scales has its place
but the real lexicon is knowing you can use all 12 notes and having some
idea as to why your options are.

While there are book worm musicians out there I think most want to know some
generalities, maybe an example or two of a cool riff and a few ideas on how
to approach making music that is your own.

Again, I think the idea is, if you want to convert the masses, is to give
some compelling reasons as to why go through the trouble.

I'd ignore the "12 is hard enough" complaints because all it is expressing
is contentment with the available number of notes.

I can tell you that on Alontone (a 12 tet site) I got compliments on
microtonal music but when I posted music composed on my 17 et guitar I
started seeing:

http://alonetone.com/vaisvil/tracks/17-noodles

-------

*staring at his stat copy in the corner.....* do you need more notes lil'
buddy? do you? ;)

That's so cool, and great tone! I want more notes too!
Interesting. I'd love to have a go at one of those myself

nice! and such a comfy sounding tuning.

-------
So---- what more do you guys need?

[Non-text portions of this message have been removed]

🔗cityoftheasleep <igliashon@...>

Carl has a most impressive trove of knowledge, which could definitely be put to good use in writing a book. The one benefit I think I have as an author is that compared to the "masters" in this field, I'm an idiot, so I know how idiots think. My math education stopped at calculus 1, and I'm usually as turned off by terse mathematical jargon as anyone. I think the concepts associated with regular temperaments are quite simple, really, and can be boiled down to a few sentences. The only thing difficult is translating the numbers to musical terms, but I feel like I've finally gotten that down enough that I can explain it to my fellow idiots, so even if they don't get the math they can get the idea. Of course, I think I'm going to impose strict limits on complexity, meaning no temperaments that require more than a 10-note MOS to achieve target triads on at least 40% of their roots. Sorry Gene et al, but I don't want to scare anyone off. I will, however, be making copious use of subgroups, though I'm not sure how many to include. I think Paul will have some good suggestions in that regard.

Also, it's extremely unlikely that this "book" will be physically published. I intend to make it freely available online somewhere, in the hopes that as many people as possible will be able to find it and access it. I suppose I might succumb if there's a demand for physical copies.

-Igs

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 7, 2011 at 6:22 PM, cityoftheasleep <igliashon@...> wrote:
> >
> > > It would help if some kind of revolutionary book on the subject were
> > > written that didn't involve lots of calculus. Something that proposes
> > > what's possible, shows people the pathway is right in front of them,
> > > gets them to "see the light," and inspires them to try for themselves,
> > > even if their initial attempts end in failure.
> >
> > I'm working on this as we speak. A "Field Guide to Alternative EDOs", which will include a "complete idiot's guide to temperament", some basics on the pros and cons of JI, DE scales and plausible triads in each EDO, and a bit more.
>
> LOL alright, I think you'd write a killer book too. And, for the
> record, so would Paul, and probably Graham or Gene too. Some day I'd
> like to write a book on this type of stuff. I just suggested Carl
> because I think he has a particular knack for pedagogy in this field,
> but to be honest you do as well.
>
> Sheesh, look at me, man, starting trouble... what am I but just a
> squirrel trying to get an acorn anyway.
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Side note...17TET seems to get good responses from just about everyone.
Seriously... :-D

________________________________
From: Chris Vaisvil <chrisvaisvil@...>
To: MakeMicroMusic@yahoogroups.com
Sent: Mon, February 7, 2011 6:00:31 PM
Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D

I'll weigh in with this book idea.

I've seen tons of stuff in 12 equal that lists every scale known to man and
a few extraterrestials as well.

Frankly I've never found that too useful. Sticking to scales has its place
but the real lexicon is knowing you can use all 12 notes and having some
idea as to why your options are.

While there are book worm musicians out there I think most want to know some
generalities, maybe an example or two of a cool riff and a few ideas on how
to approach making music that is your own.

Again, I think the idea is, if you want to convert the masses, is to give
some compelling reasons as to why go through the trouble.

I'd ignore the "12 is hard enough" complaints because all it is expressing
is contentment with the available number of notes.

I can tell you that on Alontone (a 12 tet site) I got compliments on
microtonal music but when I posted music composed on my 17 et guitar I
started seeing:

http://alonetone.com/vaisvil/tracks/17-noodles

-------

*staring at his stat copy in the corner.....* do you need more notes lil'
buddy? do you? ;)

That's so cool, and great tone! I want more notes too!
Interesting. I'd love to have a go at one of those myself

nice! and such a comfy sounding tuning.

-------
So---- what more do you guys need?

[Non-text portions of this message have been removed]

🔗cameron <misterbobro@...>

When using the supramajor and supraminor thirds in tertian harmony, 17-et is very similar to many uses of 12-tET-on-paper "expressive intonation". So it's like a strong flavor of the familiar. But you get the xenharmonic "neutral" intervals, so 17 can be quite xenharmonic as well. And it fits on a fretboard, no problem. I agree that it is an obvious choice for a potentially "popular" tuning.

--- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Side note...17TET seems to get good responses from just about everyone.
> Seriously... :-D
>
>
>
>
>
> ________________________________
> From: Chris Vaisvil <chrisvaisvil@...>
> To: MakeMicroMusic@yahoogroups.com
> Sent: Mon, February 7, 2011 6:00:31 PM
> Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D
>
>
> I'll weigh in with this book idea.
>
> I've seen tons of stuff in 12 equal that lists every scale known to man and
> a few extraterrestials as well.
>
> Frankly I've never found that too useful. Sticking to scales has its place
> but the real lexicon is knowing you can use all 12 notes and having some
> idea as to why your options are.
>
> While there are book worm musicians out there I think most want to know some
> generalities, maybe an example or two of a cool riff and a few ideas on how
> to approach making music that is your own.
>
> Again, I think the idea is, if you want to convert the masses, is to give
> some compelling reasons as to why go through the trouble.
>
> I'd ignore the "12 is hard enough" complaints because all it is expressing
> is contentment with the available number of notes.
>
> I can tell you that on Alontone (a 12 tet site) I got compliments on
> microtonal music but when I posted music composed on my 17 et guitar I
> started seeing:
>
> http://alonetone.com/vaisvil/tracks/17-noodles
>
> -------
>
> *staring at his stat copy in the corner.....* do you need more notes lil'
> buddy? do you? ;)
>
> That's so cool, and great tone! I want more notes too!
> Interesting. I'd love to have a go at one of those myself
>
> nice! and such a comfy sounding tuning.
>
> -------
> So---- what more do you guys need?
>
> [Non-text portions of this message have been removed]
>
>
>
>
> [Non-text portions of this message have been removed]
>

🔗Mike Battaglia <battaglia01@...>

I'm going to throw 16 out there as well, although I'm sure most people
on here will think I'm whacked completely out of my mind. 16-ET might
catch on as some kind of "alternate universe" tuning in which the
"whole tone" scale is 8-et instead of 6-et, and in which 135/128
vanishes instead of 81/80. I don't think that it will have as broad of
an appeal as some other EDOs in the same size range, but I think there
will be a certain niche for it nonetheless.

All of these tunings will somehow require making it so that the
beating doesn't ruin people's lives and marriages and general wealth
of being, and I'm still not sure how to do that. It isn't as simple as
just picking timbres with low 3's. I think it just means that the gap
between crappy sampled instruments vs real instruments will be much
wider for 16-TET than 12-TET.

-Mike

On Tue, Feb 8, 2011 at 10:43 AM, cameron <misterbobro@yahoo.com> wrote:
>
> When using the supramajor and supraminor thirds in tertian harmony, 17-et is very similar to many uses of 12-tET-on-paper "expressive intonation". So it's like a strong flavor of the familiar. But you get the xenharmonic "neutral" intervals, so 17 can be quite xenharmonic as well. And it fits on a fretboard, no problem. I agree that it is an obvious choice for a potentially "popular" tuning.
>
> --- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@...> wrote:
> >
> > Side note...17TET seems to get good responses from just about everyone.
> > Seriously... :-D
> >
> >
> >
> >
> >
> > ________________________________
> > From: Chris Vaisvil <chrisvaisvil@...>
> > To: MakeMicroMusic@yahoogroups.com
> > Sent: Mon, February 7, 2011 6:00:31 PM
> > Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D
> >
> >
> > I'll weigh in with this book idea.
> >
> > I've seen tons of stuff in 12 equal that lists every scale known to man and
> > a few extraterrestials as well.
> >
> > Frankly I've never found that too useful. Sticking to scales has its place
> > but the real lexicon is knowing you can use all 12 notes and having some
> > idea as to why your options are.
> >
> > While there are book worm musicians out there I think most want to know some
> > generalities, maybe an example or two of a cool riff and a few ideas on how
> > to approach making music that is your own.
> >
> > Again, I think the idea is, if you want to convert the masses, is to give
> > some compelling reasons as to why go through the trouble.
> >
> > I'd ignore the "12 is hard enough" complaints because all it is expressing
> > is contentment with the available number of notes.
> >
> > I can tell you that on Alontone (a 12 tet site) I got compliments on
> > microtonal music but when I posted music composed on my 17 et guitar I
> > started seeing:
> >
> > http://alonetone.com/vaisvil/tracks/17-noodles
> >
> > -------
> >
> > *staring at his stat copy in the corner.....* do you need more notes lil'
> > buddy? do you? ;)
> >
> > That's so cool, and great tone! I want more notes too!
> > Interesting. I'd love to have a go at one of those myself
> >
> > nice! and such a comfy sounding tuning.
> >
> > -------
> > So---- what more do you guys need?
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
> >
> > [Non-text portions of this message have been removed]
> >
>
>

🔗cameron <misterbobro@...>

16 can be very pretty. And Steve Vai has used it. :-) As far as beating, 12-tET beats plenty, and I don't think beating turns people off, quite the opposite. It's beating in JI that's the real shocker. Not only the contrast with the low/"no"-beating intervals, but JI beating tends to be relatively slow and less likely to be blurred. Wogga-wogga-wogga!

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'm going to throw 16 out there as well, although I'm sure most people
> on here will think I'm whacked completely out of my mind. 16-ET might
> catch on as some kind of "alternate universe" tuning in which the
> "whole tone" scale is 8-et instead of 6-et, and in which 135/128
> vanishes instead of 81/80. I don't think that it will have as broad of
> an appeal as some other EDOs in the same size range, but I think there
> will be a certain niche for it nonetheless.
>
> All of these tunings will somehow require making it so that the
> beating doesn't ruin people's lives and marriages and general wealth
> of being, and I'm still not sure how to do that. It isn't as simple as
> just picking timbres with low 3's. I think it just means that the gap
> between crappy sampled instruments vs real instruments will be much
> wider for 16-TET than 12-TET.
>
> -Mike
>
>
> On Tue, Feb 8, 2011 at 10:43 AM, cameron <misterbobro@...> wrote:
> >
> > When using the supramajor and supraminor thirds in tertian harmony, 17-et is very similar to many uses of 12-tET-on-paper "expressive intonation". So it's like a strong flavor of the familiar. But you get the xenharmonic "neutral" intervals, so 17 can be quite xenharmonic as well. And it fits on a fretboard, no problem. I agree that it is an obvious choice for a potentially "popular" tuning.
> >
> > --- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@> wrote:
> > >
> > > Side note...17TET seems to get good responses from just about everyone.
> > > Seriously... :-D
> > >
> > >
> > >
> > >
> > >
> > > ________________________________
> > > From: Chris Vaisvil <chrisvaisvil@>
> > > To: MakeMicroMusic@yahoogroups.com
> > > Sent: Mon, February 7, 2011 6:00:31 PM
> > > Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D
> > >
> > >
> > > I'll weigh in with this book idea.
> > >
> > > I've seen tons of stuff in 12 equal that lists every scale known to man and
> > > a few extraterrestials as well.
> > >
> > > Frankly I've never found that too useful. Sticking to scales has its place
> > > but the real lexicon is knowing you can use all 12 notes and having some
> > > idea as to why your options are.
> > >
> > > While there are book worm musicians out there I think most want to know some
> > > generalities, maybe an example or two of a cool riff and a few ideas on how
> > > to approach making music that is your own.
> > >
> > > Again, I think the idea is, if you want to convert the masses, is to give
> > > some compelling reasons as to why go through the trouble.
> > >
> > > I'd ignore the "12 is hard enough" complaints because all it is expressing
> > > is contentment with the available number of notes.
> > >
> > > I can tell you that on Alontone (a 12 tet site) I got compliments on
> > > microtonal music but when I posted music composed on my 17 et guitar I
> > > started seeing:
> > >
> > > http://alonetone.com/vaisvil/tracks/17-noodles
> > >
> > > -------
> > >
> > > *staring at his stat copy in the corner.....* do you need more notes lil'
> > > buddy? do you? ;)
> > >
> > > That's so cool, and great tone! I want more notes too!
> > > Interesting. I'd love to have a go at one of those myself
> > >
> > > nice! and such a comfy sounding tuning.
> > >
> > > -------
> > > So---- what more do you guys need?
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> >
> >
>

🔗Mike Battaglia <battaglia01@...>

On Tue, Feb 8, 2011 at 10:54 AM, cameron <misterbobro@...> wrote:
>
> 16 can be very pretty. And Steve Vai has used it. :-) As far as beating, 12-tET beats plenty, and I don't think beating turns people off, quite the opposite. It's beating in JI that's the real shocker. Not only the contrast with the low/"no"-beating intervals, but JI beating tends to be relatively slow and less likely to be blurred. Wogga-wogga-wogga!

Yeah, slow beating is very pleasant. There are random times when you
arrive at slow beating intervals in ET's as well, like when you find
near-recurrence relations in a certain ET, and it's very pleasant. But
16-TET beats a lot more than 12-TET, mostly because the third harmonic
is usually much louder than the fifth harmonic in the timbres we tend
to use. Perhaps it's just a matter of getting used to it and filtering
it out, or perhaps it's a matter of figuring out what Ron Sword is
doing here:

http://www.ronsword.com/sounds/Ron%20Sword%20-%2016-tone%20acoustic%20improvisation.mp3

Where has Steve Vai used it? What have I been missing out on? Steve
Vai is precisely the type of person I had in mind for this sort of
tuning.

-Mike

> --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I'm going to throw 16 out there as well, although I'm sure most people
> > on here will think I'm whacked completely out of my mind. 16-ET might
> > catch on as some kind of "alternate universe" tuning in which the
> > "whole tone" scale is 8-et instead of 6-et, and in which 135/128
> > vanishes instead of 81/80. I don't think that it will have as broad of
> > an appeal as some other EDOs in the same size range, but I think there
> > will be a certain niche for it nonetheless.
> >
> > All of these tunings will somehow require making it so that the
> > beating doesn't ruin people's lives and marriages and general wealth
> > of being, and I'm still not sure how to do that. It isn't as simple as
> > just picking timbres with low 3's. I think it just means that the gap
> > between crappy sampled instruments vs real instruments will be much
> > wider for 16-TET than 12-TET.
> >
> > -Mike
> >
> >
> > On Tue, Feb 8, 2011 at 10:43 AM, cameron <misterbobro@...> wrote:
> > >
> > > When using the supramajor and supraminor thirds in tertian harmony, 17-et is very similar to many uses of 12-tET-on-paper "expressive intonation". So it's like a strong flavor of the familiar. But you get the xenharmonic "neutral" intervals, so 17 can be quite xenharmonic as well. And it fits on a fretboard, no problem. I agree that it is an obvious choice for a potentially "popular" tuning.
> > >
> > > --- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@> wrote:
> > > >
> > > > Side note...17TET seems to get good responses from just about everyone.
> > > > Seriously... :-D
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > ________________________________
> > > > From: Chris Vaisvil <chrisvaisvil@>
> > > > To: MakeMicroMusic@yahoogroups.com
> > > > Sent: Mon, February 7, 2011 6:00:31 PM
> > > > Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D
> > > >
> > > >
> > > > I'll weigh in with this book idea.
> > > >
> > > > I've seen tons of stuff in 12 equal that lists every scale known to man and
> > > > a few extraterrestials as well.
> > > >
> > > > Frankly I've never found that too useful. Sticking to scales has its place
> > > > but the real lexicon is knowing you can use all 12 notes and having some
> > > > idea as to why your options are.
> > > >
> > > > While there are book worm musicians out there I think most want to know some
> > > > generalities, maybe an example or two of a cool riff and a few ideas on how
> > > > to approach making music that is your own.
> > > >
> > > > Again, I think the idea is, if you want to convert the masses, is to give
> > > > some compelling reasons as to why go through the trouble.
> > > >
> > > > I'd ignore the "12 is hard enough" complaints because all it is expressing
> > > > is contentment with the available number of notes.
> > > >
> > > > I can tell you that on Alontone (a 12 tet site) I got compliments on
> > > > microtonal music but when I posted music composed on my 17 et guitar I
> > > > started seeing:
> > > >
> > > > http://alonetone.com/vaisvil/tracks/17-noodles
> > > >
> > > > -------
> > > >
> > > > *staring at his stat copy in the corner.....* do you need more notes lil'
> > > > buddy? do you? ;)
> > > >
> > > > That's so cool, and great tone! I want more notes too!
> > > > Interesting. I'd love to have a go at one of those myself
> > > >
> > > > nice! and such a comfy sounding tuning.
> > > >
> > > > -------
> > > > So---- what more do you guys need?
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > > >
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > >
> > >
> >
>
>

🔗genewardsmith <genewardsmith@...>

🔗cameron <misterbobro@...>

There was a brief time at the end of the hair-shredding era, in which some shredders started into xenharmony, then grunge pretty much put that whole shredder scene into the underground. There was another guy with spandex pants who played a 24-tET guitar- Tesla? White Lion? I'm not an expert in those genres, a friend of mine was though.

http://www.berkleepress.com/newsletter/steve_vai.htm

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Feb 8, 2011 at 10:54 AM, cameron <misterbobro@...> wrote:
> >
> > 16 can be very pretty. And Steve Vai has used it. :-) As far as beating, 12-tET beats plenty, and I don't think beating turns people off, quite the opposite. It's beating in JI that's the real shocker. Not only the contrast with the low/"no"-beating intervals, but JI beating tends to be relatively slow and less likely to be blurred. Wogga-wogga-wogga!
>
> Yeah, slow beating is very pleasant. There are random times when you
> arrive at slow beating intervals in ET's as well, like when you find
> near-recurrence relations in a certain ET, and it's very pleasant. But
> 16-TET beats a lot more than 12-TET, mostly because the third harmonic
> is usually much louder than the fifth harmonic in the timbres we tend
> to use. Perhaps it's just a matter of getting used to it and filtering
> it out, or perhaps it's a matter of figuring out what Ron Sword is
> doing here:
>
> http://www.ronsword.com/sounds/Ron%20Sword%20-%2016-tone%20acoustic%20improvisation.mp3
>
> Where has Steve Vai used it? What have I been missing out on? Steve
> Vai is precisely the type of person I had in mind for this sort of
> tuning.
>
> -Mike
>
> > --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > I'm going to throw 16 out there as well, although I'm sure most people
> > > on here will think I'm whacked completely out of my mind. 16-ET might
> > > catch on as some kind of "alternate universe" tuning in which the
> > > "whole tone" scale is 8-et instead of 6-et, and in which 135/128
> > > vanishes instead of 81/80. I don't think that it will have as broad of
> > > an appeal as some other EDOs in the same size range, but I think there
> > > will be a certain niche for it nonetheless.
> > >
> > > All of these tunings will somehow require making it so that the
> > > beating doesn't ruin people's lives and marriages and general wealth
> > > of being, and I'm still not sure how to do that. It isn't as simple as
> > > just picking timbres with low 3's. I think it just means that the gap
> > > between crappy sampled instruments vs real instruments will be much
> > > wider for 16-TET than 12-TET.
> > >
> > > -Mike
> > >
> > >
> > > On Tue, Feb 8, 2011 at 10:43 AM, cameron <misterbobro@> wrote:
> > > >
> > > > When using the supramajor and supraminor thirds in tertian harmony, 17-et is very similar to many uses of 12-tET-on-paper "expressive intonation". So it's like a strong flavor of the familiar. But you get the xenharmonic "neutral" intervals, so 17 can be quite xenharmonic as well. And it fits on a fretboard, no problem. I agree that it is an obvious choice for a potentially "popular" tuning.
> > > >
> > > > --- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@> wrote:
> > > > >
> > > > > Side note...17TET seems to get good responses from just about everyone.
> > > > > Seriously... :-D
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > ________________________________
> > > > > From: Chris Vaisvil <chrisvaisvil@>
> > > > > To: MakeMicroMusic@yahoogroups.com
> > > > > Sent: Mon, February 7, 2011 6:00:31 PM
> > > > > Subject: Re: [MMM] Re: 12 equal and fossil fuels :-D
> > > > >
> > > > >
> > > > > I'll weigh in with this book idea.
> > > > >
> > > > > I've seen tons of stuff in 12 equal that lists every scale known to man and
> > > > > a few extraterrestials as well.
> > > > >
> > > > > Frankly I've never found that too useful. Sticking to scales has its place
> > > > > but the real lexicon is knowing you can use all 12 notes and having some
> > > > > idea as to why your options are.
> > > > >
> > > > > While there are book worm musicians out there I think most want to know some
> > > > > generalities, maybe an example or two of a cool riff and a few ideas on how
> > > > > to approach making music that is your own.
> > > > >
> > > > > Again, I think the idea is, if you want to convert the masses, is to give
> > > > > some compelling reasons as to why go through the trouble.
> > > > >
> > > > > I'd ignore the "12 is hard enough" complaints because all it is expressing
> > > > > is contentment with the available number of notes.
> > > > >
> > > > > I can tell you that on Alontone (a 12 tet site) I got compliments on
> > > > > microtonal music but when I posted music composed on my 17 et guitar I
> > > > > started seeing:
> > > > >
> > > > > http://alonetone.com/vaisvil/tracks/17-noodles
> > > > >
> > > > > -------
> > > > >
> > > > > *staring at his stat copy in the corner.....* do you need more notes lil'
> > > > > buddy? do you? ;)
> > > > >
> > > > > That's so cool, and great tone! I want more notes too!
> > > > > Interesting. I'd love to have a go at one of those myself
> > > > >
> > > > > nice! and such a comfy sounding tuning.
> > > > >
> > > > > -------
> > > > > So---- what more do you guys need?
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > >
> > > >
> > >
> >
> >
>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:

> Oh, I'm going to be giving 12-tone subsets in an
> Appendix, as often as applicable, for the sake of
> keyboardists who want to jump in as simply as possible.
> I'm just not going to treat them as "scales", since it's
> widely agreed that 10 notes is the threshold between
> "diatonic-like" and "chromatic-like". And I really think
> that needing an 11-note scale to get consonant triads on
> a measly 5 roots is just horrendously inefficient. Come
> to think of it, I should be aiming for target triads on
> at least 50% of roots, not 40%, as a 10-note scale with
> target triads on only 4 roots is pretty weak as well. I
> just don't foresee people who are used to a scale as
> efficient as the diatonic taking much interest in large,
> complex, and inefficient scales.

True fans of the meantone diatonic are likely to leave
disappointed. There really is nothing else like it. But a
JI diatonic still has triads on 5 out of 7 roots, right?
Any 5-limit regular temperament preserves that ratio. You
don't need to take an MOS as your diatonic.

The number of complete chords in a tempered MOS is

2(N - k)

where N is the number of notes in the octave and k is the
complexity (sometimes called "Graham complexity" as if
there were some other obvious way of evaluating the
complexity given an odd limit). Your criterion would then
be

2(10 - k) >= 0.4

assuming a 10 note MOS existed. You can rearrange to get k
<= 9.8. But it's worse than that, because a load of
temperaments (including Magic and Orwell) naturally give
pairs of triads on the same root. You're favoring
temperaments with a simple 3:2 and so privileging Meantone
even more.

What you want may be different to what "people" want.
Partch's 43 notes have a history after all -- but not as a
diatonic.

> Although some scales produced by 5- or 7-limit
> temperaments become much better-looking if you shift the
> target triads to something more plentiful in the scale.
> Like Semaphore or Myna--both take a while to get a decent
> number of 4:5:6 triads, but are plentiful in 6:7:9's and
> 5:6:7's (respectively).

Anything that looks like a triad (meaning no semitones) in
the 9 note Orwell scale will have all intervals
approximating 11-limit ratios. You'll have to decide how
such chords compare to the 5-limit triads other
temperaments claim to have.

The tripod scale (three augmented triads separated by
semitones) has 5-limit triads on 4 out of 9 roots. They
only require 7 out of the 9 notes, as it happens. The
other two supply alternative 9-limit thirds. Like 9 notes
of Orwell (which only differs by two notes), everything
bigger than a semitone is an 11-limit approximation.

5 notes of Semaphore is, indeed, a great scale that doesn't
register in the 5-limit (but every interval is in the
9-limit, though roughly approximated). Also 7 notes of
Mohajira (all 11-limit in 31).

Graham

🔗cityoftheasleep <igliashon@...>

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "cityoftheasleep" <igliashon@...> wrote:
>
> True fans of the meantone diatonic are likely to leave
> disappointed. There really is nothing else like it. But a
> JI diatonic still has triads on 5 out of 7 roots, right?
> Any 5-limit regular temperament preserves that ratio. You
> don't need to take an MOS as your diatonic.

No, I don't. But it's easier to explore MOS scales systematically than it is other types of scales, especially for a total of 34 different EDOs.

> The number of complete chords in a tempered MOS is
>
> 2(N - k)

What do you mean "complete chords"?

> But it's worse than that, because a load of
> temperaments (including Magic and Orwell) naturally give
> pairs of triads on the same root. You're favoring
> temperaments with a simple 3:2 and so privileging Meantone
> even more.

Only for subgroups that include 3. But if anything, I'm privileging Blackwood, as it's the only 5-limit temperament with any reasonable accuracy where every single note is the root of a consonant triad.

> What you want may be different to what "people" want.
> Partch's 43 notes have a history after all -- but not as a
> diatonic.

Well, if people want to do what Partch did, they aren't going to be interested in "A Field-Guide to Alternative EDOs".

> > Although some scales produced by 5- or 7-limit
> > temperaments become much better-looking if you shift the
> > target triads to something more plentiful in the scale.
> > Like Semaphore or Myna--both take a while to get a decent
> > number of 4:5:6 triads, but are plentiful in 6:7:9's and
> > 5:6:7's (respectively).
>
> Anything that looks like a triad (meaning no semitones) in
> the 9 note Orwell scale will have all intervals
> approximating 11-limit ratios. You'll have to decide how
> such chords compare to the 5-limit triads other
> temperaments claim to have.

But what do the triads look like? Do they approximate psychoacoustically-distinct identities? I was under the impression that Orwell temperament is a 7-limit temperament, meant to approximated 7-limit otonalities. If you're using the 9-note MOS to approximate subgroup harmonies involving ratios of 11, is that "really" Orwell? Or is it a similar (but distinct) subgroup temperament?

-Igs

🔗cityoftheasleep <igliashon@...>

No, I don't. But it's easier to explore MOS scales systematically than it is other types of scales, especially for a total of 34 different EDOs.

> The number of complete chords in a tempered MOS is
>
> 2(N - k)

What do you mean "complete chords"?

> What you want may be different to what "people" want.
> Partch's 43 notes have a history after all -- but not as a
> diatonic.

Well, if people want to do what Partch did, they aren't going to be interested in "A Field-Guide to Alternative EDOs".

-Igs

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Graham Breed
> <gbreed@...> wrote:

> > The number of complete chords in a tempered MOS is
> >
> > 2(N - k)
>
> What do you mean "complete chords"?

Containing every note of an otonality or utonality, and so
every interval of an odd limit.

> > But it's worse than that, because a load of
> > temperaments (including Magic and Orwell) naturally give
> > pairs of triads on the same root. You're favoring
> > temperaments with a simple 3:2 and so privileging
> > Meantone even more.
>
> Only for subgroups that include 3. But if anything, I'm
> privileging Blackwood, as it's the only 5-limit
> temperament with any reasonable accuracy where every
> single note is the root of a consonant triad.

How is a triad, or its root, defined when you don't have a
3?

Blackwood has an error way bigger than Meantone. You're
making the decision to favor complexity over error, as well
as counting complexity to favor fifths.

There's also this:

http://x31eq.com/cgi-bin/rt.cgi?ets=21_7&limit=5

> > What you want may be different to what "people" want.
> > Partch's 43 notes have a history after all -- but not
> > as a diatonic.
>
> Well, if people want to do what Partch did, they aren't
> going to be interested in "A Field-Guide to Alternative
> EDOs".

You don't know what people are going to be interested in.
People have taken subsets of EDOs with more than 10 notes,
sometimes influenced by Partch.

> > Anything that looks like a triad (meaning no semitones)
> > in the 9 note Orwell scale will have all intervals
> > approximating 11-limit ratios. You'll have to decide
> > how such chords compare to the 5-limit triads other
> > temperaments claim to have.
>
> But what do the triads look like? Do they approximate
> psychoacoustically-distinct identities? I was under the
> impression that Orwell temperament is a 7-limit
> temperament, meant to approximated 7-limit otonalities.
> If you're using the 9-note MOS to approximate subgroup
> harmonies involving ratios of 11, is that "really"
> Orwell? Or is it a similar (but distinct) subgroup
> temperament? -Igs

I don't know what they look like. They sound fine, played
high enough up. They'll be fuzzier in EDOs within your
limit -- you'll have to decide.

Orwell has always been 11-limit that I can remember, back
to before it had a name. It has an 11-limit complexity of
17, which is better than anything else with a reasonable
approximation, unless you don't think its approximation is
reasonable, or think Augene's is, or something.

It's no subgroup: 3, 5, 7, and 11 are all approximated
within the 9 note octave.

Graham

🔗cityoftheasleep <igliashon@...>

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> How is a triad, or its root, defined when you don't have a
> 3?

By other harmonic series relationships. 4:5:7, 7:9:11, 16:18:21, etc.

> Blackwood has an error way bigger than Meantone.

Yep. But it's still a reasonable temperament, unlike Bug or Mavila. And having 10 5-limit triads for a 10-note scale and some strong 7-limit implications seems like a pretty good counter-balance for the damage.

> You're making the decision to favor complexity over error,

Only in as much as I'm refusing to include temperaments above a certain complexity threshold. I don't think that's unreasonable.

> as well as counting complexity to favor fifths.

Only in the case of 5-limit temperaments and other 3-containing subgroups. If a temperament needs more than 10 notes to get to a 3/2, I'm not going to consider it a 3-containing temperament and will treat it as a subgroup instead. For exactly the same reason that I don't consider the 7-note MOS of Helmholtz to actually be *Helmholtz*, but just a non-optimal Meantone.

> There's also this:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=21_7&limit=5

That there is. What's your point?

> You don't know what people are going to be interested in.
> People have taken subsets of EDOs with more than 10 notes,
> sometimes influenced by Partch.

I can't please everybody. By and large the objections I've heard most about microtonality from regular musicians are "I have enough trouble with 12 notes!" and "I wouldn't even know where to begin" and "there's too much math jargon, I'm just a friggin' guitar (and/or keyboard and/or bass and/or etc.) player!" The people who raise these objections are the people I'm writing for. For people who want to learn JI, there's Doty's book. For people who want to learn the Regular Mapping Paradigm in great depth, there's your site and Paul's "Middle Path" paper and the Xenharmonic Wiki. I'm writing something for people who want to be able to apply the same basic concepts and techniques they use when working in 12-tET to other equal divisions of the octave, and don't want to do it by ear alone. Since I don't want to spend the next decade writing it, that also means sticking to scales not much bigger than the diatonic, constructed analogously to the diatonic (i.e. MOS), with well-defined *triadic* harmonic bases (and possibly tetradic as well, when relevant). The goal is to make it colorful, fun, and interesting, and to ease into the more abstract stuff gently.

> Orwell has always been 11-limit that I can remember, back
> to before it had a name. It has an 11-limit complexity of
> 17, which is better than anything else with a reasonable
> approximation, unless you don't think its approximation is
> reasonable, or think Augene's is, or something.

In Paul's "Middle Path" paper, it's listed in the 7-limit temperament section. That's why I thought that. I never understood why it would be considered "only" in the 7-limit, of course, since it has such obvious 11-limit implications.

> It's no subgroup: 3, 5, 7, and 11 are all approximated
> within the 9 note octave.

Right...but remind me again on which degree of the scale you can build a full 4:5:6:7:11 otonality? Or even a 4:5:6 triad? My point is that at the level of a 9-note MOS, you're not going to be using any full 11-limit otonalities. If you're using chords at all, you're likely going to use the chords that are plentiful, and whatever chords those are will be more indicative of what the temperament really "is" for that MOS scale. Calling it an 11-limit temperament might describe how you arrived at the scale, but it doesn't describe how the scale can be used to make music.

-Igs

🔗genewardsmith <genewardsmith@...>

🔗Graham Breed <gbreed@...>

I'm on borrowed internet time again. I'll try and pick out
some things where an answer might be helpful which is
something of a blessing anyway.

"cityoftheasleep" <igliashon@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Graham Breed
> <gbreed@...> wrote:

> > http://x31eq.com/cgi-bin/rt.cgi?ets=21_7&limit=5
>
> That there is. What's your point?

I thought it was notable in my confusion last night, but
it isn't because it needs 14 notes.

> > You don't know what people are going to be interested
> > in. People have taken subsets of EDOs with more than 10
> > notes, sometimes influenced by Partch.
>
> I can't please everybody. By and large the objections
> I've heard most about microtonality from regular
> musicians are "I have enough trouble with 12 notes!" and
> "I wouldn't even know where to begin" and "there's too
> much math jargon, I'm just a friggin' guitar (and/or
> keyboard and/or bass and/or etc.) player!" The people
> who raise these objections are the people I'm writing
> for. For people who want to learn JI, there's Doty's
<snip>
> and don't want to do it by ear alone. Since I don't
want
> to spend the next decade writing it, that also means
> sticking to scales not much bigger than the diatonic,
> constructed analogously to the diatonic (i.e. MOS), with
> well-defined *triadic* harmonic bases (and possibly
> tetradic as well, when relevant). The goal is to make it
> colorful, fun, and interesting, and to ease into the more
> abstract stuff gently.

So what are you going to have? I'm trying to follow along
here. Mavila (9&7) doesn't make it. Blackwood (10&15) does
because you go up to 10 notes. (What tuning?) That should
mean Diaschismic (12&22) and Magic (19&22) as well. I
can't think of any others before we get to subgroups.

> > Orwell has always been 11-limit that I can remember,
<snip>
> > It's no subgroup: 3, 5, 7, and 11 are all
approximated
> > within the 9 note octave.
>
> Right...but remind me again on which degree of the scale
> you can build a full 4:5:6:7:11 otonality? Or even a
> 4:5:6 triad? My point is that at the level of a 9-note
> MOS, you're not going to be using any full 11-limit
> otonalities. If you're using chords at all, you're
> likely going to use the chords that are plentiful, and
> whatever chords those are will be more indicative of what
> the temperament really "is" for that MOS scale. Calling
> it an 11-limit temperament might describe how you arrived
> at the scale, but it doesn't describe how the scale can
> be used to make music.

You can't get a 4:5:6:7:11 otonality in any 9 note MOS with
recognizable approximations that I can see. So you're not
going to get the full 11-limit otonalities either. So why
mention them? Of course 11-limit scales at this complexity
are going to be used for something else. The 9 note Orwell
is one of the best. The "something else" it gives happens
not to be the 5-limit, as you well know. Why would you
choose it and not use chords?

Almost intervals in the 9 note Orwell approximate something
in the 11-limit. It looks like an 11-limit temperament. I
don't know what else you'd call it. It isn't a subgroup
temperament because the 11-limit consonances it
approximates don't constitute a subgroup of the 11-limit.
Maybe you can find a subgroup that gets it past your
barrier, but then you wouldn't be describing what it is,
which is 11-limit.

Graham

🔗Mike Battaglia <battaglia01@...>

🔗Graham Breed <gbreed@...>

🔗cityoftheasleep <igliashon@...>

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> So what are you going to have? I'm trying to follow along
> here. Mavila (9&7) doesn't make it. Blackwood (10&15) does
> because you go up to 10 notes. (What tuning?) That should
> mean Diaschismic (12&22) and Magic (19&22) as well. I
> can't think of any others before we get to subgroups.

No, I've opted to include Mavila, despite the low accuracy, though I'm going to be presenting it with plenty of caveats. All tunings of Blackwood are in. Magic and Porcupine both (apparently, they have the same complexity in 22-EDO), Diaschismic. And a lot more, actually; I'm going to include any DE scale that produces a significant number of *discernible* (note that that doesn't mean "near-Just", necessarily) harmonic series triads and/or tetrads. Orwell is definitely going to be in there, I just have to figure out what the most plentiful triads are to explain the best way to use the scale. I'm going to be covering a lot of temperaments which are as yet unnamed, I think.

> You can't get a 4:5:6:7:11 otonality in any 9 note MOS with
> recognizable approximations that I can see. So you're not
> going to get the full 11-limit otonalities either. So why
> mention them?

Exactly.

> Of course 11-limit scales at this complexity
> are going to be used for something else. The 9 note Orwell
> is one of the best. The "something else" it gives happens
> not to be the 5-limit, as you well know. Why would you
> choose it and not use chords?

Search me. It's a great scale, one of my favorites.

> Almost intervals in the 9 note Orwell approximate something
> in the 11-limit. It looks like an 11-limit temperament. I
> don't know what else you'd call it. It isn't a subgroup
> temperament because the 11-limit consonances it
> approximates don't constitute a subgroup of the 11-limit.
> Maybe you can find a subgroup that gets it past your
> barrier, but then you wouldn't be describing what it is,
> which is 11-limit.

To figure out what subgroup I'd treat it as, I'd have to look at the most plentiful triads that would form the basis for triadic harmony in the scale. An analogous case is the 5L+3s scale found in 13, 18, 23, 31, and 41-EDO, which is generated by ~21/16, where the most reasonable triadic basis is 16:18:21. Apparently it works out to be a 2.9.21 temperament. I'll see what I can work out about Orwell, although in my past experience with the scale I did not find too many "nice" triads.

-Igs