The relationship between this list and the academic community

I have been on this list for a few years, and I have probably learned
more about music theory here than in all of my previous years of
schooling combined.

And I notice that I don't see the ideas on this forum echoed much
within the academic community. When I talk to my PhD theory student
friends, they are blissfully unaware of what goes on here, and they
don't care. They seem to view it the same way that MD's view
acupuncture. They treat it like it's some kind of "alternative theory"
movement that's just a little bit crazy.

My approach has always been to say - to hell with them. Despite this,
I have to wonder - what is going on with the academic theory
community? Is the notion that they're obsessed with serialism and set
theory perhaps a mischaracterization? There are tons of PhD theory
students that defend each year, and there are reputable theory
journals - surely it can't all be a farce.

And yet, they seem to be completely ignoring everything going on here,
relegating it more or less to the realm of "alternate tunings" rather
than "theory for the foundations of music."

I'll head down to the library and go through some journals, but I'm
also curious to hear everyone's take on it here. What does modern
theory research really entail? Are there groundbreaking developments
going on that perhaps might be missed if this list is the main source
of one's information?

Or, is it all really as backwards as it seems when I look at set theory?

-Mike

MikeB>"They seem to view it the same way that MD's view acupuncture. They treat
it like it's some kind of "alternative theory" movement that's just a little bit
crazy."

>"There are tons of PhD theory students that defend each year, and there are
>reputable theory journals - surely it can't all be a farce."

I see this the same way I see relativism (theory of relativity) vs. quantum
theory in physics. People on the leading edge think quantum theory underlies
relativism, but many physicists believe quantum theory is just random witchcraft
because they can't physically SEE visible signs of the result of quantum physics
in the physical world.

Sad to say...if we want PHDs to pay attention to us, we must start by saying
how what we do support what they do in instantly-hearable/"visible" form and
then twist it around to more ultimately useful/flexible abstract theories.
I think the most obvious serious example is to
A) Play a 12TET version of a chord
B) Play a pure JI version
C) Explain why what they are hearing sounds like an improvement based on
theories of "concordance".
D) Explain that, now that they know the "basis of why it sounds good" to an
extent...they can twist that basis around to new forms of musical expression
without losing the consistency that makes 12TET work so well. Maybe show a few
scales like Wilson's and 22TET and show how the theory they know and love
translates.
E) Explain that they can also go for less consistency based on artistic
taste...and use things like JI/roughness/etc. to custom-pick amounts of
dissonance/consonance mathematically instead of being "limited" to the palette
of 12TET. Also show them additional music theories based on more advanced
scales.

*Big* agree on this. This list is unique in my experience. (Not much time today--I'll respond to your other post tomorrow.)\

There are quite a few really brilliant people who post here. (And I'm not saying that to be nice--it's simply true.)

It can be hard, though, to get started. Much of the conversation here is very advanced, I think.

A lot of what passes for theory in schools is just teaching a conventional language so that musicians can talk to each other.

Some of the rest is just trivial but self-perpetuating.

For me, the substance of what gets discussed on this *list* is so challenging that I'm often intimidated, and I consider myself pretty good at theory, and pretty interested in it.

They say that studying at MIT can be like trying to drink from a fire-hose, and that's the way this list feels to me sometimes.

But that's mostly a *good* thing.

(Now I have to check out "Octacot" !)

Caleb

On Aug 22, 2010, at 3:44 AM, Mike Battaglia wrote:

> I have been on this list for a few years, and I have probably learned
> more about music theory here than in all of my previous years of
> schooling combined.
>
>
> -Mike
>

On 22 August 2010 15:44, Mike Battaglia
> My approach has always been to say - to hell with them. Despite this,
> I have to wonder - what is going on with the academic theory
> community? Is the notion that they're obsessed with serialism and set
> theory perhaps a mischaracterization? There are tons of PhD theory
> students that defend each year, and there are reputable theory
> journals - surely it can't all be a farce.

Kyle Gann gave a fairly depressing insider's view of this:

http://tinyurl.com/2986usj

Full URL:

http://www.artsjournal.com/postclassic/2010/06/success_is_just_another_form_o.html

Choice quote:

"""
The lack of creativity goes not from the faculty upward, but from the
boards of trustees downward. Wealthy people keep the college system
alive, and they do not do so disinterestedly. They want, in return on
their investment, a kind of cultural prestige, and a kind that cannot
be supported by any rabble-rousing populism among the faculty. Arcane,
difficult-to-follow academic work feeds that prestige. Sure, you can
write about Laurie Anderson in that milieu - but only if you do so in
jargon that talks about "postmodern modes of discourse" and
"transgendering," that makes it abstract and difficult to understand
and therefore respectable - which means nonthreatening.
"""

Ironically, given that most of us are trying to be understood, the
fact that we tend to fail means we might be in with a chance. But
I've kept my hands clean of it so far.

Graham

Interesting theme, maybe I have something to add...

I can confirm lack of interest in official music circles. This has
more reasons and all of them are in narrow connection and feedback:

- Performers, singers and conductors still don't know too much about
microtonality and its possibilities as a system. But I'm sure some of
them (not keyboard players with the exception of harpsichordists)
have some knowledge about intonation and intentional work with it in
real time during play, because they play in chamber groups or
orchestras, or sing in a capella choirs where they must be aware of
intonation. Then there are all those early music authentic movement
performers, they know at least about historical tunings. But
generally "pure" microtonal performing is not part of classical music
study. It depends on personal interest and self study, or maybe
somebody has good luck to meet a teacher for microtonality. If the
performers for microtonal music are not available, of course such
music can't be performed and there's no reason to compose it.
But exactly this is a chance for all those types of creative
musicians performing their own music, or who are good improvisers.

- Composers are limited by abilities of performers on acoustic
instruments. They will not write microtonal compositions if there's
no chance for their performing. But they can work with electronic
instruments and computers without any borders concerning
microtonality. Problem is in standard education where there's no
place for microtonality in textbooks and official curriculum. All
depends on personal interest from the side of student, and his/her
self study, or again - when teacher knows about microtonality and
writes such music, then there's a chance his/her students will follow
this direction. Then more microtonal music will be performed (even
from tape, that's enough) at concerts and help to increase interest
from the side of public.
Again this is a chance for composers who are able performers as well
- they are not dependent on performers.

- Musicological research is focused mainly on historical themes (by
this I mean all music of the past, including that one written this
year) and let's say standard music theory problems. There's still a
lot what can be done, analysis, comparing, digging in archives etc. I
didn't see much articles or essays - if any - targeting the future of
the music, in the sense of Busoni's Entwurf einer neuen Ästhetik der
Tonkunst...

But everything depends on peoples. Where there's some enthusiastic
person he/she can do a lot in popularisation and education in the
field of microtonality. I don't think anybody will block such
activities. This is what I'm doing most of my music life as a
composer, performer, musicologist, teacher and music writer. It's
true I was considered maybe to be a dreamer, crazy fool, too much
experimental or so, but I taught all my students about microtonality,
they were forced to do microtonal works in our lessons, and in the
end I had some followers among my students who started to like it
(hi, Peter P) so I could be proud of them. Yes, we are still in
minority, outsiders, or better said solitaries, but our time will
come one day. Besides all of us have nothing against common 12ET
music and can make our living from it. We are not microtonal
fundamentalists, why. It's only one of many possible ways how to make
a music.
And let's don't have any illusions: there are also superficial
fashion followers among microtonalists, people doing pseudoartistic
snobbery improvisations or experiments just because they are unable
to do "normal" music, and most of microtonal works I have heard are
quite uninteresting stuff because the authors have no deep formal
music education as musicians and as composers mainly. Really high
percent of redundancy, and pure garbage. But this is part of style
development, there's always lot of garbage, and from time to time a
diamond here and there... Microtonal music is still waiting on its
Mozarts and Chopins with steady high quality artistic output.

And don't forget - even serialism and 12tone music has still lot of
interesting, challenging and not quite exhausted fields to research.
I will name just few which I'm deeply involved in last years of my
composing in this area: symmetry of all kind, work with three/four
note motivic cells, scales and modes closed in wider interval than
octave, tone groups with more than 12 members and repeated tones,
work in grey zones between tonality/seriality, tonality/modality,
seriality/modality... nothing to say about unlimited possibilities
in domains of metrorhythm, form/tectonics/architecture, layering,
synchronicity, sound design and more...

Then all those possibilities of style synthesis, searching of common
or different elements in world music cultures and intentional work
with it... This is my life task.

So actual situation will change slowly and it must start from
concrete individuals and public events - teachers, students,
performers, composers, radio stations, CD publishers, agencies,
concert and festival organizers, musicologists, conferences, music
instruments manufacturers... Which in fact is exactly what we all
together are doing, so it's on the right path, and we just can't
expect quick results. It's a long term process. It can be another 100
years, or maybe 250 or 500, who knows. Even contemporary music uses
in fact the same material like old Greek music, for example, just the
language was changed, the way how it is used. And we want to change
basic material itself, which will ask also another language. Tough job.

Daniel Forro

P.S.: Academic community has its own rules, and it's very closed
circle. Just another fresh example: my otherwise very successful,
unusual and highly attractive concert tour with a ladies chamber
group of Japanese traditional instruments in Czech Republic this May,
where we performed historical and contemporary Japanese music besides
my newest compositions, was well visited, but for example in my
former domicile city of Brno, which I visited as a concert artist for
the first time after 7 year stay in Japan (and I'm still pretty well
known there after 30 years of my stay, and concert was well
promoted), only two of my acquaintance colleague composers came, one
82 years old composer and middle age one. As far as I could recognize
nobody of Music Conservatory and Academy teachers, performers (lot
of them my former schoolmates or colleagues) or young music students
were present. So what we can expect from such attitude? There's no
apology for them. These teachers should come in the first row,
followed by all of their students, to use such interesting and rare
opportunity to experience some unusual music. So this is a reality
I've been fighting with all my life there...

On 22 Aug 2010, at 4:44 PM, Mike Battaglia wrote:

> I have been on this list for a few years, and I have probably learned
> more about music theory here than in all of my previous years of
> schooling combined.
>
> And I notice that I don't see the ideas on this forum echoed much
> within the academic community. When I talk to my PhD theory student
> friends, they are blissfully unaware of what goes on here, and they
> don't care. They seem to view it the same way that MD's view
> acupuncture. They treat it like it's some kind of "alternative theory"
> movement that's just a little bit crazy.
>
> My approach has always been to say - to hell with them. Despite this,
> I have to wonder - what is going on with the academic theory
> community? Is the notion that they're obsessed with serialism and set
> theory perhaps a mischaracterization? There are tons of PhD theory
> students that defend each year, and there are reputable theory
> journals - surely it can't all be a farce.
>
> And yet, they seem to be completely ignoring everything going on here,
> relegating it more or less to the realm of "alternate tunings" rather
> than "theory for the foundations of music."
>
> I'll head down to the library and go through some journals, but I'm
> also curious to hear everyone's take on it here. What does modern
> theory research really entail? Are there groundbreaking developments
> going on that perhaps might be missed if this list is the main source
> of one's information?
>
> Or, is it all really as backwards as it seems when I look at set
> theory?
>
> -Mike

We of the alternate tuning community also have historically done a poor job of presenting our material in a way that is easily learnable by beginning musicians. If you want academia to pay attention to the music, get people to play it on a regular basis.

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

> And I notice that I don't see the ideas on this forum echoed much
> within the academic community. When I talk to my PhD theory student
> friends, they are blissfully unaware of what goes on here, and they
> don't care. They seem to view it the same way that MD's view
> acupuncture. They treat it like it's some kind of "alternative theory"
> movement that's just a little bit crazy.

Academic scale theory has gotten a lot more interesting lately, but there still is an allergy to considering tuning in academic circles. Some of the work involves the rediscovery of stuff Erv Wilson did, and so things like MOS are talked about, but not under that name. There has also been a resurrection of interest in 19th century work, where the lattice concepts were originated, *in* the academic theory of that time, which had a very different view of things than it does now. Any day now they are likely to rediscover Fokker, I suppose, as I've seen hints of the 7-limit lattice at work. Can the hexany be far behind?

The allergy to tuning considerations sometimes has bizarre consequences; one well-known theorist rediscovered that a meantone structure to music was intrinsic to the language and theory of common-practice music, but utterly rejected that perspective since meantone suggests consideration of tuning and considering tuning is streng verboten.

> My approach has always been to say - to hell with them. Despite this,
> I have to wonder - what is going on with the academic theory
> community? Is the notion that they're obsessed with serialism and set
> theory perhaps a mischaracterization?

They used to be completely obsessed by it, to an almost lunatic extent. It was ideological. But that's changed. The idea that 12et is the be-all and end-all of tuning is still pretty strong, but the authentic performance practice movement has done a lot of damage to it, and that grew out of musicology, which academic theorists really shouldn't be able to ignore to the extent they seem to since it's in the same damned department.

But a caveat--I've never been in a PhD program in music, so I'm looking as an outsider who is familiar with academics but not music programs beyond a few undergraduate courses.

> I'll head down to the library and go through some journals, but I'm
> also curious to hear everyone's take on it here. What does modern
> theory research really entail? Are there groundbreaking developments
> going on that perhaps might be missed if this list is the main source
> of one's information?

You might check out some of the work on scales or "neo-Riemannian" theory.

Mike wrote:

> And I notice that I don't see the ideas on this forum echoed
> much within the academic community. When I talk to my PhD
> theory student friends, they are blissfully unaware of what
> goes on here, and they don't care. They seem to view it the
> same way that MD's view acupuncture. They treat it like it's
> some kind of "alternative theory" movement that's just a
> little bit crazy.

Actually it is academic theory (serialism / music set theory)
that is the alternative theory dismissed by mainstream
musicians as crazy. The regular mapping paradigm is a clear
extension of common practice theory and it recovers all of
common practice theory (such a claim is evidently important
to set theorists, but all they can do is make pathetic claims
about tone rows in Mozart).

It is also probably the case that there is now more activity
in microtonal music than serialism -- certainly the former is
growing faster. (Though they aren't mutually exclusive.)

> Is the notion that they're obsessed with serialism and set
> theory perhaps a mischaracterization?

After decades of zero demand for serial music, there is now
a lot more diversity in what grad students can do.

> There are tons of PhD theory students that defend each
> year, and there are reputable theory journals - surely it
> can't all be a farce.

When the bubble in American secondary education pops, it will
permanently kill academic music theory as it exists today.
Watch and see.

> Or, is it all really as backwards as it seems when I look
> at set theory?

Have a look at some of their literature. What do you think?

-Carl

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

> I see this the same way I see relativism (theory of relativity) vs. quantum
> theory in physics. People on the leading edge think quantum theory underlies
> relativism, but many physicists believe quantum theory is just random witchcraft
> because they can't physically SEE visible signs of the result of quantum physics
> in the physical world.

You can't get a PhD in physics without taking coursework in quantum mechanics. And the fact that solid objects exist and chemistry works is pretty visible.

> Sad to say...if we want PHDs to pay attention to us, we must start by saying
> how what we do support what they do in instantly-hearable/"visible" form and
> then twist it around to more ultimately useful/flexible abstract theories.

Academics are all about theory, but the work here suffers from the "NIH" syndrome--Not Invented Here.

I wrote:

> When the bubble in American secondary education pops,

Sorry, I always get this wrong. It's tertiary (college). -C.

On Sun, Aug 22, 2010 at 9:54 AM, Graham Breed <gbreed@...> wrote:
>
> Choice quote:
>
> """
> The lack of creativity goes not from the faculty upward, but from the
> boards of trustees downward. Wealthy people keep the college system
> alive, and they do not do so disinterestedly. They want, in return on
> their investment, a kind of cultural prestige, and a kind that cannot
> be supported by any rabble-rousing populism among the faculty. Arcane,
> difficult-to-follow academic work feeds that prestige. Sure, you can
> write about Laurie Anderson in that milieu - but only if you do so in
> jargon that talks about "postmodern modes of discourse" and
> "transgendering," that makes it abstract and difficult to understand
> and therefore respectable - which means nonthreatening.
> """
>
> Ironically, given that most of us are trying to be understood, the
> fact that we tend to fail means we might be in with a chance. But
> I've kept my hands clean of it so far.

That sucks. You'd think they'd want weird, experimental music in novel
tunings. And you can't get any more arcane or generally more
mathematically complex than regular mapping.

I think the best approach would be to overwhelm them with
multisyllabic words, using phrases like "unison vector" and "harmonic
entropy" and "hemiennealimmal" and even "cangwu badness" as much as
possible. Yes, with words such as these, and as many greek letters as
we can find, we will surely prevail.

I think I'm going to move to Japan.

-Mike

I just want to mention to Daniel that I found your story extremely
interesting. I too feel sometimes that the "microtonality" as
"pseudoartistic snobbery" is pretty common. Outside of the performers,
composers, and musicologists though - why are the theory people not
interested?

To Michael, Caleb, and Andrew:

All of you said something along the lines of that the grad school
revolution will come once we finally start writing accessible
microtonal music. And I definitely agree with that, and think it'll
carry over onto pop music too, especially if some other low-numbered
EDO proves to be particularly versatile for emotionally resonant, yet
xenharmonic music (perhaps 22-et would be good for starters)?

But let's not forget here - to peg the actions of this list into the
"microtonality," or even worse - "alternate tunings" list ignores all
of the interesting contributions that have been made to music theory
from here. Where is harmonic entropy being studied in schools? Where
is it that they talk about meantone temperaments and the defining
factor being that 81/80 is tempered out? Where is the explanation of
tritone substitutions as arising from the fact that the diatonic scale
is not strictly proper, so the diminished fifth is an ambiguous
interval? Or that since 49/48 is tempered out, an equal tempered
tritone can approximate 7/5 and 10/7 almost equally well?

Even if one doesn't want to get into all of this hedonism about
alternate tunings, aren't those things important? It just seems silly
to me. What are music theory PhD's learning about if not stuff like
that? Yikes.

-Mike

On Sun, Aug 22, 2010 at 1:26 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > And I notice that I don't see the ideas on this forum echoed much
> > within the academic community. When I talk to my PhD theory student
> > friends, they are blissfully unaware of what goes on here, and they
> > don't care. They seem to view it the same way that MD's view
> > acupuncture. They treat it like it's some kind of "alternative theory"
> > movement that's just a little bit crazy.
>
> Academic scale theory has gotten a lot more interesting lately, but there still is an allergy to considering tuning in academic circles. Some of the work involves the rediscovery of stuff Erv Wilson did, and so things like MOS are talked about, but not under that name. There has also been a resurrection of interest in 19th century work, where the lattice concepts were originated, *in* the academic theory of that time, which had a very different view of things than it does now. Any day now they are likely to rediscover Fokker, I suppose, as I've seen hints of the 7-limit lattice at work. Can the hexany be far behind?

Ah. So that's why it's called MOS as well as Myhill's property?
Because some guy named Myhill just rediscovered what had already been
discovered?

If I just rip off Fokker's stuff, can I get a free PhD?

> The allergy to tuning considerations sometimes has bizarre consequences; one well-known theorist rediscovered that a meantone structure to music was intrinsic to the language and theory of common-practice music, but utterly rejected that perspective since meantone suggests consideration of tuning and considering tuning is streng verboten.

And all of this is a hangover from people trying to stuff all of music
theory into the set theory box?

> They used to be completely obsessed by it, to an almost lunatic extent. It was ideological. But that's changed. The idea that 12et is the be-all and end-all of tuning is still pretty strong, but the authentic performance practice movement has done a lot of damage to it, and that grew out of musicology, which academic theorists really shouldn't be able to ignore to the extent they seem to since it's in the same damned department.
>
> But a caveat--I've never been in a PhD program in music, so I'm looking as an outsider who is familiar with academics but not music programs beyond a few undergraduate courses.

I will say that I studied theory as a jazz major, so I got to learn
things a lot differently than the classical folks did. I feel like the
theory I've learned basically trumps common practice theory as a
beautiful extension, and that the stuff on this list trumps the theory
I've learned as an even more beautiful extension.

Well, at least that's what I thought, until I discovered how little JI
matters, and how much equivalence classes matter, so now I don't feel
like I understand how music works at all anymore. But that's alright.
Either way, when I see stuff like this on Wikipedia:

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

Whoop de doo, it's a frickin C7#11 chord. It even has a 13 in there as
well. Hit the big red alarm button.

So what we have is a pretty common quartal voicing for C lydian
dominant. But, this article says that it's a "synthetic chord" from a
"synthetic scale" (see http://en.wikipedia.org/wiki/Synthetic_scale).
As we can see, a synthetic scale is when you take a normal, natural
scale, and alter one of the notes without remorse or regard for basic
humanity. In this case, these enterprising theorists have come up with
the idea that this famous and awe-inspiring "mystic chord" is created
when you mess the whole tone scale up.

So I have always felt that "mainstream theory" is just a little bit
stupid, and I'm wondering how far the rabbit hole goes.

> > I'll head down to the library and go through some journals, but I'm
> > also curious to hear everyone's take on it here. What does modern
> > theory research really entail? Are there groundbreaking developments
> > going on that perhaps might be missed if this list is the main source
> > of one's information?
>
> You might check out some of the work on scales or "neo-Riemannian" theory.

I will definitely check that out, hopefully it's not too far over my head.

-Mike

On Sun, Aug 22, 2010 at 1:30 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > And I notice that I don't see the ideas on this forum echoed
> > much within the academic community. When I talk to my PhD
> > theory student friends, they are blissfully unaware of what
> > goes on here, and they don't care. They seem to view it the
> > same way that MD's view acupuncture. They treat it like it's
> > some kind of "alternative theory" movement that's just a
> > little bit crazy.
>
> Actually it is academic theory (serialism / music set theory)
> that is the alternative theory dismissed by mainstream
> musicians as crazy. The regular mapping paradigm is a clear
> extension of common practice theory and it recovers all of
> common practice theory (such a claim is evidently important
> to set theorists, but all they can do is make pathetic claims
> about tone rows in Mozart).

It is certainly the most sensible theory I've come across. If I could
just figure out how it interfaces with this Rothenberg equivalence
class stuff, and really see the big picture for everything, I'd be a
happy man...

> > There are tons of PhD theory students that defend each
> > year, and there are reputable theory journals - surely it
> > can't all be a farce.
>
> When the bubble in American secondary education pops, it will
> permanently kill academic music theory as it exists today.
> Watch and see.

I think I'm going to study medicine.

> > Or, is it all really as backwards as it seems when I look
> > at set theory?
>
> Have a look at some of their literature. What do you think?
>
> -Carl

I'll take a look at it and see. Rumor has it that literature can be
found at libraries, for free. Instead of me paying hundreds of dollars
for a membership. If the former is the case, there will be many a lit
search done.

-Mike

On Sun, Aug 22, 2010 at 1:33 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > Sad to say...if we want PHDs to pay attention to us, we must start by saying
> > how what we do support what they do in instantly-hearable/"visible" form and
> > then twist it around to more ultimately useful/flexible abstract theories.
>
> Academics are all about theory, but the work here suffers from the "NIH" syndrome--Not Invented Here.

What do you mean by this? Just referencing how much originated from
Erv Wilson and Fokker?

-Mike

Some observations I made in this aspect: there are quite a number of contemporary microtonal composers around - Georg Friedrich Haas, Klaus Huber, Edu Haubensak, several austrian composers, to name just a few; there is even an organization, the international ekmelic music society - but I have never seen any one of these here or in the various other microtonal lists and forums. It looks like microtonality IS well part of the academic music world - but just this list is not, nor the many others. It looks as if they do not even know these lists exist. I wonder why?
--
Hans Straub

>"Where is harmonic entropy being studied in schools? "
Call me a critic...but I think we all should make a deliberate effort to
figure out what each theory can/can't do before we try to "push it" to the rest
of the world. Even on this list there has been confusion IE even Paul said HE
couldn't predict certain things we thought it could. I am thinking a primer on
HE vs. odd-limit vs. mapping vs. Tenney Height vs. rootness vs.
critical-band-dissonance would help. Especially if it also explained how much
of each theory was attributable to the waveform physics of periodicity vs. the
human-ear-physiology of critical band vs. the brains supposed interpretation of
things as being a whole unit IE "rooted-ness" and "entropy".
My guess is people don't teach it because they haven't figured out that it
underlies current music theory, and not just the "weird" more advanced
micro-tonal material.

>"Where is it that they talk about meantone temperaments and the defining factor
>being that 81/80 is tempered out?"

One thing I've noticed is that things like "tempering out" seem to be worded
as more complex than they are...in the same way that, in the end of the day, all
a derivative is in calculus is a slope (albeit a slope nearing a specific point
IE x on a curve). We all too often seem to make the mistake of relating things
to more advanced terms WE know well instead of finding the creativity to put
microtonal theories in terms of "normal" musical vocabulary.

For example one way I think of temperament is just a side effect of that
taking a circle of perfect fifths (IE (3/2)^7) creates a value more than an
octave AKA power of two (IE around 17 instead of 16), so we shrink the fifth to
make it exactly an octave. And that compensation is called "tempering out".
And same sort of thing applies for circles of thirds, seconds...in other tuning
systems IE it's a simple, consistent theory...not a bunch of random
"exceptions".

>"Or that since 49/48 is tempered out, an equal tempered tri-tone can approximate
>7/5 and 10/7 almost equally well?"
Of course this sort of thing matters a lot. The sad thing, as I see it, is
that such PHDs are often thought of such things as an artifact of the technique
of a certain era or composer...and not as a direct effect of the math and
physics behind human hearing.

I'd almost compare it for them as asking "Would you rather know that Escher
was responsible for great art and what patterns he liked to use...or understand
not only mathematical constructs like tesselations underlying his work, but
knowing them well enough you can understand how they could be changed and used
in ways he had not thought of?"

Or even...
"Do you know why this consonance/dissonance/contrast works beyond the fact X
established artists used it and/or it was a product of X time period? Wouldn't
you like to?"

>"What are music theory PhD's learning about if not stuff like that? Yikes."
Simply put, music has sadly seem to have become more about re-stating history
than learning why things work and extending those patterns. The fact lots of
researchers realize starting on a new path could make a lot of their old
research seem "trashed" does not help our marketing "push" any either. How
would you feel if you spent your life studying Beethoven only to find that 40%
of the "magical modulations" you studied were attributable to a simple tempering
between two fractions and a changing of root-ness in two dyads from a large
percent of the chords he used?

That's a huge danger to some people I'm guessing...realizing that a lot of
music is NOT magic and can often be reduced to numbers to a fair extent.

On 23 August 2010 14:43, Mike Battaglia <battaglia01@...> wrote:

> Or that since 49/48 is tempered out, an equal tempered
> tritone can approximate 7/5 and 10/7 almost equally well?

50/49.

There's also 100/99 which allows for tritone substitutions. You make
a dominant seventh by adding a minor third to a major triad. The
tritone is 6/5 * 6/5 = 36/25. 11/8 * 100/99 = 25/18. So the
complement of the tritone in the dominant seventh can be substituted
with an 11/8, and you can put a complete chord under that.

You can also use a 16/9 seventh. The tritone is 16/9 * 4/5 = 64/45.
You can substitute that with a 10/7 if you temper out 10/7 * 45/64 =
225/224. So you can make that substitution in any Marvel temperament.

Graham

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

> Ah. So that's why it's called MOS as well as Myhill's property?
> Because some guy named Myhill just rediscovered what had already been
> discovered?

That came out of a paper by John Clough the music theorist and Gerry Myerson the number theorist. Gerry told me that Clough came to him wanting him to put the professional mathematician polish on the work he was trying to do with scale theory, and Gerry provided proofs. John Myhill, another mathematician, pointed out the centrality of what came to be called "Myhill's property" to the work they were doing, and so it got named after him. The Clough and Myerson paper had a big impact in starting interest in scale theory in academic circles.

> > The allergy to tuning considerations sometimes has bizarre consequences; one well-known theorist rediscovered that a meantone structure to music was intrinsic to the language and theory of common-practice music, but utterly rejected that perspective since meantone suggests consideration of tuning and considering tuning is streng verboten.
>
> And all of this is a hangover from people trying to stuff all of music
> theory into the set theory box?

More a hangover from the conviction that God created 12edo, and then rested, saying it was very good.

On Mon, Aug 23, 2010 at 12:29 PM, Graham Breed <gbreed@...> wrote:
>
> On 23 August 2010 14:43, Mike Battaglia <battaglia01@...> wrote:
>
> > Or that since 49/48 is tempered out, an equal tempered
> > tritone can approximate 7/5 and 10/7 almost equally well?
>
> 50/49.

Right, that's what I said!

> There's also 100/99 which allows for tritone substitutions. You make
> a dominant seventh by adding a minor third to a major triad. The
> tritone is 6/5 * 6/5 = 36/25. 11/8 * 100/99 = 25/18. So the
> complement of the tritone in the dominant seventh can be substituted
> with an 11/8, and you can put a complete chord under that.

So one tritone would be 11/8, and the other would be 16/11, which
becomes equivalent to 36/25? That sounds like a cool idea, but would
it lead to the same kind of tritone subs that we have now, where you
can have C-G- E-Bb and go right to C#-F#-E-A#? I don't see how you
could substitute anything here.

> You can also use a 16/9 seventh. The tritone is 16/9 * 4/5 = 64/45.
> You can substitute that with a 10/7 if you temper out 10/7 * 45/64 =
> 225/224. So you can make that substitution in any Marvel temperament.

That's true, and I suppose you could map things that way as well.
Although as with the above example, this would only resemble classical
tritone subs if 64/45 and its inverse were equated, which if we're
using marvel means that 50/49 gets nixed.

But I suppose, taking your logic further - perhaps tritone subs aren't
really tied down to the ambiguity (or versatility) of sqrt(2). Even if
you're in JI, you could still do tritone subs just by retuning the 7/5
to 10/7 and having that little intonational shift, which would
probably not sound too bad. But if we're trying to explain 12-tet, I
think a large part of the reason they "work" so well is that the
interval is ambiguous in the diatonic scale. And, however it's
functioning from a periodic standpoint, whether 7/5 or 64/45, it can
function the same way as the inverse of that interval. I always
assumed that dom7 chords are very rough 7-limit chords, although I
suppose that they don't have to be.

-Mike

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

> > Academics are all about theory, but the work here suffers from the "NIH" syndrome--Not Invented Here.
>
> What do you mean by this? Just referencing how much originated from
> Erv Wilson and Fokker?

I mean the stuff you read about on the tuning list, not just Wilson and Fokker but regular mapping stuff and etc, is NIH so far as academic music theory is concerned.

>"But I suppose, taking your logic further - perhaps tritone subs aren't
really tied down to the ambiguity (or versatility) of sqrt(2). Even if
you're in JI, you could still do tritone subs just by retuning the 7/5
to 10/7 and having that little intonational shift, which would
probably not sound too bad."

But either way...we're talking a not-so-hot over 13 cents difference in the
shift (IE between 7/5 and sqrt(2) or 10/7 and square root of 2).
Would it be fair to pitch this to musical academics as "12TETs tri-tone does a
decent job of approximating the true mathematical representation of chords
formed using it...but still is significantly far enough from perfect that you
could gain by learning how and why the perfect form works".

General statement: it still amazes me all the hoopla that has been going on
in comparing Just Intonation to temperament. It seems to me Just Intonation has
an advantage in that it can be explained in great detail using simple fractions
but temperament has a huge advantage in allowing more equal distribution of
rooted-ness and accuracy. Moreover it seems to me there's a stigma floating
around that tempered scales can't or shouldn't be reduced to nearby (often
fairly high limit IE 13-odd-limit) JI dyads to make them more readily
analyze-able.

Is there any problem with, say, simply taking a tempered scale, rounding its
ratios to the lowest limit fractions within about 7-cents of them, and then
seeing what kinds of chords are possible with those fractions?

Surely, I figure, it we did that we can at least say which chords are
available and how consonant they are on a dyadic basis (IE in how many
individual dyads in possible chords are either fairly low limit), if not also on
a triadic basis (realizing something that can only be reduced to, say, a
26:29:34 chord representation may be a bit much).

Hi Mike~
i would add to that you can do the same thing within a JI system also

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

> Is there any problem with, say, simply taking a tempered scale, rounding its
> ratios to the lowest limit fractions within about 7-cents of them, and then
> seeing what kinds of chords are possible with those fractions?

--

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

On 24 August 2010 02:36, Mike Battaglia <battaglia01@...> wrote:

> So one tritone would be 11/8, and the other would be 16/11, which
> becomes equivalent to 36/25? That sounds like a cool idea, but would
> it lead to the same kind of tritone subs that we have now, where you
> can have C-G- E-Bb and go right to C#-F#-E-A#? I don't see how you
> could substitute anything here.

No, it'd lead to different substitutions and different music theory.
From what I've tried it sounds pretty good. With C-G-E-Bb, the E-Bb
is the tritone. With this substitution, E is the 11 and Bb is the 16
(check I got that right). So the substituted chord is a Bb major,
with added E that should be higher than the F. Maybe Bb-F-D-E-Bb.

> That's true, and I suppose you could map things that way as well.
> Although as with the above example, this would only resemble classical
> tritone subs if 64/45 and its inverse were equated, which if we're
> using marvel means that 50/49 gets nixed.

Yes, that's what's assumed, but it leads to the dominant seventh being
the same as the 7-limit harmonic seventh. When you move nearer to JI
it pulls the harmony out of kilter. So what you can do is subsitute a
real harmonic seventh.

Take C-G-E-Bb again. E-Bb isn't 7/5 (that would be E-A#) so it must
be 10/7. E is harmonic number 7 and Bb is harmonic number 5. So the
substituted chord is a Gb major. Db-Gb-E-Bb.

With both these examples, C-G-E-Bb may not be the voicing you'd really
want to start with.

> But I suppose, taking your logic further - perhaps tritone subs aren't
> really tied down to the ambiguity (or versatility) of sqrt(2). Even if
> you're in JI, you could still do tritone subs just by retuning the 7/5
> to 10/7 and having that little intonational shift, which would
> probably not sound too bad. But if we're trying to explain 12-tet, I
> think a large part of the reason they "work" so well is that the
> interval is ambiguous in the diatonic scale. And, however it's
> functioning from a periodic standpoint, whether 7/5 or 64/45, it can
> function the same way as the inverse of that interval. I always
> assumed that dom7 chords are very rough 7-limit chords, although I
> suppose that they don't have to be.

This is what's suggested. I haven't been presented with evidence that
anything breaks when you make the intervals unequal. There probably
is a sense in which the ear is recognizing symmetric divisions. But
how sensitive is it? If 400 cents can substitute for a 5/4, why not
11/8 for a half-octave?

Graham

On Tue, Aug 24, 2010 at 1:16 AM, Graham Breed <gbreed@...> wrote:
>
> On 24 August 2010 02:36, Mike Battaglia <battaglia01@...> wrote:
>
> > So one tritone would be 11/8, and the other would be 16/11, which
> > becomes equivalent to 36/25? That sounds like a cool idea, but would
> > it lead to the same kind of tritone subs that we have now, where you
> > can have C-G- E-Bb and go right to C#-F#-E-A#? I don't see how you
> > could substitute anything here.
>
> No, it'd lead to different substitutions and different music theory.
> From what I've tried it sounds pretty good. With C-G-E-Bb, the E-Bb
> is the tritone. With this substitution, E is the 11 and Bb is the 16
> (check I got that right). So the substituted chord is a Bb major,
> with added E that should be higher than the F. Maybe Bb-F-D-E-Bb.

Ah, I see. Another interesting possibility is what happens in 22-et,
which is that 27/20 and 11/8 get equated. So chords like C Eb+ G Bb+ D
F+ can change to C E- G Bb D F+, where - and + denote one step of
22-et and the naming is by fifths.

> > That's true, and I suppose you could map things that way as well.
> > Although as with the above example, this would only resemble classical
> > tritone subs if 64/45 and its inverse were equated, which if we're
> > using marvel means that 50/49 gets nixed.
>
> Yes, that's what's assumed, but it leads to the dominant seventh being
> the same as the 7-limit harmonic seventh. When you move nearer to JI
> it pulls the harmony out of kilter. So what you can do is subsitute a
> real harmonic seventh.
>
> Take C-G-E-Bb again. E-Bb isn't 7/5 (that would be E-A#) so it must
> be 10/7. E is harmonic number 7 and Bb is harmonic number 5. So the
> substituted chord is a Gb major. Db-Gb-E-Bb.

Wait, this is assuming we're in some marvel temperament that doesn't
eliminate 50/49 now? As in, 31-tet or something?

> With both these examples, C-G-E-Bb may not be the voicing you'd really
> want to start with.
>
> > But I suppose, taking your logic further - perhaps tritone subs aren't
> > really tied down to the ambiguity (or versatility) of sqrt(2). Even if
> > you're in JI, you could still do tritone subs just by retuning the 7/5
> > to 10/7 and having that little intonational shift, which would
> > probably not sound too bad. But if we're trying to explain 12-tet, I
> > think a large part of the reason they "work" so well is that the
> > interval is ambiguous in the diatonic scale. And, however it's
> > functioning from a periodic standpoint, whether 7/5 or 64/45, it can
> > function the same way as the inverse of that interval. I always
> > assumed that dom7 chords are very rough 7-limit chords, although I
> > suppose that they don't have to be.
>
> This is what's suggested. I haven't been presented with evidence that
> anything breaks when you make the intervals unequal. There probably
> is a sense in which the ear is recognizing symmetric divisions. But
> how sensitive is it? If 400 cents can substitute for a 5/4, why not
> 11/8 for a half-octave?

I don't know. It could possibly work out. But it would change things a
bit - one of the real strengths of tritone substitutions in 12-tet are
that not only does it temper 50/49, but also 128/125. C7 doesn't just
become Gb7, but the full C altered scale becomes the full Gb lydian
dominant scale, and both of these work for dominant 7 chords.

So for our viewers at home, you have the altered scale, which is

C Db Eb Fb Gb Ab Bb C

Except, it's usually used as a dominant 7 chord going to minor, and
since 128/125 vanishes it's often "treated" as though it were actually
harmonically spelled

C Db D# E F# (G#/Ab) Bb C

That is, instead of treating it like a super-dark alteration to
Locrian (Locrian b4) you treat it like it's a scale with both a b2 and
a #2, and a major third. And note that the fifth mode of this scale is
Gb lydian dominant, which is

Gb Ab Bb C Db Eb Fb Gb

This is also used over a dom7 chord in a lot of cases. So the idea is
that the tritone sub concept applies to these scales these scales are
"equivalent" - e.g. you could play Dm7b5 -> G7alt -> Cm, or you could
play Dm7b5 -> Db9#11 -> Cm, and the same notes are used in each case.

Either way, the fact is that even if you don't use the above scales,
most of the same melodies are playable over C7 and F#7 without any
intonational shifts whatsoever. Perhaps this is more of a practical
consideration rather than a psychoacoustic one, however.

-Mike

-Mike

On 25 August 2010 07:36, Mike Battaglia <battaglia01@...> wrote:
> On Tue, Aug 24, 2010 at 1:16 AM, Graham Breed <gbreed@...> wrote:
>>
>> On 24 August 2010 02:36, Mike Battaglia <battaglia01@...> wrote:

>> Take C-G-E-Bb again. E-Bb isn't 7/5 (that would be E-A#) so it must
>> be 10/7. E is harmonic number 7 and Bb is harmonic number 5. So the
>> substituted chord is a Gb major. Db-Gb-E-Bb.
>
> Wait, this is assuming we're in some marvel temperament that doesn't
> eliminate 50/49 now? As in, 31-tet or something?

Any of the numerous marvel temperaments, like Meantone, Magic,
Miracle, Orwell, and so on. It'll work even in Pajara but the chord
types won't be distinguished. The notation there implies meantone.

The 11/8 substition I gave works in Magic. There are other classes
that temper out the 100/99 but they don't do it as accurately.

> I don't know. It could possibly work out. But it would change things a
> bit - one of the real strengths of tritone substitutions in 12-tet are
> that not only does it temper 50/49, but also 128/125. C7 doesn't just
> become Gb7, but the full C altered scale becomes the full Gb lydian
> dominant scale, and both of these work for dominant 7 chords.

It'd change things, yes.

> So for our viewers at home, you have the altered scale, which is
>
> C Db Eb Fb Gb Ab Bb C

Where does that come from? It doesn't include F-B or E-Bb.

> Except, it's usually used as a dominant 7 chord going to minor, and
> since 128/125 vanishes it's often "treated" as though it were actually
> harmonically spelled
>
> C Db D# E F# (G#/Ab) Bb C

If you're using generalized meantone, that gives you a different scale.

> That is, instead of treating it like a super-dark alteration to
> Locrian (Locrian b4) you treat it like it's a scale with both a b2 and
> a #2, and a major third. And note that the fifth mode of this scale is
> Gb lydian dominant, which is
>
> Gb Ab Bb C Db Eb Fb Gb
>
> This is also used over a dom7 chord in a lot of cases. So the idea is
> that the tritone sub concept applies to these scales these scales are
> "equivalent" - e.g. you could play Dm7b5 -> G7alt -> Cm, or you could
> play Dm7b5 -> Db9#11 -> Cm, and the same notes are used in each case.

Diatonic scales only work, with their usual harmonies, in meantone.
If you want tritone equivalence of such scales, you need the tritone
to be a perfect half-octave. That means the diatonic has to be tuned
to 12-equal. So congratulations, you've isolated a phenomenon that
requires 12-equal. But you haven't shown there aren't other things
you can do in other tuning systems.

> Either way, the fact is that even if you don't use the above scales,
> most of the same melodies are playable over C7 and F#7 without any
> intonational shifts whatsoever. Perhaps this is more of a practical
> consideration rather than a psychoacoustic one, however.

I think a lot of these are rules that help musicians understand what's
hapening. But I think these temperament-driven equivalences (and
there are plenty of them, each implying a unison vector) are
interesting ways to build harmony.

Graham

>"Diatonic scales only work, with their usual harmonies, in meantone.
If you want tritone equivalence of such scales, you need the tritone
to be a perfect half-octave."
True...but using square root of two as the period (as my Silver-section scale
does) would also achieve the same effect...correct?

> Diatonic scales only work, with their usual harmonies, in meantone.

How come superpyth gets no love around here? :(

> If you want tritone equivalence of such scales, you need the tritone
> to be a perfect half-octave. That means the diatonic has to be tuned
> to 12-equal. So congratulations, you've isolated a phenomenon that
> requires 12-equal. But you haven't shown there aren't other things
> you can do in other tuning systems.

Right. The context in which I made my original point was that even for
all of these people in academia who are terrified of other tunings,
there's at the very least still a ton of insight to be gained into
existing 12-equal music by using regular mapping. And applying a
regular mapping perspective to 12-tet can certainly in itself lead to
new scales and harmonic ideas - consider that 12-tet supports pajara,
and all of the decatonic scales apply to 12-tet as well. And consider
that 12-tet has excellent approximations to 17/16 and 19/16, which
could possibly lead to some interesting musical territory (it implies
256/255 vanishes, among other things).

So as you've pointed out, the reason the above substitution works is
that it's the only 5-limit rank 1 temperament eliminating 81/80 and
128/125 (and 50/49 if we're going to go up to the 7-limit). ...Well,
isn't that important knowledge? Even if you're completely
xenharmoniphobic, is that not worthwhile knowledge to disseminate?
Especially being as the goal of music theory is to understand how
music works, even if only in 12-tet.

But wrt to your 11/8 substitution ideas, another one that makes for
some strange chord progressions is in 22-equal, where 55/54 vanishes,
and hence 27/20 and 11/8 are equated. So you can play chord
progressions like C Eb+ G Bb+ D F+ -> C E- G Bb D F+, where the F is
held constant. It's pretty puntastic.

> > Either way, the fact is that even if you don't use the above scales,
> > most of the same melodies are playable over C7 and F#7 without any
> > intonational shifts whatsoever. Perhaps this is more of a practical
> > consideration rather than a psychoacoustic one, however.
>
> I think a lot of these are rules that help musicians understand what's
> hapening. But I think these temperament-driven equivalences (and
> there are plenty of them, each implying a unison vector) are
> interesting ways to build harmony.

Indeed. Now, if I could only figure out the "big picture" of how JI
fits into all of this, I'd be set for life. The fact that meantone[7]
and superpyth[7] can substitute for each other basically destroyed any
idea that I had of temperament being a warping of JI.

-Mike

I am late in commenting on this thread which places my comment out of order which i am sorry for.

From what i understand of the academic community is that they put a priority on actual composed music and are interested in theory only as it explains those works. Perhaps this is a safeguard from pure speculations. So i think it breaks down to it will accept a bad theory by a good composer before it will accept a good theory by a bad one or not one at all. I am not quite sure you can remedy that. The best proof will always be good music applying a theory.

--

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

Kraig>"From what i understand of the academic community is that they put a
priority on actual composed music and are interested in

theory only as it explains those works."

So we seem to get stuck with the following double standard. To make our
theories provable...we need great music (not just considered great to us
microtonalists, but also to the masses). But to get great music (in that sense)
often takes lots of musicians, with only the top few out of millions of aspiring
ones making such music. But to get so many musicians doing that in an art, you
need for them to come in wanting to learn the theory. Which in the case of
micro-tonal (again) requires the theories to be proved. It's a huge loop.

Again it seems to point to my old suggestion of having a major pop act use
micro-tonal as a staple of their style. If someone on the same level as the
Beatles, The Who, Beethoven, The Rolling Stones...who was known well for decades
used microtonallity extensively...then you'd IMVHO get tons of musicians wanting
to learn it and, out of those, a few greats to keep the theory having the status
of "being worth passing on to the next generation".

Another issue...I like liquid drum and bass and abstract trance music such as
BT and Way Out West. Which, admittedly, is never going to get anywhere near the
popularity of bands like The Beatles or classical legends like Beethoven. And
to be real...I think neo-classical music, punk rock (with the exception perhaps
of the genre's Godfathers, the Ramones), metal, world music, and many of the
other genres focused on here have the same issue when it comes to lacking the
level of popularity needed to get people to "study micro-tonal works" on a scale
large enough to break into the realm of equal public awareness with 12TET.

My guess is the best way to get micro-tonal music famous is to have a leading
rock band with decent sex appeal take it over. Hey, it's what the Beatles,
Doors, Rolling Stones, Pearl Jam, Nirvana...and tons of teens got into music
because of them and sometimes ended up starting very successful bands using
musical techniques learned from them. Start with a simple garage band, get more
complex later on.
Another admitted path to being a classic/widely-memorable artist is hip-hop
(2PAC, Notorious Big)...but then lyrics and beats often take precedence over the
actual music theory.
And the ones who take on the more advanced side of those techniques became the
Joe Pass's and new Beethoven's of the world.

Now my question is where would we find such a musician to get the pattern
started?

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

> Now my question is where would we find such a musician to get the pattern
> started?

You seem to be assuming that academic music people pay attention to popular music, which mostly they don't. Even when they do, they are not going to stick Beethoven in with a list of 20th century rock groups.

Gene wrote:

>Even when they do, they are not going to stick Beethoven in
>with a list of 20th century rock groups.

Which is of course another grievous oversight. -Carl

Indeed, Pink Floyd is extremely theory based music. But the theory is
only accessible when under the influence of lysergic acid diethylamide
or mescaline.

On Fri, Aug 27, 2010 at 4:07 PM, Carl Lumma <carl@...> wrote:
>
>
>
> Gene wrote:
>
> >Even when they do, they are not going to stick Beethoven in
> >with a list of 20th century rock groups.
>
> Which is of course another grievous oversight. -Carl
>

>> Now my question is where would we find such a musician to get the pattern
>> started?

>"You seem to be assuming that academic music people pay attention to popular
>music, which mostly they don't. Even when they do, they are not going to stick
>Beethoven in with a list of 20th century rock groups."

Put it this way. Take someone in college taking a music degree (either jazz
or classical) and ask them what got them big into music. There's a huge chance
it's not going to be, say, Debussy...and more likely to be the Beatles or
something "even" more cheesy. And for those who really did get into music
because of the theoretical works of more "off the deep end" artists...how many
have actually gotten the chance to be in a group popular enough to be on the
news or some other medium that changed a popular style?

An easy example, my brother got into music because of rock, earned a jazz
guitarist degree in college, and now plays mostly rock as a cover-band. Sure
his academic training helps...but what really gets his shows going crazy is when
he injects a jazz-level solo into a song people can easily understand in such a
way that does not ditch relate-able emotion for technique. Saying I'm insisting
academic people "must pay attention to popular music" seems kind of like saying
that because he does cover songs he must have no respect for jazz...you CAN pay
attention to both. I'm saying you can have a huge hand in academia, but the
chances of that spinning over and, say, creating a new genre or acceptance of
non-academic micro-tonal music are likely much smaller than someone with a
balanced view of academia and pop.

From rock to early punk, blues to jazz, r&b to funk to disco, rock to metal
to industrial...just about every recent major musical movement within the last
40 or so years has been one popular style (IE with at least one huge hit)
inspiring someone to create another. Would big-beat have become so big if the
Chemical Brothers and Fatboy Slim weren't able to make it pop up on charts? Or
funk have become so popular if people like Chubby Checkers weren't around
promoting R&B so well? Or would industrial music have come around if it
weren't for both heavy psychedelic rock and breakthrough groups like "The
Prodigy"?

Now if you compare early blues to modern industrial they seem as different
as night and day...but I think it's fair to say they come from a chain of
influence by popular groups, not because, say, some guy came up to a blues
player and told him he should try E-minor scales, distorted leads, beat-boxes,
and creepy sound effects just because a master of theory invented or suggested
them.

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

My greater point is; we can't just push people into wanting to learn
micro-tonal music by telling them what it is and why it's great with a lot of
intellectual authority. You can't make many people want to "join a religion"
just by being the world's expert on that religion. IMVHO we need examples, not
just solid academic explanations but fleeting examples...like the kind of
examples groups like The Supremes, The Ramones, Led Zepplin, Kraftwerk, and
countless others who "crossed us over" to new genres. Note, many of these WERE
academically inclined, BT and Metallica being two huge examples...but they
didn't let academics be the be-and-end all of their work either.

Coming back to Kraig's point...the music world follows the studies of
existing works of music that are already considered great and tries to extract
theory from it. It does NOT only have to apply to academics studying the
classics in music history...it could be as simple as a teenager reading tabs in
Guitar World Magazine on the long path to becoming the kind of level my brother
is at today. Or something much bigger.

:) I don't care much for Floyd and I wasn't referring to
theory. Just to the fact that, any time you have a popular
genre of music with a culture that rewards people for working
hard at it, some of it is gonna be good. This stereotypical
academic music person wants us to believe that anything with
a drum kit in it is bad? That's just absurd on the face of it.
Similarly, rock fans would have you believe nobody was making
or enjoying good music 200 years ago. Also pretty absurd.
The more likely explanation is that both groups have deficient
listening skills, and probably cultural bias too.

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Indeed, Pink Floyd is extremely theory based music. But the
> theory is only accessible when under the influence of lysergic
> acid diethylamide or mescaline.
>
> On Fri, Aug 27, 2010 at 4:07 PM, Carl Lumma <carl@...> wrote:
> >
> > Gene wrote:
> >
> > >Even when they do, they are not going to stick Beethoven in
> > >with a list of 20th century rock groups.
> >
> > Which is of course another grievous oversight. -Carl
> >
>

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

> Put it this way. Take someone in college taking a music degree (either jazz
> or classical) and ask them what got them big into music. There's a huge chance
> it's not going to be, say, Debussy...and more likely to be the Beatles or
> something "even" more cheesy.

Judging by the people I met at Indiana University, this is not at all true of students at the top music departments or schools.

And for those who really did get into music
> because of the theoretical works of more "off the deep end" artists...how many
> have actually gotten the chance to be in a group popular enough to be on the
> news or some other medium that changed a popular style?

I don't think Bach, Beethoven or Mozart count as off the deep end.

> An easy example, my brother got into music because of rock, earned a jazz
> guitarist degree in college, and now plays mostly rock as a cover-band.

You could get a jazz guitarist degree at Berklee, probably, but I really wonder how many of the top-rated departments would allow that even in this day and age? I mean places like Indiana, Julliard, Yale, Rochester or the New England Conservatory.

> Saying I'm insisting
> academic people "must pay attention to popular music" seems kind of like saying
> that because he does cover songs he must have no respect for jazz...you CAN pay
> attention to both.

I'm not saying they shouldn't, I'm saying they mostly don't.

My experience, when I went to college for music and *really* had to listen
to classical music (of any sub-genre) I had to mentally switch gears to
appreciate either classical or rock music (at the time prog rock like Peter
Gabriel Genesis, Gentle Giant, Yes, etc.). That could be a common perception
- and if so the reason why the audiences don't exchange well.

My opinion on this subject is I don't think rock OR electronic music of any
genre has the same complexity of the vast majority of the classical music
catalog. There is a vast difference in the degree of thought behind (most)
classical music. Rock and electronic music since the 60's has leaned on
timbre to make up for the lack of harmonic complexity. There are really good
rock pieces (Dance with the Moonlit Knight by Genesis say) but they are the
exception. And included are some really hard to play solo instrumental parts
- but those still do not compare to the best of the classical solo
instrument repertoire. I really don't know enough about Jazz to talk to it
but I suspect the general level of complexity is less.

(as an aside - What amazed me (and got my respect) was that Schoenberg in
his theory book gives legitimacy to popular music - complexity is a
continuum you could say - and popular music is on the low complexity end of
that continuum. )

Now - does complexity equal good, no, it doesn't - exhibit A is what the
majority of the world thinks of serialism.

I will assert that when you combine the appeal of popular music with the
complexity of the best Western classical tradition has to offer you have a
piece of music that is special. And in that sense rock, electro music in my
opinion has not achieved that level of "good".

And explains why composers like Debussy, Bach, and Beethoven are remembered
and why Lynyd Skynyrd, Aphex Twin and Squarepusher won't be. The Beatles
will last a bit longer - but hundreds of years... unlikely.

Chris

On Fri, Aug 27, 2010 at 7:06 PM, Carl Lumma <carl@...> wrote:

>
>
> :) I don't care much for Floyd and I wasn't referring to
> theory. Just to the fact that, any time you have a popular
> genre of music with a culture that rewards people for working
> hard at it, some of it is gonna be good. This stereotypical
> academic music person wants us to believe that anything with
> a drum kit in it is bad? That's just absurd on the face of it.
> Similarly, rock fans would have you believe nobody was making
> or enjoying good music 200 years ago. Also pretty absurd.
> The more likely explanation is that both groups have deficient
> listening skills, and probably cultural bias too.
>
> -Carl
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > Indeed, Pink Floyd is extremely theory based music. But the
> > theory is only accessible when under the influence of lysergic
> > acid diethylamide or mescaline.
> >
> > On Fri, Aug 27, 2010 at 4:07 PM, Carl Lumma <carl@...> wrote:
> > >
> > > Gene wrote:
> > >
> > > >Even when they do, they are not going to stick Beethoven in
> > > >with a list of 20th century rock groups.
> > >
> > > Which is of course another grievous oversight. -Carl
> > >
> >
>
>
>

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

> You could get a jazz guitarist degree at Berklee, probably, but
> I really wonder how many of the top-rated departments would
> allow that even in this day and age? I mean places like Indiana,
> Julliard, Yale, Rochester or the New England Conservatory.

Incidentally, I was a CS student at IU, but they had a rule
that conservatory classes had to be open to students of all the
other schools. I tested out of a semester of theory, took a
semester of theory, and studied composition and jazz piano.
Then I lived in New York for a year with one of my best friends
while he got his trumpet degree at Juilliard. In both cases,
the students I met were pretty open to different genres. More
than the average person on the street I would say. The more
accurate characterization was, they would only listen to music
*that involved their instrument* and this holds for my friends
with the rock band too -- if it doesn't have guitar, they're
not interested.

-Carl

Is there an explanation somewhere of what this means?

I apologize for repetition for many of you, but I'm only now getting around to trying out these tunings.

http://x31eq.com/temper/pregular.html

In particular, if I click on, say, "Orwell", I get this:

Orwell

Equal Temperament Mappings
2 3 5 7 11
[< 31 49 72 87 107 ]
< 22 35 51 62 76 ]>

Reduced Mapping
2 3 5 7 11
[< 1 0 3 1 3 ]
< 0 7 -3 8 2 ]>

Generator Tunings (cents)
[1200.604, 271.563>

Step Tunings (cents)
[28.640, 14.217>

Tuning Map (cents)
<1200.604, 1900.940, 2787.125, 3373.107, 4144.939]

Complexity 2.050464
Adjusted Error 3.981596 cents
TOP-RMS Error 1.150939 cents/octave

http://x31eq.com/cgi-bin/rt.cgi?ets=31_22&error=5.0&limit=11&invariant=7_-3_8_2_1_0_3_1_3

I'd like to be able to generate my own Scala file based on this info, and to understand what these numbers mean.

On an unrelated note, I thought 41-et looked really good on paper, but it didn't attract me greatly on first encounter, and I
notice that there's not that much out there on the interwebz about it. Partch doesn't mention it in Genesis of a Music. Any thoughts?

Caleb

Definitely if a major popular group did microtones many would become interested.
But in order for that to happen it will have to offer something that can't be done otherwise. which is why the notion of putting old wine in new bottles seems to get nowhere. Sonic youths work with microtones yet it doesn't seem to inspired much as the basic frame work is little different from where they came from.
There is hence nothing 'essential' about the use here.
I am not picking on them because of this. just how the dynamics and i don't think they have any real interest in making it popular.
It works for them as artist which is the only concern one can expect them or anyone to have.

Much classical music was popular music and much of it was entertainment before it was high art.
It seems that one has to be accomplish at least in some degree before the other.
And I agree with Carl about people only interested in their instrument or style really it really is a myopic approach to the great work that is done by talented people in all fields.
i would like to mention the variety of world music that for the most part is microtonal in relationship to the west.
There are great works here also. the west calls them 'ethnic' when in fact much of this is more classical in existing in a highly develop form long before the west common practice period.
--

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> My opinion on this subject is I don't think rock OR electronic music of any
> genre has the same complexity of the vast majority of the classical music
> catalog. There is a vast difference in the degree of thought behind (most)
> classical music.

True, but bear in mind that a vast amount of brainless bubblegum classical music got written, but since people don't care about, it very seldom gets performed. Also, classical music is often on a much larger scale, which gives plenty of scope for your thoughts if you have any thoughts. The survivors of this Darwinian process are very impressive creatures indeed.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
The more
> accurate characterization was, they would only listen to music
> *that involved their instrument* and this holds for my friends
> with the rock band too -- if it doesn't have guitar, they're
> not interested.

The conventional wisdom I heard from the IU students I sometimes hung with was that instrumentalists were not always the intellectual type, and that went double for opera singers. But composition and theory students were another species of cat.

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
>
> Is there an explanation somewhere of what this means?
>
> I apologize for repetition for many of you, but I'm only now getting around to trying out these tunings.
>
> http://x31eq.com/temper/pregular.html

See if this helps any:

http://xenharmonic.wikispaces.com/Creating+Scala+scl+files+for+rank+two+temperaments

> On an unrelated note, I thought 41-et looked really good on paper, but it didn't attract me greatly on first encounter, and I
> notice that there's not that much out there on the interwebz about it. Partch doesn't mention it in Genesis of a Music. Any thoughts?

What about 46, 53 or 58? 58 is the smallest equal temperament which can support the Genesis scale, by the way.

As you know Kraig, I completely agree. My most favorite music
are those works with which I have had ecstatic listening
experiences. Once you get to ecstatic there is no higher.
And I've had that with some of the Western masters, and with
traditional music from several places in Asia and Africa.
Our lives have changed a lot, but ears have not. Any culture
with centuries to work on it is liable to hit the target.
And you know, your own thoughts on this (to say nothing of
your own "ethnic" music) have over the years, played a big role
in my listening. So thanks. -Carl

Kraig wrote:
> i would like to mention the variety of world music that for
> the most part is microtonal in relationship to the west.
> There are great works here also. the west calls them 'ethnic'
> when in fact much of this is more classical in existing in a
> highly develop form long before the west common practice period.

Carillon.mp3 - NICE! Very playful with lots of layers...very confident and
striving yet managing loads of would-be-conflicting tonal color riding the edge
between consonance and dissonance quite beautifully. What scale(s) does this
one use?

DecaTonic Swing - Paul Elrich in 22TET, right? A bit past the edge for me far
as "average dissonance"...but I could see how others would love it. What makes
this one different from many of the other more dissonant (to my ears, at least)
pieces is that it isn't random-sounding in tonal contrast. Meaning it doesn't
just teeter suddenly from extreme dissonance to high dissonance and
back...there's a firm sense of controlled progression.

NoMoreSorrow - Sounds kinda like vocal JI and Barbershop Quartet, eh? Almost
too pure, but with just enough human-ness in it (love those portamentos as
well!) to keep from running into the mechanical sound some 5-limit and Adaptive
JI pieces have to my ears.

________________________________
From: Carl Lumma <carl@...>
To: tuning@yahoogroups.com
Sent: Fri, August 27, 2010 8:09:14 PM
Subject: [tuning] Re: The relationship between this list and the academic
community

As you know Kraig, I completely agree. My most favorite music
are those works with which I have had ecstatic listening
experiences. Once you get to ecstatic there is no higher.
And I've had that with some of the Western masters, and with
traditional music from several places in Asia and Africa.
Our lives have changed a lot, but ears have not. Any culture
with centuries to work on it is liable to hit the target.
And you know, your own thoughts on this (to say nothing of
your own "ethnic" music) have over the years, played a big role
in my listening. So thanks. -Carl

Kraig wrote:
> i would like to mention the variety of world music that for
> the most part is microtonal in relationship to the west.
> There are great works here also. the west calls them 'ethnic'
> when in fact much of this is more classical in existing in a
> highly develop form long before the west common practice period.

Michael wrote:

> Carillon.mp3 - NICE! Very playful with lots of layers...very
> confident and striving yet managing loads of would-be-
> conflicting tonal color riding the edge between consonance and
> dissonance quite beautifully. What scale(s) does this one use?

Arists and tunings are in the ID3 tags, as explained.

> DecaTonic Swing - Paul Elrich in 22TET, right?

Yes.

> NoMoreSorrow - Sounds kinda like vocal JI and Barbershop
> Quartet, eh? Almost too pure, but with just enough human-ness
> in it (love those portamentos as well!) to keep from running
> into the mechanical sound some 5-limit and Adaptive
> JI pieces have to my ears.

It's a genuine barbershop quartet alright.

-Carl

On Fri, Aug 27, 2010 at 9:31 PM, Carl Lumma <carl@...> wrote:

>
>
> Michael wrote:
>
> > NoMoreSorrow - Sounds kinda like vocal JI and Barbershop
> > Quartet, eh? Almost too pure, but with just enough human-ness
> > in it (love those portamentos as well!) to keep from running
> > into the mechanical sound some 5-limit and Adaptive
> > JI pieces have to my ears.
>
> It's a genuine barbershop quartet alright.
>
>
Gas House Gang, I assume. Barbershop quartets don't get much better than
that.

Dave Bowen
Tenor - Great Northern Union 1992- Present
Tenor - Vocal Majority 1978 - 1992

About my missing the ID3 info: Doh...turns out Media Player Classic ignores
those ID3's (before I had just figured you forgot to include them by accident).

Ok so here goes:

Hans-Andre Stamm - Carillon (wow this is good...where can I hear more?!).
And...what scale is it in (this doesn't appear to be listed in the ID3 tag)?

3-plus-4 - Joe Monzo (same here...wow this is almost demostyle crossed with
acid-jazz...very playful sounding). You say extended JI but I'm wondering...how
extended (IE what limit)?

No More Sorrow - Gas House Gang

Now this gets me...Gas House Gang (while it is "pure" Barbershop Quartet) is
full-on 9-limit JI. And 3-plus-4 is also "extended JI". And it sounds more
relaxed and "composed" to me than much if not most 5-limit I've heard. :-)
Surely there must be something deeper behind all this...seriously I think I
could convince a good few live musicians I know (who generally hate microtonal)
to take both of those seriously despite their being "notoriously high limit".

-- In tuning@yahoogroups.com, David Bowen <dmb0317@...> wrote:

> Gas House Gang, I assume. Barbershop quartets don't get much
> better than that.

Indeed. It was hard to pick a favorite track.

> Dave Bowen
> Tenor - Great Northern Union 1992- Present
> Tenor - Vocal Majority 1978 - 1992

Hey, Vocal Majority!

-Carl

Michael wrote:

> Hans-Andre Stamm - Carillon (wow this is good...where can
> I hear more?!).

I have been unable to get that album. I have some of his
other stuff though. I should write to him.

> And...what scale is it in (this doesn't appear to be listed
> in the ID3 tag)?

If it doesn't say, I don't know.

> 3-plus-4 - Joe Monzo (same here...wow this is almost demostyle
> crossed with acid-jazz...very playful sounding). You say
> extended JI but I'm wondering...how extended (IE what limit)?

Try Joe's web site or try asking him. Sweet tune though
for sure.

> Now this gets me...Gas House Gang (while it is "pure"
> Barbershop Quartet) is full-on 9-limit JI.

Yup. The only verified case of > 5-limit JI spontaneously
evolving in music.

> seriously I think I could convince a good few live musicians
> I know (who generally hate microtonal) to take both of those
> seriously despite their being "notoriously high limit".

Surprisingly, most listeners don't think anything is
unusual about barbershop, though many recognize there's
something distinctive about the sound.

- Carl Lumma
North Pennsmen 1996-7

Oh, and I updated it recently. So if you don't have
Alphapanther by Carlo Serafini, redownload or get it
from Carlo directly:

http://www.seraph.it/dep/int/alphapanther.mp3

-Carl

Thanks, that's exactly the kind of explanation I was looking for. From your recommendation a few weeks ago, 58 is already on my practice list. I'll check out the others.

I also ordered Little Miss Scale Oven--maybe using it will teach me a thing or two.

On Aug 27, 2010, at 8:59 PM, genewardsmith wrote:

>
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> >
> > Is there an explanation somewhere of what this means?
> >
> > I apologize for repetition for many of you, but I'm only now getting around to trying out these tunings.
> >
> > http://x31eq.com/temper/pregular.html
>
> See if this helps any:
>
> http://xenharmonic.wikispaces.com/Creating+Scala+scl+files+for+rank+two+temperaments
>
> > On an unrelated note, I thought 41-et looked really good on paper, but it didn't attract me greatly on first encounter, and I
> > notice that there's not that much out there on the interwebz about it. Partch doesn't mention it in Genesis of a Music. Any thoughts?
>
> What about 46, 53 or 58? 58 is the smallest equal temperament which can support the Genesis scale, by the way.
>
>

I tried to understand these numbers, with a bunch of examples, but couldn't.

The explanation seems to work with Scala, which I don't have.

Can someone tell me how to use the numbers below to calculate a scale by hand?

With one example of explicit instructions, I'll get the idea.

srutar worksheet
entered: 22 and 24, with 13 limit
Srutar

Equal Temperament Mappings
2 3 5 7 11 13
[< 22 35 51 62 76 81 ]
< 24 38 56 67 83 89 ]>

Reduced Mapping
2 3 5 7 11 13
[< 2 3 5 5 7 8 ]
< 0 2 -4 7 -1 -7 ]>

Generator Tunings (cents)
[600.016, 52.299>

Step Tunings (cents)
[27.566, 24.732>

Tuning Map (cents)
<1200.033, 1904.646, 2790.888, 3366.172, 4147.816, 4434.041]

Complexity 3.102128
Adjusted Error 5.179710 cents
TOP-RMS Error 1.399755 cents/octave

Can I simply multiply 52.299 by all integers up to some value to get my tuning?

I'm looking for a "what you do if all you have is a hand calculator" explanation.

Caleb

On Aug 28, 2010, at 8:18 AM, caleb morgan wrote:

> Thanks, that's exactly the kind of explanation I was looking for.
>
>>
>>
>>
>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>> >
>> >
>> > Is there an explanation somewhere of what this means?
>> >
>> > I apologize for repetition for many of you, but I'm only now getting around to trying out these tunings.
>> >
>> > http://x31eq.com/temper/pregular.html
>>
>> See if this helps any:
>>
>> http://xenharmonic.wikispaces.com/Creating+Scala+scl+files+for+rank+two+temperaments
>>
>> > On an unrelated note, I thought 41-et looked really good on paper, but it didn't attract me greatly on first encounter, and I
>> > notice that there's not that much out there on the interwebz about it. Partch doesn't mention it in Genesis of a Music. Any thoughts?
>>
>> What about 46, 53 or 58? 58 is the smallest equal temperament which can support the Genesis scale, by the way.
>>
>
>
>

Carl>"Yup. The only verified case of > 5-limit JI spontaneously evolving in
music...Surprisingly, most listeners don't think anything is unusual about
barbershop, though many recognize there's something distinctive about the
sound."

Hmm....do Barbershop Quartets often use 9-limit JI on purpose to build up
"ringing chords" where the overtones build into a "mysterious" fifth voice (and
what are some good mathematical/acoustic examples of that that would be
impossible in 3 or 5-limit)? Or I wonder why the choice for 9-limit JI became
so prevalent (or has it)? Regardless, I think Gas House Gang is a superb
example of just how organic and accessible fairly complex microtonal scale and
styles of harmony can be.

Michael wrote:

> Hmm....do Barbershop Quartets often use 9-limit JI on
> purpose to build up "ringing chords" where the overtones build
> into a "mysterious" fifth voice (and what are some good
> mathematical/acoustic examples of that that would be impossible
> in 3 or 5-limit)? Or I wonder why the choice for 9-limit
> JI became so prevalent (or has it)? Regardless, I think
> Gas House Gang is a superb example of just how organic and
> accessible fairly complex microtonal scale and styles of
> harmony can be.

It's actually pretty rare to hear 9-limit otonal chords
like that in barbershop. In fact GHG is the only quartet
I can think of that's done it (No More Sorrow and Sit Down,
You're Rockin' the Boat in particular) though I haven't
followed quartets since the late '90s.

Barbershop is usually characterized as 7-limit, though who
knows everything they may be singing? The guy who knows
the most is Aaron Wolf. Aaron?

-Carl

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> Generator Tunings (cents)
> [600.016, 52.299>

> Tuning Map (cents)
> <1200.033, 1904.646, 2790.888, 3366.172, 4147.816, 4434.041]

> Can I simply multiply 52.299 by all integers up to some value to get my tuning?

You mean to get your scale? First decide if you want pure octaves or tempered ones. By hand, I'd suggest pure octaves, which means you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over. Then take those notes, and adjoin to them the ones you get by adding 600 to each of them, giving you a full octaves worth of scale.

As for the tuning itself, the tuning map gives it to you. Pick a note, say 11/6. This is |-1 -1 0 0 1 0> in terms of its prime factorization. So (-1)*1200.033 + (-1)*1904.646 + (1)*4147.816 gives you the tuning. You can multiply by 1200/1200.033 if you want a pure octaves tuning.

It might help to look at how an untempered, Just, tuning map looks.
1/1 0.000
2/1 1200.000
3/1 1901.955
5/1 2786.314
7/1 3368.826
11/1 4151.318
13/1 4440.528

The tuning map is showing the value, in cents (logarithmic), of each prime-numbered partial. Only the prime-numbered partials are necessary to show, as you can reckon any other number with the primes, 6 is 2*3 for example, as you know I suppose (but for anyone reading along).

Compare the above to:

> Tuning Map (cents)
> <1200.033, 1904.646, 2790.888, 3366.172, 4147.816, 4434.041]

If you run 11/6 through the Just tuning map, you wind up with the cents value of... 11/6.

Gene wrote:
> You mean to get your scale? First decide if you want pure octaves or tempered ones. By hand, I'd suggest pure octaves, which means you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over. Then take those notes, and adjoin to them the ones you get by adding 600 to each of them, giving you a full octaves worth of scale.
>
> As for the tuning itself, the tuning map gives it to you. Pick a note, say 11/6. This is |-1 -1 0 0 1 0> in terms of its prime factorization. So (-1)*1200.033 + (-1)*1904.646 + (1)*4147.816 gives you the tuning. You can multiply by 1200/1200.033 if you want a pure octaves tuning.
>

Thanks to both of you.

Trying this out--correct my mistakes.

http://x31eq.com/temper/net.html

I entered 36 and 41 in the upper box "number of steps to the octave" and 13 for my limit in the lower box.

There was the following output:

Rodan 2 dimensions higher

Equal Temperament Mappings
2 3 5 7 11 13
[< 36 57 83 101 124 133 ]
< 41 65 95 115 142 152 ]>

Reduced Mapping
2 3 5 7 11 13
[< 1 1 -1 3 -2 0 ]
< 0 3 17 -1 28 19 ]>

Generator Tunings (cents)
[1200.151, 234.118>

Step Tunings (cents)
[2.349, 27.209>

Tuning Map (cents)
<1200.151, 1902.506, 2779.863, 3366.334, 4155.015, 4448.251]

Complexity 3.363236
Adjusted Error 5.682300 cents
TOP-RMS Error 1.535574 cents/octave

you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over.

Then, following Gene's intructions, (I think):

234.118 x
1200 ÷
1200.151 =
234.0885 ◊ (This is my generator?)

I stopped multiplying at 42, because that was so close to a multiple of 1200 cents.

multiplying my generator by every N up to 41, I get the following:

! Rodan 2 dimensions higher?
41-note
41
!

!0 0
27.19 36
56.74 31
86.3 26
115.86 21
145.41 16
174.98 11
204.53 6
234.09 1
261.27 37
290.83 32
320.39 27
349.95 22
379.5 17
409.06 12
438.62 7
468.18 2
495.36 38
554.49 28
584.03 23
613.59 18
643.15 13
672.71 8
702.26 3
724.92 33
729.45 39
788.57 29
818.12 24
847.68 19
877.24 14
906.8 9
936.35 4
959.01 34
963.54 40
1022.66 30
1052.21 25
1081.77 20
1111.33 15
1140.9 10
1170.44 5
1193.1 35
2/1

Did I do this right?

I notice it is quite similar to 41EDO except it seems to omit some pitches?

(I don't think I did it right, but I'm not sure.)

If I did this right, what would be the advantage over 41EDO?

Caleb

On Aug 28, 2010, at 7:16 PM, cameron wrote:

> It might help to look at how an untempered, Just, tuning map looks.
> 1/1 0.000
> 2/1 1200.000
> 3/1 1901.955
> 5/1 2786.314
> 7/1 3368.826
> 11/1 4151.318
> 13/1 4440.528
>
> The tuning map is showing the value, in cents (logarithmic), of each prime-numbered partial. Only the prime-numbered partials are necessary to show, as you can reckon any other number with the primes, 6 is 2*3 for example, as you know I suppose (but for anyone reading along).
>
> Compare the above to:
>
> > Tuning Map (cents)
> > <1200.033, 1904.646, 2790.888, 3366.172, 4147.816, 4434.041]
>
> If you run 11/6 through the Just tuning map, you wind up with the cents value of... 11/6.
>
> Gene wrote:
> > You mean to get your scale? First decide if you want pure octaves or tempered ones. By hand, I'd suggest pure octaves, which means you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over. Then take those notes, and adjoin to them the ones you get by adding 600 to each of them, giving you a full octaves worth of scale.
> >
> > As for the tuning itself, the tuning map gives it to you. Pick a note, say 11/6. This is |-1 -1 0 0 1 0> in terms of its prime factorization. So (-1)*1200.033 + (-1)*1904.646 + (1)*4147.816 gives you the tuning. You can multiply by 1200/1200.033 if you want a pure octaves tuning.
> >
>
>

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> Reduced Mapping
> 2 3 5 7 11 13
> [< 1 1 -1 3 -2 0 ]
> < 0 3 17 -1 28 19 ]>
>
> Generator Tunings (cents)
> [1200.151, 234.118>

> you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over.

No, because this is a completely different problem. The Generator Tunings above should be used. If reducing to a stretched octave of 1200.151 cents would be a problem, take the octave to be 1200.0 cents and multiply 234.118 by 1200/1200.151, obtaining 243.0874. Now iterate that, reducing to the octave when it goes over, and stop when you feel you've got enough notes.

What's the difference, then, between "Rodan two dimensions higher" and 41EDO?

I'm thinking I should give up, and just try out various Scala files that people post here.

I've tried and failed to understand this "regular mapping" thing.

My conscience tells me I shouldn't waste my time; I should leave math to the mathematicians. I'm pretty discouraged.

But, I've got plenty to practice, before narrowing it down at some future point.

I've got uneven 36-note 11-limit Just scale. Uneven 48-note 13-limit Just scale.

Epimorphic 13-limit Gene Ward Smith Just scale, with tweaks to make the fifths wider and a few other things. (Strengthening the /13 ratios so that there are a few more).

Plus, I've got 58EDO, 41EDO, and 31EDO to learn.

This is more than enough.

But I can't help wondering what I'm missing. (No, I don't mean I'm missing a feeling of mathematical competence--that I'll never have.)

Is there a fairly complete tuning with between 36 and 58 pitches that has a good 13 limit, fifths quite close but slightly narrower or wider than 3:2, octaves narrow or stretched? With perhaps a little beating, compared to JI?

With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes? Other than the ones I mentioned above?

If so, if anyone would be kind enough to spoon-feed me the Scala files?

Gene Ward Smith has done this a fair amount already.

I look at notationally parsimonious things like this, and despair:

31 & 41 & 46 & 58 & 72

Equal Temperament Mappings
2 3 5 7 11 13
[< 31 49 72 87 107 115 ]
< 58 92 135 163 201 215 ]
< 46 73 107 129 159 170 ]
< 72 114 167 202 249 266 ]
< 41 65 95 115 142 152 ]>

Reduced Mapping
2 3 5 7 11 13
[< 1 0 0 0 -3 0 ]
< 0 1 0 0 2 0 ]
< 0 0 1 0 -1 0 ]
< 0 0 0 1 2 0 ]
< 0 0 0 0 0 1 ]>

Generator Tunings (cents)
[1200.174, 1901.664, 2786.626, 3367.914, 4440.528>

Step Tunings (cents)
[3.104, 3.671, 4.127, 7.357, 4.182>

Tuning Map (cents)
<1200.174, 1901.664, 2786.626, 3367.914, 4152.010, 4440.528]

Complexity 0.000707
Adjusted Error 0.720359 cents
TOP-RMS Error 0.194669 cents/octave

temperament finding scripts

The thing about Cameron's explanation is that it just was a format for showing something about Just Intonation that was already obvious, so I couldn't learn from it. It seemed to be a strange way of telling me something I already knew.

Sorry to bother you all, I remain eager to try things if they are put concretely.

Caleb

On Aug 29, 2010, at 2:27 PM, genewardsmith wrote:

>
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> > Reduced Mapping
> > 2 3 5 7 11 13
> > [< 1 1 -1 3 -2 0 ]
> > < 0 3 17 -1 28 19 ]>
> >
> > Generator Tunings (cents)
> > [1200.151, 234.118>
>
> > you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over.
>
> No, because this is a completely different problem. The Generator Tunings above should be used. If reducing to a stretched octave of 1200.151 cents would be a problem, take the octave to be 1200.0 cents and multiply 234.118 by 1200/1200.151, obtaining 243.0874. Now iterate that, reducing to the octave when it goes over, and stop when you feel you've got enough notes.
>
>

This may sound silly, but I realized the cure for my ennui is to go through the Scala archives and check out the scales roughly 30-60 notes in size.

I learn from specific examples.

Since this is hundreds (and hundreds!) of scales, I should be occupied for some time.

Many familiar names here in the archives--all the usual perps and suspects.

Caleb

Still, I'd like to know what a "Rodan two dimensions higher" scale is, concretely.

Caleb

On Aug 29, 2010, at 2:39 PM, caleb morgan wrote:

>
> What's the difference, then, between "Rodan two dimensions higher" and 41EDO?
>
>
> I'm thinking I should give up, and just try out various Scala files that people post here.
>
> I've tried and failed to understand this "regular mapping" thing.
>
> My conscience tells me I shouldn't waste my time; I should leave math to the mathematicians. I'm pretty discouraged.
>
> But, I've got plenty to practice, before narrowing it down at some future point.
>
> I've got uneven 36-note 11-limit Just scale. Uneven 48-note 13-limit Just scale.
>
> Epimorphic 13-limit Gene Ward Smith Just scale, with tweaks to make the fifths wider and a few other things. (Strengthening the /13 ratios so that there are a few more).
>
> Plus, I've got 58EDO, 41EDO, and 31EDO to learn.
>
> This is more than enough.
>
>
> But I can't help wondering what I'm missing. (No, I don't mean I'm missing a feeling of mathematical competence--that I'll never have.)
>
> Is there a fairly complete tuning with between 36 and 58 pitches that has a good 13 limit, fifths quite close but slightly narrower or wider than 3:2, octaves narrow or stretched? With perhaps a little beating, compared to JI?
>
> With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes? Other than the ones I mentioned above?
>
> If so, if anyone would be kind enough to spoon-feed me the Scala files?
>
> Gene Ward Smith has done this a fair amount already.
>
> I look at notationally parsimonious things like this, and despair:
>
>
> 31 & 41 & 46 & 58 & 72
>
> Equal Temperament Mappings
> 2 3 5 7 11 13
> [< 31 49 72 87 107 115 ]
> < 58 92 135 163 201 215 ]
> < 46 73 107 129 159 170 ]
> < 72 114 167 202 249 266 ]
> < 41 65 95 115 142 152 ]>
>
> Reduced Mapping
> 2 3 5 7 11 13
> [< 1 0 0 0 -3 0 ]
> < 0 1 0 0 2 0 ]
> < 0 0 1 0 -1 0 ]
> < 0 0 0 1 2 0 ]
> < 0 0 0 0 0 1 ]>
>
> Generator Tunings (cents)
> [1200.174, 1901.664, 2786.626, 3367.914, 4440.528>
>
> Step Tunings (cents)
> [3.104, 3.671, 4.127, 7.357, 4.182>
>
> Tuning Map (cents)
> <1200.174, 1901.664, 2786.626, 3367.914, 4152.010, 4440.528]
>
> Complexity 0.000707
> Adjusted Error 0.720359 cents
> TOP-RMS Error 0.194669 cents/octave
>
> temperament finding scripts
>
>
> The thing about Cameron's explanation is that it just was a format for showing something about Just Intonation that was already obvious, so I couldn't learn from it. It seemed to be a strange way of telling me something I already knew.
>
> Sorry to bother you all, I remain eager to try things if they are put concretely.
>
> Caleb
>
>
>
>
>
> On Aug 29, 2010, at 2:27 PM, genewardsmith wrote:
>
>>
>>
>>
>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>>
>> > Reduced Mapping
>> > 2 3 5 7 11 13
>> > [< 1 1 -1 3 -2 0 ]
>> > < 0 3 17 -1 28 19 ]>
>> >
>> > Generator Tunings (cents)
>> > [1200.151, 234.118>
>>
>> > you should take 52.299 and multiply it by 600/600.016. Now take that and multiply it by integers up to some value, reducing it to the range 0-600 when it goes over.
>>
>> No, because this is a completely different problem. The Generator Tunings above should be used. If reducing to a stretched octave of 1200.151 cents would be a problem, take the octave to be 1200.0 cents and multiply 234.118 by 1200/1200.151, obtaining 243.0874. Now iterate that, reducing to the octave when it goes over, and stop when you feel you've got enough notes.
>>
>
>
>

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> Still, I'd like to know what a "Rodan two dimensions higher" scale is, concretely.

There's a scale called "rodan41.scl" in the Scala directory which you could take a look at.

On 30 August 2010 02:39, caleb morgan <calebmrgn@...> wrote:
>
>
> What's the difference, then, between "Rodan two dimensions higher" and 41EDO?

You don't need 41 notes of Rodan. You can stop at 36 notes and get
the 13-limit harmony you asked for.

> Is there a fairly complete tuning with between 36 and 58
> pitches that has a good 13 limit, fifths quite close but
> slightly narrower or wider than 3:2, octaves narrow or
> stretched?  With perhaps a little beating, compared to JI?

There's a kind of meantone that has a higher error than your Rodan
variant, but gives 13-limit harmony with 19 notes:

http://x31eq.com/cgi-bin/rt.cgi?ets=31_12&error=6&limit=13&invariant=1_4_10_18_15_1_0_-4_-13_-25_-20

For lower error, a kind of Miracle:

http://x31eq.com/cgi-bin/rt.cgi?ets=31_10&error=6&limit=13&invariant=6_-7_-2_15_-3_1_1_3_3_2_4

It gives plenty of 13-limit harmony with 31 notes (Canasta). If you
need more than 36 notes, you can take it to 41 (Stud Loco) and it'll
be slightly different to 41 note equal temperament.

> With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes?  Other than the ones I mentioned above?
> If so, if anyone would be kind enough to spoon-feed me the Scala files?

Sorry, I don't have an easy way to make Scala files now. There should
be miracles in the archives.

> Gene Ward Smith has done this a fair amount already.
> I look at notationally parsimonious things like this,  and despair:
<snip>
> Reduced Mapping
> 2 3 5 7 11 13
> [< 1 0 0 0 -3 0 ]
> < 0 1 0 0 2 0 ]
> < 0 0 1 0 -1 0 ]
> < 0 0 0 1 2 0 ]
> < 0 0 0 0 0 1 ]>

Why are you looking at that? What it tells you is to tune up 7-limit
JI and add 13. With a bit if fine tuning you can get intervals of 11
without adding them explicitly.

Graham

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> Is there a fairly complete tuning with between 36 and 58 pitches that has a good 13 limit, fifths quite close but slightly narrower or wider than 3:2, octaves narrow or stretched? With perhaps a little beating, compared to JI?

> With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes? Other than the ones I mentioned above?
>
> If so, if anyone would be kind enough to spoon-feed me the Scala files?

I didn't cook this up to correspond to your requirements, but some people may find it interesting. Lots of good fifths, some a little sharp, some a little flat. It's strictly proper and constant structure, so there's a good deal of regularity. Good 13 limit. However, octaves are pure and it has only 31 notes. It's a mutant form of Valentine[31], where the generator ranges between 77.398 and 79.440 cents, with the mutations introduced to improve on the 13-limit tuning.

Probably I could get closer to what you want by starting with something with a few more notes.

! valamute.scl
Mutant Valentine[31] 13-limit least squares optimum
31
!
47.8285
78.0488
125.6858
155.4471
203.8093
233.2741
281.4630
312.7138
359.1733
391.1125
437.2653
468.6727
500.0802
546.2329
578.1721
624.6316
655.8824
704.0713
733.5361
781.8983
811.6596
859.2966
889.5169
937.3454
966.6831
1015.4920
1044.1791
1093.1663
1121.8534
1170.6623
1200.0000

Thanks for your answer. I thought I was on the right track trying to use the below information to make a tuning or scale, but I can see I'm not. I'd love to be able to make use of these scales, but I need step-by-step instruction for hand calculation. It seems like it ought to be quite simple, but something isn't adding up.

This is partly because I don't know what the correct result for 31 or 41 tones, in this case, should look like, so I have nothing to guide me.

I'd like to take the mapping information, and hand-calculate with it to make a Scala file. I don't have Scala, as I'm running a Mac, but I do use PianoTeq, which can read Scala files.

Miracle

Equal Temperament Mappings
2 3 5 7 11 13
[< 31 49 72 87 107 115 ]
< 10 16 23 28 35 37 ]>

Reduced Mapping
2 3 5 7 11 13
[< 1 1 3 3 2 4 ]
< 0 6 -7 -2 15 -3 ]>

Generator Tunings (cents)
[1200.135, 116.760>

Step Tunings (cents)
[32.531, 19.166>

Tuning Map (cents)
<1200.135, 1900.697, 2783.083, 3366.884, 4151.676, 4450.259]

The name, Miracle, tells me that this scale relates somehow to a family of tunings or scales, which might be related to a comma called Miracle. The page of comma-names I found didn't mention Miracle, so perhaps this is wrong. But I seem to recall one. So the name "Miracle" is just a fluke relating to some comma, if this is correct.

Now, here's where I get a little confused.

I try to work with the numbers given here to see what the pattern is. I do this, because there are no directions about how to use these numbers. The directions direct you to plug them into the Scala program, which I don't have.

So, I'm wondering how to hand-calculate with them, and I'm looking for the relationship between these numbers. This is all I want to know: A simple how-to, for each "rank" of temperament. (I want to be able to work with tunings with more than 2 generators.)

So here goes, and you can see that I don't know what I'm doing.

Generator Tunings (cents)
[1200.135, 116.760>

0 0
84.225 11 wrong?
116.76 1
201.12 12 wrong? This would put the step size at 32.4, which doesn't match the Step Tuning data.
233.52 2
350.28 3
467.04 4
583.8 5
700.56 6
817.32 7
934.08 8
1050.84 9
1167.6 10

I start multiplying the generator 116.76 out within a modulus of 1200, and already I'm not sure if I should be using an octave.

The generator 116.76 times 31 = 3619.56 cents, that is, 3 octaves plus 19 cents, so this generator is a little large, perhaps. But I can see that I'm close.

If I use 1200.135 as my "octave" modulus, and multiply by 3, I get 3600.405. Divide this by 116.76, and I get 30.8359...so I can see I'm still wrong.

If I take 1200/1200.135 and multiply that by 116.76, I get 116.7468..., which again doesn't help me, because if I multiply that by 31 I get 3619.153...

I start calculating, but I don't know if I should use a modulus of 1200.135 or 1200 or something else.

Why isn't the generator 116.14 cents?

How do I use "step tunings" to calculate with?

What is the relationship between the two given Generator tunings here?

from the explanation in "paradigm": For equal temperaments, the step size is the generator. For a strict linear temperament, you can always choose one generator to be the octave. The other generator is then simply called "the generator". For any regular temperament that approximates the octave, you can still choose one of the generators so that it equally divides the octave. This is then known as "the period". Unequal temperaments where the period doesn't equal the octave are a hallmark of the regular mapping paradigm.

Again, I just want to know how to work with these numbers--forget all the questions I asked, which just illustrate my confusion. They were intended to show that I take this seriously, and I'm trying to understand what to do.
It looks like it should be simple, but it isn't.

The basic idea of generators and a modulus is quite familiar to me, from other work.

The basic question is: How to hand-calculate with the given information to come up with the tuning/scale that you intended.

caleb

On Aug 29, 2010, at 7:54 PM, Graham Breed wrote:

> On 30 August 2010 02:39, caleb morgan <calebmrgn@...> wrote:
> >
> >
> > What's the difference, then, between "Rodan two dimensions higher" and 41EDO?
>
> You don't need 41 notes of Rodan. You can stop at 36 notes and get
> the 13-limit harmony you asked for.
>
> > Is there a fairly complete tuning with between 36 and 58
> > pitches that has a good 13 limit, fifths quite close but
> > slightly narrower or wider than 3:2, octaves narrow or
> > stretched? With perhaps a little beating, compared to JI?
>
> There's a kind of meantone that has a higher error than your Rodan
> variant, but gives 13-limit harmony with 19 notes:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=31_12&error=6&limit=13&invariant=1_4_10_18_15_1_0_-4_-13_-25_-20
>
> For lower error, a kind of Miracle:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=31_10&error=6&limit=13&invariant=6_-7_-2_15_-3_1_1_3_3_2_4
>
> It gives plenty of 13-limit harmony with 31 notes (Canasta). If you
> need more than 36 notes, you can take it to 41 (Stud Loco) and it'll
> be slightly different to 41 note equal temperament.
>
> > With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes? Other than the ones I mentioned above?
> > If so, if anyone would be kind enough to spoon-feed me the Scala files?
>
> Sorry, I don't have an easy way to make Scala files now. There should
> be miracles in the archives.
>
> > Gene Ward Smith has done this a fair amount already.
> > I look at notationally parsimonious things like this, and despair:
> <snip>
> > Reduced Mapping
> > 2 3 5 7 11 13
> > [< 1 0 0 0 -3 0 ]
> > < 0 1 0 0 2 0 ]
> > < 0 0 1 0 -1 0 ]
> > < 0 0 0 1 2 0 ]
> > < 0 0 0 0 0 1 ]>
>
> Why are you looking at that? What it tells you is to tune up 7-limit
> JI and add 13. With a bit if fine tuning you can get intervals of 11
> without adding them explicitly.
>
> Graham
>

On 30 August 2010 20:48, caleb morgan <calebmrgn@...> wrote:

> The name, Miracle, tells me that this scale relates somehow to a family of tunings or scales, which might be related to a comma called Miracle.  The page of comma-names I found didn't mention Miracle, so perhaps this is wrong.  But I seem to recall one.  So the name "Miracle" is just a fluke relating to some comma, if this is correct.

The name doesn't come from a comma, and although you could reverse
engineer a "miracle comma" it wouldn't be important because Miracle
isn't special in the 5-limit.

> So here goes, and you can see that I don't know what I'm doing.
> Generator Tunings (cents)
> [1200.135, 116.760>
>
> 0 0
> 84.225 11 wrong?

It's right. 32.531*2 + 19.166

> 116.76 1
> 201.12 12 wrong?  This would put the step size at 32.4, which doesn't match the Step Tuning data.

So the step size is 0.1 cents out? That doesn't matter.

> 233.52 2
> 350.28 3
> 467.04 4
> 583.8 5
> 700.56 6
> 817.32 7
> 934.08 8
> 1050.84 9
> 1167.6 10
> I  start multiplying the generator 116.76 out within a modulus of 1200, and already I'm not sure if I should be using an octave.

You should be using an octave, because the "Reduced Mapping" starts with a 1.

> If I take 1200/1200.135 and multiply that by 116.76, I get 116.7468..., which again doesn't help me, because if I multiply that by 31 I get 3619.153...

116.75 would be a valid generator if you want to keep octaves at 1200
cents. But there's a range of valid generators anyway.

> I start calculating, but I don't know if I should use a modulus of 1200.135 or 1200 or something else.

1200.135 goes with 116.76, 1200 goes with 116.75

> How do I use "step tunings" to calculate with?

When you get to a 41 note scale, there should be 31 steps of 32.531
cents and 10 steps of 19.166 cents.

31*32.531 + 10*19.166 = 1200.121

You need a scientific calculator for that to work as is. It's close
enough to the right octave.

The roughly 19 cent steps are evenly distributed within the octave.
You can use this fact to build the scale. But if you know how to use
the single generator within the octave that's enough.

> What is the relationship between the two given Generator tunings here?

They're for the two different step sizes.

> Again, I just want to know how to work with these numbers--forget all the questions I asked, which just illustrate my confusion.  They were intended to show that I take this seriously, and I'm trying to understand what to do.
> It looks like it should be simple, but it isn't.
> The basic idea of generators and a modulus is quite familiar to me, from other work.

It looks like you have it basically correct, but you think you must be
doing something wrong.

Graham

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> I'd like to take the mapping information, and hand-calculate with it to make a Scala file. I don't have Scala, as I'm running a Mac, but I do use PianoTeq, which can read Scala files.

The Scala download page

http://www.huygens-fokker.org/scala/downloads.html

gives extensive instructions for downloading and installing on a Mac. It sounds as if it might be a pain, depending on what you already have installed, but should be possible.

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> ...
> Is there a fairly complete tuning with between 36 and 58 pitches that has a good 13 limit, fifths quite close but slightly narrower or wider than 3:2, octaves narrow or stretched? With perhaps a little beating, compared to JI?
>
> With fairly consistent--but not necessarily entirely consistent--patterns of number-of-keys corresponding to interval sizes? Other than the ones I mentioned above?
>
> If so, if anyone would be kind enough to spoon-feed me the Scala files?
> ...
> Sorry to bother you all, I remain eager to try things if they are put concretely.
>
> Caleb

Hi Caleb,

You might be interested in the 41-tone version of HTT (which is also available in subsets of 29 and 17 tones/octave):
/tuning-math/message/7574

For brief explanations of how the intervals are tempered, see:
/makemicromusic/topicId_6820.html#6847
/tuning-math/message/10586

--George