Musical Set Theory

> I'd like to stimulate discussion on this issue, I have been
> corresponding with John Wild out at Harvard who has compiled a large
> database of sets with interval vectors, all the way up to 30-tet.

I would be interested to see this list. It could be compositionally
useful.

>
> ***It seems a "hot item" these days in Academia... well, OK, at least
> at Columbia, cf. Chris Bailey, to examine microtonality through the
> lens of "musical set theory..." I think it's a good development,
> since at least it gets microtonality studied at such places.

Actually, I think I am the only one doing that.

Main reason being, most composers are rather ANTI-musical-set-theory, at
least when it gets any more technical than "the opening motive of the
piece is transposed, inverted, etc. to form the basis of the harmony of
the piece," and even that idea is pretty passe in academic circles.

The idea that "musical set theory" is de riguer in academia today is silly
(though I suppose it's true for a few 60+ year old professors), I am at
Cincinnati Conservatory right now, and the most popular composer "gods"
are John Adams and the whole "Bang on a Can" scene.

> However, there is still an even *more* exciting intellectual study
> just going after the ratios and such like of just intonation theory
> and temperaments and harmonic entropy... as we have been doing on
> these lists. Personally, I think these studies are even more
> pertinent and practical than set theory for "real" composing...

I think "musical set theory" is simply an extension of this . . .
i.e., what you are discussing is basically "scale design", right?
And essentially, a scale is a set of pitches or pitch-classes.

The only additional thing that "musical set theory" can do for you is to
enable you to work at the motivic level also---you can work with ordered
motives or unordered "sets", and derive melodies and harmonies from these.
These are typically 3 or 4 or 5 note sets (at least in 12-TET). Then of
course you can explore the interaction of these smaller units with larger
"scale-sized" units.

So yeah. . . ideally musical set theory , as it exists, IS the grand
Unified Theory that some folks have been wondering about.

>
> ...But wouldn't it be exciting if one could join these two sides of
> music theory (musical set theory and tuning theory) into some
> unifing principle? Group Theory may hold the key...
>
> Paul Hj

See above. . .

>
> ***Well, knowledge is power... (since when? :) but the danger, I
> think lies in the generally-accepted compositional procedures used
> with these kind of methodologies... ie., people tend to manipulate
> sets rather than to actually *listen* to the material.
>
> If something *audible* comes out of this kind of study, so much the
> better. I'm just saying that, generally speaking, that's *not* the
> direction composition has taken with these approaches in the past...
> maybe because it's just too easy to compose this way without
> listening to the material... :)

Well, I definitely take the attitude that "theoretical manipulations are
no excuse for a music that does not kick ass."

Having said that, however, I think the attitude way back when was that
writing with these procedures might lead our ears to new things that we
might hear as "kicking ass" that we wouldn't have expected before.

Obviously, this wasn't always the case, and now we can be more critical.
. . . but there is something to be said for experimenting, and leading
one's ears in new directions. Which may mean yes--occasionally composing
without listening. No garuntee of success of course.

>
> Errm... But you cannot blame the methodologies for this, can you?
> Composing without listening is definitely a thing NOT to be done. If a
> composer does so, all the worse for him - but that's hardly the
> methodology's fault; i'd rather call it a wrong understanding what is
> appropriate or even lacking mastery of the method.

What do you think of John Cage? I believe he stopped composing "by ear"
in any sense of the word--after 1950.

I would say the results are mixed. . .sometimes fantastic, sometimes not
so exciting. Though he would probably say that's my fault.

>
> I occasionally hear arguments like this in the context of questions
> like whether you should study counterpoint or Schenkerian analysis or
> music theory at all, and there they are not more convincing to me...

Shenker? But with that you HAVE to listen to do it right?

--- In tuning@yahoogroups.com, Christopher Bailey <chris@m...> wrote:

/tuning/topicId_52942.html#52942

>> > ***It seems a "hot item" these days in Academia... well, OK, at
least
> > at Columbia, cf. Chris Bailey, to examine microtonality through
the
> > lens of "musical set theory..." I think it's a good development,
> > since at least it gets microtonality studied at such places.
>
>
> Actually, I think I am the only one doing that.
>

###There have been articles in Perspectives of New Music on this
topic, and I believe I have heard other references coming
from "academia..." Maybe you were the only person doing this at
Columbia, Chris...

Main reason being, most composers are rather ANTI-musical-set-
theory, at
> least when it gets any more technical than "the opening motive of
the
> piece is transposed, inverted, etc. to form the basis of the
harmony of
> the piece," and even that idea is pretty passe in academic circles.
>
> The idea that "musical set theory" is de riguer in academia today
is silly
> (though I suppose it's true for a few 60+ year old professors), I
am at
> Cincinnati Conservatory right now, and the most popular
composer "gods"
> are John Adams and the whole "Bang on a Can" scene.
>

###I was a guest composer there, so I'm familiar with the
environment. It's not one of the more "academic" centers...
(gratefully...)

>
>
> > However, there is still an even *more* exciting intellectual
study
> > just going after the ratios and such like of just intonation
theory
> > and temperaments and harmonic entropy... as we have been doing on
> > these lists. Personally, I think these studies are even more
> > pertinent and practical than set theory for "real" composing...
>
> I think "musical set theory" is simply an extension of this . . .
> i.e., what you are discussing is basically "scale design", right?
> And essentially, a scale is a set of pitches or pitch-classes.
>

###No, I believe the approach is entirely different. Selecting
pitches with regard to their harmonic approximations is *far* afield
from rotating sets of pitches, IMHO...

> The only additional thing that "musical set theory" can do for you
is to
> enable you to work at the motivic level also---you can work with
ordered
> motives or unordered "sets", and derive melodies and harmonies from
these.
> These are typically 3 or 4 or 5 note sets (at least in 12-TET).
Then of
> course you can explore the interaction of these smaller units with
larger
> "scale-sized" units.
>
>
> So yeah. . . ideally musical set theory , as it exists, IS the
grand
> Unified Theory that some folks have been wondering about.
>

###I remain thoroughly unconvinced...

> >
> > Errm... But you cannot blame the methodologies for this, can you?
> > Composing without listening is definitely a thing NOT to be done.
If a
> > composer does so, all the worse for him - but that's hardly the
> > methodology's fault; i'd rather call it a wrong understanding
what is
> > appropriate or even lacking mastery of the method.
>
>
> What do you think of John Cage? I believe he stopped composing "by
ear"
> in any sense of the word--after 1950.
>

###I don't consider any of his later work "music..." but he didn't
think so either, so we are in total agreement... :)

JP

> >> > ***It seems a "hot item" these days in Academia... well, OK,
at

> > Actually, I think I am the only one doing that.
> >
>
> ###There have been articles in Perspectives of New Music on this
> topic, and I believe I have heard other references coming
> from "academia..." Maybe you were the only person doing this at
> Columbia, Chris...
>
>

Who then? I think Julia Werntz takes an intuitive approach . . .
I know there are some theorists who have written articles, but I
don't think I've heard much microtonal, set-manipulated music . .
I would like to meet people who are interested in that, though . .

> >

> > I think "musical set theory" is simply an extension of
this . . .
> > i.e., what you are discussing is basically "scale design", right?
> > And essentially, a scale is a set of pitches or pitch-classes.
> >
>
> ###No, I believe the approach is entirely different. Selecting
> pitches with regard to their harmonic approximations is *far*
afield
> from rotating sets of pitches, IMHO...
>

Yes, but once you've selected your pitches with regard to harmonic
approximations, then you've got use them in a piece. My point is
that "musical set theory" can give you tools to help you do that.

Not that you HAVE to work that way, but just that you CAN if you
want.

Of course, it's more complex when you're using non-Equal-Tempered
source scales, since things can't just be tranposed and inverted
willy-nilly.

But, in those cases, the lattices that we all love so much
essentially tell you what kind of musical-set-theory operations you
can do within your scale-set, that will preserve intervals and hence
sound-quality. I.e., you can clearly see what transpositions,
inversions, etc. are possible.

Of course, the possitibilities may be very limited, and one might
also be very interested in transposing something in such a way that
it DOESN't sound the same, etc.

But the point is that all of these things can be related to musical
set theory in the end. A scale is a musical-set, so if you're using
a scale, you're using a musical-set. And if you're doing something
motivic or in any way algorithmic to it, then what you're doing can
probably be described in those terms. Though you might not think of
them that way . . . .

on 21/3/04 13:08, Dylan at chris@music.columbia.edu wrote:

>
>>>>> ***It seems a "hot item" these days in Academia... well, OK,
> at
>
>>> Actually, I think I am the only one doing that.
>>>
>>
>> ###There have been articles in Perspectives of New Music on this
>> topic, and I believe I have heard other references coming
>> from "academia..." Maybe you were the only person doing this at
>> Columbia, Chris...
>>
>>
>
> Who then? I think Julia Werntz takes an intuitive approach . . .
> I know there are some theorists who have written articles, but I
> don't think I've heard much microtonal, set-manipulated music . .
> I would like to meet people who are interested in that, though . .
>
>

I think Bill Alves has worked like this. Seems a valid way to deal with JI
in particular.

--- In tuning@yahoogroups.com, "Dylan" <chris@m...> wrote:

/tuning/topicId_52942.html#52959

> But the point is that all of these things can be related to musical
> set theory in the end. A scale is a musical-set, so if you're
using
> a scale, you're using a musical-set. And if you're doing
something
> motivic or in any way algorithmic to it, then what you're doing
can
> probably be described in those terms. Though you might not think
of
> them that way . . . .

***I guess my only point is an obvious one... that the method of
working with visual lattices (as I, personally, have been doing with
xenharmonic scales) is far different from manipulating sets of such
pitches... as a working method...

JP