"spheres" of various -tets; and aurally sensible set theory

I believe the word "sphere" is equal to Allen Forte's term "set-class".

I.e. 037 in 12-tet is in the same "set-class" as 047, since they are
related by inversion.

As a composer working with set-theory tools, I tend to have problems with
notions of sets being "equivalent" to their inversions. I also think that
the issue of "What's in the bass", i.e. "inversion" in the tonal-music
sense of 1st, 2nd, 3rd, etc., is much too much glossed over in set theory
studies in general; when it is in fact, very important to the SOUND of the
music. Of course, these thoughts will not be anything new to most folks
on this list.

Hence, I am writing a piece in 19-tet, which uses as a harmonic "basic
unit", the sets

0 3 6 11 13 16 = C D E G Ab Bb or transpositions
0 3 6 11 12 16 = C D E G G# Bb " "
0 3 6 11 12 15 = C D E G G# A# " "

These three sets, are, I think, auditorally far more related to one
another (sounding as "tweaked" versions of one another, and of the 12-tet
set 0 2 4 7 8 10) than they are, in sound, to their "inversions", in the
set-theory sense. (for example, 0 3 5 10 13 16)

So I set some rules for myself in my piece: never use these sets in the
set-theoretical inversion, and, as much as possible, use the sets in "root
position."---i.e. with "0" at the bottom, in the bass. . .

I am very much after a kind of general "sound" being attached to my piece,
and that sound would be derived from the Just Intonation chord

8:9:10:12:13:14

Hence, it seems that the "8" should be in the bass as much as possible.

At some point, I'll post some pretty jpeg examples of all this.. . .

CB

--- In MakeMicroMusic@y..., Christopher Bailey <cb202@c...> wrote:

> As a composer working with set-theory tools, I tend to have problems with
> notions of sets being "equivalent" to their inversions. I also think that
> the issue of "What's in the bass", i.e. "inversion" in the tonal-music
> sense of 1st, 2nd, 3rd, etc., is much too much glossed over in set theory
> studies in general; when it is in fact, very important to the SOUND of the
> music. Of course, these thoughts will not be anything new to most folks
> on this list.

Ouch! I wish theorists hadn't taken to calling this stuff "set theory", since it certainly isn't what mathematicians call set theory. Combinatorics and group theory is more like it.

Gene,

{you wrote...}
>Ouch! I wish theorists hadn't taken to calling this stuff "set theory"...

And I thought "set theory" was to attempt to win 3 out of 5 of them in Men's Singles... :)

Cheers,
Jon