Set theory (ammendment)

After sending, I checked out Xenakis and realized at least one of my
statements was in error. (I get my tuning list in digest format, so
others may have already pointed this out.) Xenakis' sieve theory (those
new to this: it starts in the chapter "Towards a Metamusic") actually DOES
include plenty of provision for ratio-derived scale elements by examining
what happens when the "elementary displacements" are variously examined as
tempered semitones, Aristoxenean segments (1/12-tones), commas of Didymos
(81/80), etc. etc. Sieve theory does not require either equal or
non-equal temperaments, but straddles or generalizes in such a way that
both are, or can be, included. Also, none of Xenakis' sieve theory
*requires* octave equivalence, as he notes, but he certainly favors it in
this particular treatment. He uses sieve theory to get at some extremely
complex scale structures, both historical and synthetic.

Steve