source file: m1456.txt
Date: Tue, 23 Jun 1998 13:19:15 -0400

Subject: Gary, Hahn, symmetricity

From: Rick Sanford <76122.2237@compuserve.com>

>>Paul Hahn wrote:
>> Hmm.  What about a mode like (in 12TET) 0, 1, 4, 6, 7, 10 (steps of
>> 1-3-2-1-3-2)?  It's symmetric at the tritone, but it has three different
>> stepsizes.

Careful - why do you call this a Mode?

>>Gary Morrison wrote:
>>    Easley Blackwood identified those as "symmetric modes".
>>I'm curious about the scope of that term though.  Do any of you folks
>>know if it covers scales constructed from ANY repeating pattern (perhaps
>>limited to a 2-long pattern?) of intervals?  Would a wholetone scale in
>>12TET be a symmetric mode?

Guys:

My reference on these ideas appears in an article on "Transpositionally
Invariant Sets"
from about 1992 in Journal of Music Theory. I forget the author.
It talks about scales that are raw, with no 'single irregularity' 
(like one and only one tritone, etc.).  

And, incidentally, I am familar with some of the 15TET work of others,
including
Mr. Blackwood.  My own "Apples and Oranges"(1985), performed first at Mills
College,
contains 15TET counterpoint.

Rick S.