Limits of JI model?

Gary Morrison asked :
> How specifically does the term "symmetric mode" apply to this? (dim
scale)

100%!!

> I presume that a diminished scale is a special case of a symmetric mode,
in
> particular where the two-step repeating pattern spans a minor third?

I haven't really studied symmetric modes (aka limited transposition???),
but this is exact. My point was that these scales are "artificial" (read
"ET", as opposed to "JI").

4tET should not be interpreted as 1/1 19/16 tritone 5/3, but as valid chord
by itself. When using a diminished chord or scale, all notes are of equal
importance. The ambiguity is intended, and is it allows the composer to
modulate. This, of course, can not be explained by JI theory. And what
about supramajor third stacks? (Like in 88cet and 22tet, to name only two)
I do not think that 9/7 is half of 5/3. One thing that I can accept is that
8/22 octave is half of 16/22 octave. I do use JI models, and find them very
useful, but they can not justify all that I hear! Not that JI theory is
incomplete, but maybe there exist some music that is "ET only".
*********

I suppose that symetric modes are all seperated by the half-octave? This
would mean that only even ET's can have true symetric modes.

Another interesting mode is 0 1 4 5 8 9 12, but I have only seen heard of
it once.

I feel like calculating some "theoretical" charts about ET
representation, chromatic vs diatonic semitones, etc. Actually, if you
solve the equation 5c+7d for positive integer values of c and d, you get
interesting results! Like 5, 7, 12, 15, 19, 22, 31, etc...
This will be on my web site soon.

-Kami



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