Symmetry (was Barbershop and Equal-Step Tuning)

On Thu, 25 Sep 1997, Carl Lumma wrote:
> There was also another term that Ivor used, "symmetry". He never defined it
> too well, but he complained that 12-tone was too symmetric, and that when
> one first began Xenharmonic exploration, it was crucial to "knock the ear
> out" with a non-symmetric tuning like 19-tone. Could this be the same
> thing, Ivor's term for consistency?

It seems to me what Ivor was getting at was probably the fact that 12
has many factors, which allows one to create what theorists call "scales
of limited transposition". E.g. 3 1 3 1 3 1 has only four different
transpositions, because transposed by 4 steps it's unchanged. (You can
create such a scale because 4 is a divisor of 12.) OTOH, in 19TET it's
impossible to create such scales, because 19 is prime.

--pH http://library.wustl.edu/~manynote <*>
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "



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