RE: mod groups & rhythm

Gary wrote,

>I suspect though that pitch and rhythm are fundamentally different when
>it comes to temperament. Tempering pitches is meaningful because our ears
>hear in a manner that could perhaps be described as simultaneously in
>linear and logarithmic frequency scales.

During my month away from the list, I too came up with the idea of rhythmic
temperament, and so was pleasantly suprised to find that it had been
discussed in my absence.

Although Gary's point has some merit, perhaps he is forgetting that
logarthmic relationships arise from application of a given multiplicative
factor, in this case a ratio, several times. There is nothing in the nature
of rhythm that prevents this from having significance.

For example, one can, in the course of a piece, reinterpret triplets as
quarter-notes, a rhythmic modulation by a factor of 3/2. Repeat this three
more times, and you will have accelerated by a factor of 81/16. Now
interpret every fifth note as the basic pulse, and you will be at 81/80 of
the original tempo.

Of course, no one will notice that you have not returned to the original
tempo. But what if you had left the original tempo in place through the
entire process, in one voice or a drumbeat? You would want to come back to
it at the end. The polyrhythms in the middle of the process would be too
complex to hear mathematically, anyway, so why not "temper" them, so that
the 81/80 becomes a 1/1? Each time the triplets are introduced, they could
be played a tiny bit too slow, the exact amount of tempering being identical
to that of meantone tuning.


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Date: Thu, 2 Jan 1997 13:55:19 -0800
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