RE: 68TET and the Byzantine scale

>Dans la musique byzantine, le ton fut stabilise, lors de la reforme de
>Chrysanthe, a 12 degres-commas pour le grand ton et 9 pour le petit ton
>entier; cependant, ce degre-comma est different du precedent. Il est ici la
>68e partie de l'octave (racine 68e de 2). Plus tard, le degre-comma devint
>la 72e partie de l'octave. Le grand ton prit alors 12 degres-commas et le
>petit ton, 10. La musique byzantine ne parle pas de demi-tons, mais de tons
>minime (7 degres-commas sur l'echelle a 68 degres par octave; 8 sur
>l'echelle a 72 degres).


Kami,

This is implying that the a scale similar to the basic Hindu scale or the
Arabic "Rast" scale might be tuned 12,9,7,12,12,9,7 in 68TET and
12,10,8,12,12,10,8 in 72TET. Much closer to 5-limit just intonation are
12,10,6,12,12,10,6 in 68TET (which reduces to the famous 34TET) and
12,11,7,12,12,11,7 in 72TET. Probably the difference is intentional, as
these scales represent a compromise between the just or schismatic scales of
Hindu and medieval Arabic music and the present tuning of the Arabic "Rast"
scale, which would be represented as 12,8,8,12,12,8,8 in 68TET or
12,9,9,12,12,9,9 in 72TET. Notice that these representations reduce to 17TET
and 24TET respectively, which are the most common descriptions of modern
Arabic tuning.

I personally don't know anything about Byzantine music, but this appears to
be nothing more than a construct specifically designed to represent a
compromise between two systems. Note that in 72-TET, we can "morph" smoothly
between the standard tunings of the West, India, Byzantium, and Arabia, in
that order or backwards. Do some timbre-morphing along with it and you've
got a cool idea for a composition!

-Paul E.


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