68TET and the Byzantine scale

Here is a surprising text that I found in a dictionary of music :

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).

Does anyone know more about this musical system?

-Kami


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Ed,

>> If it is tuned "in frequency ratios of 4x:5x:6x:7x where x=some
fundamental
>>frequency," then it is consonant. If it is tuned according to
>>a diatonic scale with six consonant triads, it is dissonant.
> Paul, the diatonic scale I use has many more than six consonant triads,
>I don't understand....I tune according to a "root" not a scale. Please
>elaborate on "dissonant".

I don't know what you mean. Can you elaborate? This is what I mean. Take C
major, a common diatonic scale. As usually defined, it has six consonant
triads: C, Dm, Em, F, G, Am. These triads are in fact consonant when 12-,
19-, 31-tET, or meantone temperament is used to tune the scale. In all of
these cases, G B D F will be dissonant, and in meantone or 31-tET, a closer
approximation to a 4:5:6:7 chord built on G can be found than that which
arises from the diatonic scale. That chord is notatod G B D E#. However,
this chord will not sound correct in C major, despite its acoustical purity:
the note "F" is expected, and an out-of-tune version is put in its place. In
addition, the "clash" in G B D F is essential to the feeling that it needs
to resolve to the tonic chord, C E G.

-Paul


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