Byzantine tuning, Kami reply

RE Byzantine 68-tet: I don't think the Greek Orthodox Church really
considered playing in 68-tet, but rather thought of constructing the
tetrachords of its liturgical music in 28 parts rather like the Aristoxenian
30 parts of classical Greek theory. I found a number of such tetrachords
in a book by Octavio Tiby, "La Musica Byzantina," Fratelli Bocia,
Milan, 1938. The tetrachords are 12 +13+ 3; 12 + 5 + 11;. 12 + 9 + 7;
and 9 + 12 + 7. In this system, the whole tone has 12 parts (212 cents),
and the octave consists of two such tetrachords and 12 parts for the
disjunctive tone. Hence the formula is 28 + 12 + 28 = 68 parts for the
octave. 12 + 5 + 11 is a pretty fair "Phrygian" tetrachord, but 3 parts
is roughly a 1/4-tone and 9 parts 3/4 of a tone.

Other writers on Byzantine music, including Xenakis in "Musiques
Formelles," give quite different tunings in the 30 parts-to-the-4th system.

--John


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