More on Higher Primes in Greek Music

After I sent my post this AM, I remembered that the sequences 1/1 9/8
81/64 and 1/1 2/1 4/1 also illustrate the geometric mean in Greek theory.

Also, I was in the UCSD library today and looked at Thomas Mathiessen's
"Apollo's Lyre," a massive work on Greek music. Although it has gotten
mixed reviews from specialists, I recommend it. One of its strengths is
the discussion of aulos tunings and Mathiessen's experiences with
replicas. I might add that the surviving auloi he studied do not have
equidistant fingerholes. He found that changing reeds from beating-reed
to double-reed would change the pitch by at least a third and expand or
contract all the intervals by up to 50%. Similarly, he could easily bend
the pitch each note by 25 to 50 cents without much effort. In fact,
staying on pitch was quite difficult. In agreement with Jim French's
findings, the character of the reed was also very important.
Clearly the aulos was a flexible, virtuoso instrument.

BTW, I also saw a glowing review of Johnny Reinhard's microtonal
performance in Kazan in 1999 (?) in 20th Century Music.

--John