RE: 5-Limit in India?

John Chalmers wrote,

>I read a paper in an ethnomusicology journal that
>suggested that the 22 tone scale grew out of the modes of the 12-tone
>Pythagorean series. I gave my copy of the paper to Erv Wilson, who agreed,
>but I don't recall the details any more. Hence one could use essentially 5
>limit intervals while not recognizing 5 as a factor at all.

I believe that the sa- and ma- gramas were tuned by ear (with 5-limit
intervals) by musicians before theorists decided to quantify them in
terms of a 22-tone scale. A 22-tone Pythagorean series, aka the union of
11 modes of the 12-tone Pythagorean series, approximates the
hypothetical 5-limit gramas with a maximum error of 2 cents (the
skhisma). The Pythagorean series was more important in ancient musical
theory than it is now; for example the medieval Arabs used a 17-tone
Pythagorean series to quantify some apparently 5-limit scales. When I
said India achieved the 5-limit before the West I was thinking it terms
of presently existing musical traditions; the music of ancient Greece
>is, to my knowledge, a lost art.



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