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Ennealimmal temperament

🔗genewardsmith@juno.com

11/13/2001 11:17:14 PM

The two generators for this are 2^(1/9) and g=48.99 cents, which is a
close approximation to 36/35. The temmperament is just in the 7-limit
for practical purposes; with a fifth sharp by 0.065 cents, a major
third by 0.05 cents and a 7 flat by .139 cents. The temperament is so
close to just that in fact one may simply use 27/25 in the place of
2^(1/9) and 36/35 in the place of 'a'. Thus the 7-limit, involving
four primes, can be very closely approximated by these two rational
numbers:

(27/25)^4 / (36/35)^3 ~ 5/4 (0.325 cents sharp)
(27/25)^6 / (36/35)^2 ~ 3/2 (0.07 cents flat)
(27/25)^8 / (36/35)^2 ~ 7/4 (0.466 cents flat)
(27/25)^9 ~ 2 (0.862 cents flat)

This is really quite remarkable. The ennealimma rules!