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Sesquisexta

🔗Gene Ward Smith <gwsmith@svpal.org>

5/1/2004 3:14:12 AM

On MMM Margo wrote:

"Telling how I came to use a tuning system such as Peppermint 24 or
20-tET, and briefly explaining what an unfamiliar or less familiar
name means (e.g. Sesquisexta, simply the Latin term for "7:6," since
this tuning has two 12-note Pythagorean chains of pure fifths at a 7:6
apart)."

One way to do this would be to have a chain of 23 fifths, 22 of them
pure fifths and one a sharp fifth of size 16777216/11160261 =
|24 -13 0 -1>, or 705.76 cents. This would give a wolf of size
19683/14336, which is 548.77 cents, pretty close to an 11/8. We could
have for instance 11 pure fifths, what we might call a Sesquisexta
fifth of 705.76 cents, another 11 pure fifths, and the wolf,
completing the cycle of 24. This gives us what amounts to an irregular
tuning of septimal schismic on 24 notes; after 15 fifths (which would
necessarily include a Sesquisexta fifth) we end up at a pure 12/7,
which is where septimal schismic maps it.