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well-temperaments

🔗"Paul H. Erlich" <PErlich@...>

5/12/1998 3:16:03 PM
Paul Hahn wrote,

>Paul Erlich has mentioned that he's been messing with a
>"well-temperament" variation in his 22TET work

This is right in my paper (have you read it?). 12-tone well-temperaments
give certain heptatonic keys with good overall 5-limit harmony and other
keys with better 3-limit harmony but bad ratios of 5. Similarly, the
22-tone well-temperament in my paper gives certain decatonic keys with
good overall 7-limit harmony, and other decatonic keys which approach
Indian tuning, having better 5-limit harmony but bad ratios of 7.

>but I doubt he considers
>it significantly de-22-ated. (-ized?)

Basically, that's true, although the 5-limit keys in 12-tone
well-temperaments sound like they could come from 31, and the 5-limit
keys in 22-tone well-temperaments sound like they could come from 34.