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optimal meantone fifths

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

2/18/1997 4:41:26 PM
From: PAULE

In case anyone cares, the exact sizes of perfect fifth in the meantone
temperaments I described are
(2+(7*log(5)-2*log(3))/log(2))/26 octaves, for the equal-weighted case, and
(66+(175*log(5)-66*log(3))/log(2))/634 octaves, for the limit-weighted case.
Lucy's fifth is 1/2+1/(4*pi) octaves.

A nice way to justify Lucy tuning is that it gives better minor thirds than
1/4-comma meantone, but better major thirds than 1/3-comma meantone. The
usual compromise is 2/7-comma meantone, but Lucy's tuning, being 3/10 comma
meantone, leans toward 1/3-comma meantone, and so favors the minor third.

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