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9&11 limit copoptimal pajara

🔗Gene Ward Smith <gwsmith@svpal.org>

7/4/2004 12:13:34 PM

The 9 and 11 limit poptimal ranges intersect, and 78 or 100 equal work
as copops for them. The 7-limit range is a tad higher, and 22 is
excellent for that. The 5-limit temperament of course really isn't
pajara at all, but it has 114 or 148 as possibles.

The 78-et fifth is 707.692 cents, 5.737 cents sharp. The 100-et
poptimal fifth is of course not the meantone fifth of 50-et of 696
cents, but the sharper fifth of exactly 708 cents, 6.045 cents sharp.
The 100-et version of Paul's favorite 10 and 12 note scales come out
exactly in terms of cents, like meantone does in 50, and 100-equal was
one of the things which turned up when I went looking for something
which did a good job for both meantone and pajara. It looks to me it's
really better than 88 for that.