Gentle region

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This is the version of Oct 30, 2012. For an alternative version see: Gentle region (extended version)

Margo Schulter, in a tuning list posting, defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later amending that to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of 29edo, 46edo, 75edo, 104edo, 109edo, 121edo, 145edo, 155edo, 162edo, 167edo, 179edo, 191edo, 201edo, 213edo, 225edo and 237edo, plus 63edo and 80edo in the extended region.

EDO generator cents comment
17\29 703.448
61\104 703.846
44\75 704.000
71\121 704.132
27\46 704.348
64\109 704.587 Boundary of smaller "gentle region"
37\63 704.762
47\80 705.000 Boundary of larger "gentle region"
10\17 705.882

See also