Gentle region
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 | ||||