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.
Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of Superpyth temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for middle-eastern (Arabic, Turkish, Persian) tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in arabic music. (The interval notated as C-E will have the character of a larger Pythagorean - or super-Pythagorean - major third.)
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.
The extended gentle region is further divided into two subregions:
- "lower gentle": 703.4¢ (near 17\29) to 704.3¢ (near 27\46)
- "upper gentle": 704.3¢ to 705.0¢ (near 10\17, or more accurately 47\80).
46edo is effectively the boundary between lower and upper neogothic.
| EDO Generator | Fifth | Dim 4th | Comments | |||
|---|---|---|---|---|---|---|
| 17\29 | 703.448 | 372.416 | ||||
| 703.711 | 370.312 | Margo Schulter's MET-24 fifth | ||||
| 61\104 | 703.846 | 369.231 | Neo-gothic theory of harmony | |||
| 44\75 | 704.000 | 368.000 | ||||
| 71\121 | 704.132 | 366.942 | ||||
| 27\46 | 704.348 | 365.217 | ||||
| 64\109 | 704.587 | 363.303 | Boundary of smaller "gentle region" | |||
| 37\63 | 704.762 | 361.905 | ||||
| 47\80 | 705.000 | 360.000 | Boundary of larger "gentle region" | |||
| 10\17 | 705.882 | 352.941 | ||||