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.

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

See also