31edo/Individual degrees: Difference between revisions

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== 3\31 – major semitone, diatonic semitone, large minor 2nd or minor 2nd ==

The larger and clunkier of the 31edo semitones. In meantone, it is the ''diatonic semitone'' which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. 3\31 stands in for just ratios 16:15 (111.73¢); 15:14 (119.44¢) and others. It is notable that two of these make an 8/7; this implies that the 3\31 is a ''secor'' and generates [[Miracle|miracle temperament]]. It represents 343:320 (120.16¢) and 14:13 (128.29¢), and five of these give a 7/5, meaning it generates [[~~Subgroup temperaments~~#Mercy|mercy temperament]]. The Pythagorean apotome 2187:2048 (113.69¢) is close to 3\31 in value, but is not consistent with the mapping of the primes 2 and 3 in 31edo (in fact the apotome of 31edo is the previous degree 2\31).

The larger and clunkier of the 31edo semitones. In meantone, it is the ''diatonic semitone'' which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. 3\31 stands in for just ratios 16:15 (111.73¢); 15:14 (119.44¢) and others. It is notable that two of these make an 8/7; this implies that the 3\31 is a ''secor'' and generates [[Miracle|miracle temperament]]. It represents 343:320 (120.16¢) and 14:13 (128.29¢), and five of these give a 7/5, meaning it generates [[Quince_clan#Mercy|mercy temperament]]. The Pythagorean apotome 2187:2048 (113.69¢) is close to 3\31 in value, but is not consistent with the mapping of the primes 2 and 3 in 31edo (in fact the apotome of 31edo is the previous degree 2\31).

MOS Scales generated by 3\31

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 == 3\31 – major semitone, diatonic semitone, large minor 2nd or minor 2nd ==
-The larger and clunkier of the 31edo semitones. In meantone, it is the ''diatonic semitone'' which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. 3\31 stands in for just ratios 16:15 (111.73¢); 15:14 (119.44¢) and others. It is notable that two of these make an 8/7; this implies that the 3\31 is a ''secor'' and generates [[Miracle|miracle temperament]]. It represents 343:320 (120.16¢) and 14:13 (128.29¢), and five of these give a 7/5, meaning it generates [[Subgroup temperaments#Mercy|mercy temperament]]. The Pythagorean apotome 2187:2048 (113.69¢) is close to 3\31 in value, but is not consistent with the mapping of the primes 2 and 3 in 31edo (in fact the apotome of 31edo is the previous degree 2\31).
+The larger and clunkier of the 31edo semitones. In meantone, it is the ''diatonic semitone'' which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. 3\31 stands in for just ratios 16:15 (111.73¢); 15:14 (119.44¢) and others. It is notable that two of these make an 8/7; this implies that the 3\31 is a ''secor'' and generates [[Miracle|miracle temperament]]. It represents 343:320 (120.16¢) and 14:13 (128.29¢), and five of these give a 7/5, meaning it generates [[Quince_clan#Mercy|mercy temperament]]. The Pythagorean apotome 2187:2048 (113.69¢) is close to 3\31 in value, but is not consistent with the mapping of the primes 2 and 3 in 31edo (in fact the apotome of 31edo is the previous degree 2\31).
 MOS Scales generated by 3\31