31edo/Individual degrees: Difference between revisions

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== 12\31 – narrow 4th, subfourth or down 4th ==

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). Although 31edo does not offer reasonable approximations of the 17th or 13th harmonics, 12\31 is less than 0.09¢ flat of the [[17-limit]] interval [[17/13]] (464.43¢); combining this with 17\31's 1.1-cent-sharp approximation to [[19/13]] yields a good 13:17:19, which helps make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-odd-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-odd-limit consonances. Generates [[A-Team]] and [[semisept]] temperaments.

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). Although 31edo does not offer reasonable approximations of the 17th or 13th harmonics, 12\31 is less than 0.09¢ flat of the [[17-limit]] interval [[17/13]] (464.43¢); combining this with 17\31's 1.08-cent-sharp approximation to [[19/13]] yields a good 13:17:19, which helps make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-odd-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-odd-limit consonances. Generates [[A-Team]] and [[semisept]] temperaments.

MOS Scales generated by 12\31

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 == 12\31 – narrow 4th, subfourth or down 4th ==
-Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). Although 31edo does not offer reasonable approximations of the 17th or 13th harmonics, 12\31 is less than 0.09¢ flat of the [[17-limit]] interval [[17/13]] (464.43¢); combining this with 17\31's 1.1-cent-sharp approximation to [[19/13]] yields a good 13:17:19, which helps make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-odd-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-odd-limit consonances. Generates [[A-Team]] and [[semisept]] temperaments.
+Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). Although 31edo does not offer reasonable approximations of the 17th or 13th harmonics, 12\31 is less than 0.09¢ flat of the [[17-limit]] interval [[17/13]] (464.43¢); combining this with 17\31's 1.08-cent-sharp approximation to [[19/13]] yields a good 13:17:19, which helps make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-odd-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-odd-limit consonances. Generates [[A-Team]] and [[semisept]] temperaments.
 MOS Scales generated by 12\31