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¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help 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-limit consonances, and the only intervals ~~in the 31edo octave~~ that are not 15-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¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help 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-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-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¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help 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-limit consonances, and the only intervals in the 31edo octave that are not 15-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¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help 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-limit consonances, and the only intervals larger than 2\31 and smaller than 29\31 that are not 15-limit consonances. Generates [[A-Team]] and [[semisept]] temperaments.
 MOS Scales generated by 12\31