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-=31edo MOS Scales=
+{{MOSes in EDO}}
-Since 31 is a prime number, any interval of a 31-tone equal scale ([[31edo|31 equal divisions of the octave]] or 31 equal divisions of a non-octave interval), when stacked, will continue generating new intervals until all 31 tones have been included. Thus, it is ripe for moment of symmetry scalesmithery. The diagram below shows every generator from 1\31 (one degree of 31edo) to 15\31 (15 degrees of 31edo), and two [[MOSScales|moment of symmetry scales]] that one can produce with that generator. The bold lines outline a scale with ten or fewer tones; the lighter lines add some more tones. The exact stopping-point of the generation process in these examples is, admittedly, somewhat arbitrary. Scales with a greater number of tones can be produced by continuing the generating process, until all 31 tones have been included.
+== Pergen Names ==
+Temperaments supported by 31edo may also be referred by [[pergen]] names.
-[[File:31edo_mos_families.jpg|alt=31edo_mos_families.jpg|31edo_mos_families.jpg]]
+* 1\31 = (P8, P4/13)
+* 2\31 = (P8, P5/9)
-[[:File:31edo_mos_families.pdf|31edo mos families.pdf]]
+* 3\31 = (P8, P5/6)
+* 4\31 = (P8, P11/11)
-Note that many of the names above are outdated or just plain wrong. Here's the [[pergen|pergen]] names for 31edo's rank-2 scales:
+* 5\31 = (P8, ccP4/15)
+* 6\31 = (P8, P5/3)
-\31 = (P8, P4/13)
+* 7\31 = (P8, P12/7)
+* 8\31 = (P8, ccP5/10)
-\31 = (P8, P5/9)
+* 9\31 = (P8, P5/2)
+* 10\31 = (P8, ccP5/8)
-\31 = (P8, P5/6)
+* 11\31 = (P8, P11/4)
+* 12\31 = (P8, c⁵P4/14)
-\31 = (P8, P11/11)
+* 13\31 = (P8, P5)
+* 14\31 = (P8, c⁵P4/12)
-\31 = (P8, WWP4/15)
+* 15\31 = (P8, ccP4/5)
-\31 = (P8, P5/3)
-\31 = (P8, P12/7)
-\31 = (P8, WWP5/10)
-\31 = (P8, P5/2)
-\31 = (P8, WWP5/8)
-\31 = (P8, P11/4)
-\31 = (P8, W⁵P4/14)
-\31 = (P8, P5)
-\31 = (P8, W⁵P4/12)
-\31 = (P8, WWP4/5)
------
-==MOS Scales of 31edo by cardinality==
-===Tritonic===
-Slender[3] 1 1 29
-Valentine[3] 2 2 27
-Miracle[3] 3 3 25
-Nusecond[3] 4 4 23
-Hemithirds[3] 5 5 21
-Mothra[3] 6 6 19
-Orwell[3] 7 7 17
-Myna[3] 8 8 15
-Mohajira[3] 9 9 13
-Würschmidt[3] 10 10 11
-Squares[3] 11 11 9
-Semisept[3] 12 12 7
-Meantone[3] 13 13 5
-Casablanca[3] 14 14 3
-Tritonic[3] 15 15 1
-===Tetratonic===
-Slender[4] 1 1 1 28
-Valentine[4] 2 2 2 25
-Miracle[4] 3 3 3 22
-Nusecond[4] 4 4 4 19
-Hemithirds[4] 5 5 5 16
-Mothra[4] 6 6 6 13
-Orwell[4] 7 7 7 10
-Myna[4] 8 8 8 7
-Mohajira[4] 9 9 9 4
-Würschmidt[4] 10 10 10 1
-===Pentatonic===
-Slender[5] 1 1 1 1 27
-Valentine[5] 2 2 2 2 23
-Miracle[5] 3 3 3 3 19
-Nusecond[5] 4 4 4 4 15
-Hemithirds[5] 5 5 5 5 11
-Mothra[5] 6 6 6 6 7
-Orwell[5] 7 7 7 7 3
-Squares[5] 2 9 2 9 9
-Semisept[5] 5 7 5 7 7
-Meantone[5] 8 5 8 5 5
-Casablanca[5] 11 3 11 3 3
-Tritonic[5] 14 1 14 1 1
-===Hexatonic===
-Slender[6] 1 1 1 1 1 26
-Valentine[6] 2 2 2 2 2 21
-Miracle[6] 3 3 3 3 3 16
-Nusecond[6] 4 4 4 4 4 11
-Hemithirds[6] 5 5 5 5 5 6
-Mothra[6] 6 6 6 6 6 1
-===Heptatonic===
-Slender[7] 1 1 1 1 1 1 25
-Valentine[7] 2 2 2 2 2 2 19
-Miracle[7] 3 3 3 3 3 3 13
-Nusecond[7] 4 4 4 4 4 4 7
-Hemithirds[7] 5 5 5 5 5 5 1
-Myna[7] 1 7 1 7 1 7 7
-Mohajira[7] 5 4 5 4 5 4 4
-Würschmidt[7] 9 1 9 1 9 1 1
-Meantone[7] 3 5 5 3 5 5 5
-Casablanca[7] 8 3 3 8 3 3 3
-Tritonic[7] 13 1 1 13 1 1 1
-===Octatonic===
-Slender[8] 1 1 1 1 1 1 1 24
-Valentine[8] 2 2 2 2 2 2 2 17
-Miracle[8] 3 3 3 3 3 3 3 10
-Nusecond[8] 4 4 4 4 4 4 4 3
-Squares[8] 2 2 7 2 2 7 2 7
-Semisept[8] 5 5 2 5 5 2 5 2
-===Nonatonic===
-Slender[9] 1 1 1 1 1 1 1 1 23
-Valentine[9] 2 2 2 2 2 2 2 2 15
-Miracle[9] 3 3 3 3 3 3 3 3 7
-Orwell[9] 4 3 4 3 4 3 4 3 3
-Casablanca[9] 5 3 3 3 5 3 3 3 3
-Tritonic[9] 12 1 1 1 12 1 1 1 1
-===Decatonic===
-Slender[10] 1 1 1 1 1 1 1 1 1 22
-Valentine[10] 2 2 2 2 2 2 2 2 2 13
-Miracle[10] 3 3 3 3 3 3 3 3 3 4
-Mohajira[10] 1 4 4 1 4 4 1 4 4 4
-Würschmidt[10] 8 1 1 8 1 1 8 1 1 1
-===Hendecatonic===
-Slender[11] 1 1 1 1 1 1 1 1 1 1 21
-Valentine[11] 2 2 2 2 2 2 2 2 2 2 11
-Miracle[11] 3 3 3 3 3 3 3 3 3 3 1
-Mothra[11] 5 1 5 1 5 1 5 1 5 1 1
-Myna[11] 1 1 6 1 1 6 1 1 6 1 6
-Squares[11] 2 2 2 5 2 2 2 5 2 2 5
-Casablanca[11] 2 3 3 3 3 2 3 3 3 3 3
-Tritonic[11] 11 1 1 1 1 11 1 1 1 1 1
-===Dodecatonic===
-Slender[12] 1 1 1 1 1 1 1 1 1 1 1 20
-Valentine[12] 2 2 2 2 2 2 2 2 2 2 2 9
-Meantone[12] 3 3 2 3 2 3 3 2 3 2 3 2
-===Tridecatonic===
-Slender[13] 1 1 1 1 1 1 1 1 1 1 1 1 19
-Valentine[13] 2 2 2 2 2 2 2 2 2 2 2 7
-Hemithirds[13] 4 1 4 1 4 1 4 1 4 1 4 1 1
-Orwell[13] 1 3 3 1 3 3 1 3 3 1 3 3 3
-Würschmidt[13] 7 1 1 1 7 1 1 1 7 1 1 1 1
-Semisept[13] 3 2 3 2 2 3 2 3 2 2 3 2 2
-Tritonic[13] 10 1 1 1 1 1 10 1 1 1 1 1 1
-===Tetradecatonic===
-Slender[14] 1 1 1 1 1 1 1 1 1 1 1 1 1 18
-Valentine[14] 2 2 2 2 2 2 2 2 2 2 2 2 2 5
-Squares[14] 2 2 2 2 3 2 2 2 2 3 2 2 2 3
-===Pentadecatonic===
-Slender[15] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17
-Valentine[15] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
-Nusecond[15] 1 3 1 3 1 3 1 3 1 3 1 3 1 3 3
-Myna[15] 1 1 1 5 1 1 1 5 1 1 1 5 1 1 5
-Tritonic[15] 9 1 1 1 1 1 1 9 1 1 1 1 1 1 1
-===Hexadecatonic===
-Slender[16] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16
-Valentine[16] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
-Mothra[16] 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 1
-Würschmidt[16] 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 1
-===Heptadecatonic===
-Slender[17] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15
-Mohajira[17] 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 3
-Squares[17] 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1
-Tritonic[17] 8 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1
-===Octadecatonic===
-Slender[18] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14
-Semisept[18] 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2
-===Nonadecatonic===
-Slender[19] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13
-Hemithirds[19] 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1
-Myna[19] 1 1 1 1 4 1 1 1 1 4 1 1 1 1 4 1 1 1 4
-Würschmidt[19] 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 1
-Meantone[19] 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2
-Tritonic[19] 7 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1
-===Icosatonic===
-Slender[20] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12
-Casablanca[20] 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1
-===Icosihenatonic===
-Slender[21] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11
-Miracle[21] 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1
-Mothra[21] 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 1
-Tritonic[21] 6 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1
-===Icosiditonic===
-Slender[22] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10
-Orwell[22] 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2
-Würschmidt[22] 4 1 1 1 1 1 1 4 1 1 1 1 1 1 4 1 1 1 1 1 1 1
-===Icositritonic===
-Slender[23] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
-Nusecond[23] 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 2
-Myna[23] 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 3
-Tritonic[23] 5 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1
-===Icositetratonic===
-Slender[24] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8
-Mohajira[24] 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2
-===Icosipentatonic===
-Slender[25] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7
-Hemithirds[25] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1
-Würschmidt[25] 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
-Tritonic[25] 4 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1
-===Icosihexatonic===
-Slender[26] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6
-Mothra[26] 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
-===Icosiheptatonic===
-Slender[27] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5
-Myna[27] 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2
-Tritonic[27] 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
-===Icosioctatonic===
-Slender[28] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
-Würschmidt[28] 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
-===Icosinonatonic===
-Slender[29] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
-Tritonic[29] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-===Tricontatonic===
-Slender[30] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
+== Gallery ==
+[[File:31edo_mos_families.jpg|alt=31edo_mos_families.jpg|none|frame|MOS families of 31edo, with selected MOS scales for each generator.]]
 [[Category:31edo]]

List of MOS scales in 31edo: Difference between revisions