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List of MOS scales in 31edo: Difference between revisions

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Ganaram inukshuk (talk | contribs)
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Added a mos table that was generated using a VBA script I've been working on and pasted into the editor. Feel free to edit if need be.
Ganaram inukshuk (talk | contribs)
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Mostly formatting changes: the diagram towards the top of the page is given its own section; the list of scales by note count is made into a list (kind of); the comprehensive scale table is given some minor edits (removing temperament[31] scales)
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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 [[MOS Scale]]s 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.
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.
 
== MOS Families of 31edo ==
The following diagram shows every generator from 1\31 (one degree of 31edo) to 15\31 (15 degrees of 31edo), and two [[MOS Scale]]s 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.


[[File:31edo_mos_families.jpg|alt=31edo_mos_families.jpg|31edo_mos_families.jpg]]
[[File:31edo_mos_families.jpg|alt=31edo_mos_families.jpg|31edo_mos_families.jpg]]


Note that many of the names above are outdated or just plain wrong. Here's the [[pergen]] names for 31edo's rank-2 scales:
=== Pergen Names ===
Note that many of the names above are outdated or just plain wrong; most of these names are based on temperaments and pre-TANMANS naming schemes. Here are the [[pergen]] names for 31edo's rank-2 scales:


* 1\31 = (P8, P4/13)
* 1\31 = (P8, P4/13)
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* 15\31 = (P8, ccP4/5)
* 15\31 = (P8, ccP4/5)


== MOS Scales by Generator Size ==
== MOS Scales by Generator Pair ==
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:
 
* The table denotes each family using a [[Horogram#Rectangular Horogram|rectangular horogram]], starting with 1L 1s and [[MOS Diagrams|adding notes]] until all 31 notes are added.
* For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
* TAMNAMS names are used wherever possible.
 
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
! colspan="35" |Single-Period Scales for 31 Equal Division of the Octave
! colspan="35" |Single-Period Scales for 31 Equal Division of the Octave
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|1
|1
|
|
|slender[31]
|
|-
|-
! colspan="31" |Steps for  Generators 29\31 and 2\31
! colspan="31" |Steps for  Generators 29\31 and 2\31
Line 1,955: Line 1,964:
|1
|1
|
|
|myna[31]
|
|-
|-
! colspan="31" |Steps for  Generators 22\31 and 9\31
! colspan="31" |Steps for  Generators 22\31 and 9\31
Line 2,482: Line 2,491:
|1
|1
|
|
|squares[31]
|
|-
|-
! colspan="31" |Steps for  Generators 19\31 and 12\31
! colspan="31" |Steps for  Generators 19\31 and 12\31
Line 3,206: Line 3,215:
===Tritonic===
===Tritonic===


Slender[3] 1 1 29
* 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


Valentine[3] 2 2 27
===Tetratonic===


Miracle[3] 3 3 25
* 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


Nusecond[3] 4 4 23
===Pentatonic===


Hemithirds[3] 5 5 21
* 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


Mothra[3] 6 6 19
===Hexatonic===


Orwell[3] 7 7 17
* 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


Myna[3] 8 8 15
===Heptatonic===


Mohajira[3] 9 9 13
* 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


Würschmidt[3] 10 10 11
===Octatonic===


Squares[3] 11 11 9
* 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


Semisept[3] 12 12 7
===Nonatonic===


Meantone[3] 13 13 5
* 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


Casablanca[3] 14 14 3
===Decatonic===


Tritonic[3] 15 15 1
* 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


===Tetratonic===
===Hendecatonic===


Slender[4] 1 1 1 28
* 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


Valentine[4] 2 2 2 25
===Dodecatonic===


Miracle[4] 3 3 3 22
* 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


Nusecond[4] 4 4 4 19
===Tridecatonic===


Hemithirds[4] 5 5 5 16
* 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


Mothra[4] 6 6 6 13
===Tetradecatonic===


Orwell[4] 7 7 7 10
* 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


Myna[4] 8 8 8 7
===Pentadecatonic===


Mohajira[4] 9 9 9 4
* 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


Würschmidt[4] 10 10 10 1
===Hexadecatonic===


===Pentatonic===
* 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


Slender[5] 1 1 1 1 27
===Heptadecatonic===


Valentine[5] 2 2 2 2 23
* 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


Miracle[5] 3 3 3 3 19
===Octadecatonic===


Nusecond[5] 4 4 4 4 15
* 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


Hemithirds[5] 5 5 5 5 11
===Nonadecatonic===


Mothra[5] 6 6 6 6 7
* 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


Orwell[5] 7 7 7 7 3
===Icosatonic===


Squares[5] 2 9 2 9 9
* 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


Semisept[5] 5 7 5 7 7
===Icosihenatonic===


Meantone[5] 8 5 8 5 5
* 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


Casablanca[5] 11 3 11 3 3
===Icosiditonic===


Tritonic[5] 14 1 14 1 1
* 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


===Hexatonic===
===Icositritonic===


Slender[6] 1 1 1 1 1 26
* 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


Valentine[6] 2 2 2 2 2 21
===Icositetratonic===


Miracle[6] 3 3 3 3 3 16
* 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


Nusecond[6] 4 4 4 4 4 11
===Icosipentatonic===


Hemithirds[6] 5 5 5 5 5 6
* 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


Mothra[6] 6 6 6 6 6 1
===Icosihexatonic===


===Heptatonic===
* 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


Slender[7] 1 1 1 1 1 1 25
===Icosiheptatonic===


Valentine[7] 2 2 2 2 2 2 19
* 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


Miracle[7] 3 3 3 3 3 3 13
===Icosioctatonic===


Nusecond[7] 4 4 4 4 4 4 7
* 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


Hemithirds[7] 5 5 5 5 5 5 1
===Icosinonatonic===
 
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
* 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===
===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
* 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


[[Category:31edo]]
[[Category:31edo]]
Retrieved from "https://en.xen.wiki/w/List_of_MOS_scales_in_31edo"