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)
Line 21: Line 25:
* 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]]

Revision as of 20:14, 8 April 2022

Since 31 is a prime number, any interval of a 31-tone equal scale (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 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.

31edo_mos_families.jpg

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)
  • 2\31 = (P8, P5/9)
  • 3\31 = (P8, P5/6)
  • 4\31 = (P8, P11/11)
  • 5\31 = (P8, ccP4/15)
  • 6\31 = (P8, P5/3)
  • 7\31 = (P8, P12/7)
  • 8\31 = (P8, ccP5/10)
  • 9\31 = (P8, P5/2)
  • 10\31 = (P8, ccP5/8)
  • 11\31 = (P8, P11/4)
  • 12\31 = (P8, c⁵P4/14)
  • 13\31 = (P8, P5)
  • 14\31 = (P8, c⁵P4/12)
  • 15\31 = (P8, ccP4/5)

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. A few notes:

  • The table denotes each family using a rectangular horogram, starting with 1L 1s and 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.
Single-Period Scales for 31 Equal Division of the Octave
Steps for Generators 30\31 and 1\31 Mos Step Ratio TAMNAMS Name Temperament
30 1 1L 1s 30:1
29 1 1 1L 2s 29:1 slender[3]
28 1 1 1 1L 3s 28:1 slender[4]
27 1 1 1 1 1L 4s 27:1 slender[5]
26 1 1 1 1 1 1L 5s 26:1 slender[6]
25 1 1 1 1 1 1 1L 6s 25:1 slender[7]
24 1 1 1 1 1 1 1 1L 7s 24:1 slender[8]
23 1 1 1 1 1 1 1 1 1L 8s 23:1 slender[9]
22 1 1 1 1 1 1 1 1 1 1L 9s 22:1 slender[10]
21 1 1 1 1 1 1 1 1 1 1 1L 10s 21:1 slender[11]
20 1 1 1 1 1 1 1 1 1 1 1 1L 11s 20:1 slender[12]
19 1 1 1 1 1 1 1 1 1 1 1 1 1L 12s 19:1 slender[13]
18 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 13s 18:1 slender[14]
17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 14s 17:1 slender[15]
16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 15s 16:1 slender[16]
15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 16s 15:1 slender[17]
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 17s 14:1 slender[18]
13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 18s 13:1 slender[19]
12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 19s 12:1 slender[20]
11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 20s 11:1 slender[21]
10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 21s 10:1 slender[22]
9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 22s 9:1 slender[23]
8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 23s 8:1 slender[24]
7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24s 7:1 slender[25]
6 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 1L 25s 6:1 slender[26]
5 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 1L 26s 5:1 slender[27]
4 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 1L 27s 4:1 slender[28]
3 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 1L 28s 3:1 slender[29]
2 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 1L 29s 2:1 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 1 1 31edo 1
Steps for Generators 29\31 and 2\31 Mos Step Ratio TAMNAMS Name Temperament
29 2 1L 1s 29:2
27 2 2 1L 2s 27:2 valentine[3]
25 2 2 2 1L 3s 25:2 valentine[4]
23 2 2 2 2 1L 4s 23:2 valentine[5]
21 2 2 2 2 2 1L 5s 21:2 valentine[6]
19 2 2 2 2 2 2 1L 6s 19:2 valentine[7]
17 2 2 2 2 2 2 2 1L 7s 17:2 valentine[8]
15 2 2 2 2 2 2 2 2 1L 8s 15:2 valentine[9]
13 2 2 2 2 2 2 2 2 2 1L 9s 13:2 valentine[10]
11 2 2 2 2 2 2 2 2 2 2 1L 10s 11:2 valentine[11]
9 2 2 2 2 2 2 2 2 2 2 2 1L 11s 9:2 valentine[12]
7 2 2 2 2 2 2 2 2 2 2 2 2 1L 12s 7:2 valentine[13]
5 2 2 2 2 2 2 2 2 2 2 2 2 2 1L 13s 5:2 valentine[14]
3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1L 14s 3:2 valentine[15]
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15L 1s 2:1 valentine[16]
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 1 1 31edo 1
Steps for Generators 28\31 and 3\31 Mos Step Ratio TAMNAMS Name Temperament
28 3 1L 1s 28:3
25 3 3 1L 2s 25:3 miracle[3]
22 3 3 3 1L 3s 22:3 miracle[4]
19 3 3 3 3 1L 4s 19:3 miracle[5]
16 3 3 3 3 3 1L 5s 16:3 miracle[6]
13 3 3 3 3 3 3 1L 6s 13:3 miracle[7]
10 3 3 3 3 3 3 3 1L 7s 10:3 miracle[8]
7 3 3 3 3 3 3 3 3 1L 8s 7:3 miracle[9]
4 3 3 3 3 3 3 3 3 3 1L 9s 4:3 miracle[10]
1 3 3 3 3 3 3 3 3 3 3 10L 1s 3:1 miracle[11]
1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 10L 11s 2:1 miracle[21]
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 1 1 31edo 1
Steps for Generators 27\31 and 4\31 Mos Step Ratio TAMNAMS Name Temperament
27 4 1L 1s 27:4
23 4 4 1L 2s 23:4 nusecond[3]
19 4 4 4 1L 3s 19:4 nusecond[4]
15 4 4 4 4 1L 4s 15:4 nusecond[5]
11 4 4 4 4 4 1L 5s 11:4 nusecond[6]
7 4 4 4 4 4 4 1L 6s 7:4 nusecond[7]
3 4 4 4 4 4 4 4 7L 1s 4:3 pine nusecond[8]
3 3 1 3 1 3 1 3 1 3 1 3 1 3 1 8L 7s 3:1 nusecond[15]
2 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 8L 15s 2:1 nusecond[23]
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 1 1 31edo 1
Steps for Generators 26\31 and 5\31 Mos Step Ratio TAMNAMS Name Temperament
26 5 1L 1s 26:5
21 5 5 1L 2s 21:5 hemithirds[3]
16 5 5 5 1L 3s 16:5 hemithirds[4]
11 5 5 5 5 1L 4s 11:5 hemithirds[5]
6 5 5 5 5 5 1L 5s 6:5 hemithirds[6]
1 5 5 5 5 5 5 6L 1s 5:1 archeotonic hemithirds[7]
1 1 4 1 4 1 4 1 4 1 4 1 4 6L 7s 4:1 hemithirds[13]
1 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 6L 13s 3:1 hemithirds[19]
1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 6L 19s 2:1 hemithirds[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 1 1 1 1 1 1 1 31edo 1
Steps for Generators 25\31 and 6\31 Mos Step Ratio TAMNAMS Name Temperament
25 6 1L 1s 25:6
19 6 6 1L 2s 19:6 mothra[3]
13 6 6 6 1L 3s 13:6 mothra[4]
7 6 6 6 6 1L 4s 7:6 mothra[5]
1 6 6 6 6 6 5L 1s 6:1 machinoid mothra[6]
1 1 5 1 5 1 5 1 5 1 5 5L 6s 5:1 mothra[11]
1 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 5L 11s 4:1 mothra[16]
1 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 5L 16s 3:1 mothra[21]
1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 5L 21s 2:1 mothra[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 1 1 1 1 1 1 31edo 1
Steps for Generators 24\31 and 7\31 Mos Step Ratio TAMNAMS Name Temperament
24 7 1L 1s 24:7
17 7 7 1L 2s 17:7 orwell[3]
10 7 7 7 1L 3s 10:7 orwell[4]
3 7 7 7 7 4L 1s 7:3 manic orwell[5]
3 3 4 3 4 3 4 3 4 4L 5s 4:3 orwelloid orwell[9]
3 3 3 1 3 3 1 3 3 1 3 3 1 9L 4s 3:1 orwell[13]
2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 9L 13s 2:1 orwell[22]
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 1 1 31edo 1
Steps for Generators 23\31 and 8\31 Mos Step Ratio TAMNAMS Name Temperament
23 8 1L 1s 23:8
15 8 8 1L 2s 15:8 myna[3]
7 8 8 8 3L 1s 8:7 myna[4]
7 7 1 7 1 7 1 4L 3s 7:1 smitonic myna[7]
6 1 6 1 1 6 1 1 6 1 1 4L 7s 6:1 myna[11]
5 1 1 5 1 1 1 5 1 1 1 5 1 1 1 4L 11s 5:1 myna[15]
4 1 1 1 4 1 1 1 1 4 1 1 1 1 4 1 1 1 1 4L 15s 4:1 myna[19]
3 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 4L 19s 3:1 myna[23]
2 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 1 4L 23s 2:1 myna[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 1 1 1 1 1 31edo 1
Steps for Generators 22\31 and 9\31 Mos Step Ratio TAMNAMS Name Temperament
22 9 1L 1s 22:9
13 9 9 1L 2s 13:9 mohajira[3]
4 9 9 9 3L 1s 9:4 mohajira[4]
4 4 5 4 5 4 5 3L 4s 5:4 mosh mohajira[7]
4 4 4 1 4 4 1 4 4 1 7L 3s 4:1 dicotonic mohajira[10]
3 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 7L 10s 3:1 mohajira[17]
2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 7L 17s 2:1 mohajira[24]
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 1 1 31edo 1
Steps for Generators 21\31 and 10\31 Mos Step Ratio TAMNAMS Name Temperament
21 10 1L 1s 21:10
11 10 10 1L 2s 11:10 würschmidt[3]
1 10 10 10 3L 1s 10:1 würschmidt[4]
1 1 9 1 9 1 9 3L 4s 9:1 mosh würschmidt[7]
1 1 1 8 1 1 8 1 1 8 3L 7s 8:1 sephiroid würschmidt[10]
1 1 1 1 7 1 1 1 7 1 1 1 7 3L 10s 7:1 würschmidt[13]
1 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 3L 13s 6:1 würschmidt[16]
1 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 5 3L 16s 5:1 würschmidt[19]
1 1 1 1 1 1 1 4 1 1 1 1 1 1 4 1 1 1 1 1 1 4 3L 19s 4:1 würschmidt[22]
1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3L 22s 3:1 würschmidt[25]
1 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 2 3L 25s 2:1 würschmidt[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 1 1 1 1 31edo 1
Steps for Generators 20\31 and 11\31 Mos Step Ratio TAMNAMS Name Temperament
20 11 1L 1s 20:11
9 11 11 2L 1s 11:9 squares[3]
9 9 2 9 2 3L 2s 9:2 antipentic squares[5]
7 2 7 2 2 7 2 2 3L 5s 7:2 sensoid squares[8]
5 2 2 5 2 2 2 5 2 2 2 3L 8s 5:2 squares[11]
3 2 2 2 3 2 2 2 2 3 2 2 2 2 3L 11s 3:2 squares[14]
1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 14L 3s 2:1 squares[17]
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 1 1 31edo 1
Steps for Generators 19\31 and 12\31 Mos Step Ratio TAMNAMS Name Temperament
19 12 1L 1s 19:12
7 12 12 2L 1s 12:7 semisept[3]
7 7 5 7 5 3L 2s 7:5 antipentic semisept[5]
2 5 2 5 5 2 5 5 5L 3s 5:2 oneirotonic semisept[8]
2 2 3 2 2 3 2 3 2 2 3 2 3 5L 8s 3:2 semisept[13]
2 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 13L 5s 2:1 semisept[18]
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 1 1 31edo 1
Steps for Generators 18\31 and 13\31 Mos Step Ratio TAMNAMS Name Temperament
18 13 1L 1s 18:13
5 13 13 2L 1s 13:5 meantone[3]
5 5 8 5 8 2L 3s 8:5 pentic meantone[5]
5 5 5 3 5 5 3 5L 2s 5:3 diatonic meantone[7]
2 3 2 3 2 3 3 2 3 2 3 3 7L 5s 3:2 m-chromatic meantone[12]
2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 12L 7s 2:1 meantone[19]
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 1 1 31edo 1
Steps for Generators 17\31 and 14\31 Mos Step Ratio TAMNAMS Name Temperament
17 14 1L 1s 17:14
3 14 14 2L 1s 14:3 casablanca[3]
3 3 11 3 11 2L 3s 11:3 pentic casablanca[5]
3 3 3 8 3 3 8 2L 5s 8:3 antidiatonic casablanca[7]
3 3 3 3 5 3 3 3 5 2L 7s 5:3 joanatonic casablanca[9]
3 3 3 3 3 2 3 3 3 3 2 9L 2s 3:2 casablanca[11]
1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 2 11L 9s 2:1 casablanca[20]
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 1 1 31edo 1
Steps for Generators 16\31 and 15\31 Mos Step Ratio TAMNAMS Name Temperament
16 15 1L 1s 16:15
1 15 15 2L 1s 15:1 tritonic[3]
1 1 14 1 14 2L 3s 14:1 pentic tritonic[5]
1 1 1 13 1 1 13 2L 5s 13:1 antidiatonic tritonic[7]
1 1 1 1 12 1 1 1 12 2L 7s 12:1 joanatonic tritonic[9]
1 1 1 1 1 11 1 1 1 1 11 2L 9s 11:1 tritonic[11]
1 1 1 1 1 1 10 1 1 1 1 1 10 2L 11s 10:1 tritonic[13]
1 1 1 1 1 1 1 9 1 1 1 1 1 1 9 2L 13s 9:1 tritonic[15]
1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 8 2L 15s 8:1 tritonic[17]
1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 7 2L 17s 7:1 tritonic[19]
1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 6 2L 19s 6:1 tritonic[21]
1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 5 2L 21s 5:1 tritonic[23]
1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 4 2L 23s 4:1 tritonic[25]
1 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 3 2L 25s 3:1 tritonic[27]
1 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 2 2L 27s 2:1 tritonic[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 1 1 1 31edo 1

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
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