List of MOS scales in 31edo: Difference between revisions

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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.
{{MOSes in EDO}}


== MOS Families of 31edo ==
== Pergen Names ==
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.
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]]
 
=== 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Note that many of the names above are outdated or just plain wrong; most of these names are based on temperaments and pre-TANMANS naming schemes.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 25: Line 20:
* 15\31 = (P8, ccP4/5)
* 15\31 = (P8, ccP4/5)


== MOS Scales by Generator Pair ==
== Gallery ==
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:
[[File:31edo_mos_families.jpg|alt=31edo_mos_families.jpg|none|frame|MOS families of 31edo, with selected MOS scales for each generator.]]
 
* 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"
! colspan="35" |Single-Period Scales for 31 Equal Division of the Octave
|-
! colspan="31" |Steps  for Generators 30\31 and 1\31
!Mos
!Step  Ratio
![[TAMNAMS]]  Name
!Temperament
|-
| colspan="30" |30
|1
|[[1L 1s]]
|30:1
|
|
|-
| colspan="29" |29
|1
|1
|[[1L 2s]]
|29:1
|
|slender[3]
|-
| colspan="28" |28
|1
|1
|1
|[[1L 3s]]
|28:1
|
|slender[4]
|-
| colspan="27" |27
|1
|1
|1
|1
|[[1L 4s]]
|27:1
|
|slender[5]
|-
| colspan="26" |26
|1
|1
|1
|1
|1
|[[1L 5s]]
|26:1
|
|slender[6]
|-
| colspan="25" |25
|1
|1
|1
|1
|1
|1
|[[1L 6s]]
|25:1
|
|slender[7]
|-
| colspan="24" |24
|1
|1
|1
|1
|1
|1
|1
|[[1L 7s]]
|24:1
|
|slender[8]
|-
| colspan="23" |23
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 8s]]
|23:1
|
|slender[9]
|-
| colspan="22" |22
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 9s]]
|22:1
|
|slender[10]
|-
| colspan="21" |21
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 10s]]
|21:1
|
|slender[11]
|-
| colspan="20" |20
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 11s]]
|20:1
|
|slender[12]
|-
| colspan="19" |19
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 12s]]
|19:1
|
|slender[13]
|-
| colspan="18" |18
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 13s]]
|18:1
|
|slender[14]
|-
| colspan="17" |17
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 14s]]
|17:1
|
|slender[15]
|-
| colspan="16" |16
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 15s]]
|16:1
|
|slender[16]
|-
| colspan="15" |15
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 16s]]
|15:1
|
|slender[17]
|-
| colspan="14" |14
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 17s]]
|14:1
|
|slender[18]
|-
| colspan="13" |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]
|-
| colspan="12" |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]
|-
| colspan="11" |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]
|-
| colspan="10" |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]
|-
| colspan="9" |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]
|-
| colspan="8" |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]
|-
| colspan="7" |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]
|-
| colspan="6" |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]
|-
| colspan="5" |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]
|-
| colspan="4" |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]
|-
| colspan="3" |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]
|-
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 29\31 and 2\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="29" |29
| colspan="2" |2
|[[1L 1s]]
|29:2
|
|
|-
| colspan="27" |27
| colspan="2" |2
| colspan="2" |2
|[[1L 2s]]
|27:2
|
|valentine[3]
|-
| colspan="25" |25
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 3s]]
|25:2
|
|valentine[4]
|-
| colspan="23" |23
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 4s]]
|23:2
|
|valentine[5]
|-
| colspan="21" |21
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 5s]]
|21:2
|
|valentine[6]
|-
| colspan="19" |19
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 6s]]
|19:2
|
|valentine[7]
|-
| colspan="17" |17
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 7s]]
|17:2
|
|valentine[8]
|-
| colspan="15" |15
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 8s]]
|15:2
|
|valentine[9]
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 9s]]
|13:2
|
|valentine[10]
|-
| colspan="11" |11
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 10s]]
|11:2
|
|valentine[11]
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 11s]]
|9:2
|
|valentine[12]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 12s]]
|7:2
|
|valentine[13]
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 13s]]
|5:2
|
|valentine[14]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 14s]]
|3:2
|
|valentine[15]
|-
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="31" |Steps for  Generators 28\31 and 3\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="28" |28
| colspan="3" |3
|[[1L 1s]]
|28:3
|
|
|-
| colspan="25" |25
| colspan="3" |3
| colspan="3" |3
|[[1L 2s]]
|25:3
|
|miracle[3]
|-
| colspan="22" |22
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 3s]]
|22:3
|
|miracle[4]
|-
| colspan="19" |19
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 4s]]
|19:3
|
|miracle[5]
|-
| colspan="16" |16
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 5s]]
|16:3
|
|miracle[6]
|-
| colspan="13" |13
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 6s]]
|13:3
|
|miracle[7]
|-
| colspan="10" |10
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 7s]]
|10:3
|
|miracle[8]
|-
| colspan="7" |7
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 8s]]
|7:3
|
|miracle[9]
|-
| colspan="4" |4
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 9s]]
|4:3
|
|miracle[10]
|-
|1
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[10L 1s]]
|3:1
|
|miracle[11]
|-
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 27\31 and 4\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="27" |27
| colspan="4" |4
|[[1L 1s]]
|27:4
|
|
|-
| colspan="23" |23
| colspan="4" |4
| colspan="4" |4
|[[1L 2s]]
|23:4
|
|nusecond[3]
|-
| colspan="19" |19
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 3s]]
|19:4
|
|nusecond[4]
|-
| colspan="15" |15
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 4s]]
|15:4
|
|nusecond[5]
|-
| colspan="11" |11
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 5s]]
|11:4
|
|nusecond[6]
|-
| colspan="7" |7
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 6s]]
|7:4
|
|nusecond[7]
|-
| colspan="3" |3
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[7L 1s]]
|4:3
|pine
|nusecond[8]
|-
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|[[8L 7s]]
|3:1
|
|nusecond[15]
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 26\31 and 5\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="26" |26
| colspan="5" |5
|[[1L 1s]]
|26:5
|
|
|-
| colspan="21" |21
| colspan="5" |5
| colspan="5" |5
|[[1L 2s]]
|21:5
|
|hemithirds[3]
|-
| colspan="16" |16
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[1L 3s]]
|16:5
|
|hemithirds[4]
|-
| colspan="11" |11
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[1L 4s]]
|11:5
|
|hemithirds[5]
|-
| colspan="6" |6
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[1L 5s]]
|6:5
|
|hemithirds[6]
|-
|1
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[6L 1s]]
|5:1
|archeotonic
|hemithirds[7]
|-
|1
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|[[6L 7s]]
|4:1
|
|hemithirds[13]
|-
|1
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|[[6L 13s]]
|3:1
|
|hemithirds[19]
|-
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 25\31 and 6\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="25" |25
| colspan="6" |6
|[[1L 1s]]
|25:6
|
|
|-
| colspan="19" |19
| colspan="6" |6
| colspan="6" |6
|[[1L 2s]]
|19:6
|
|mothra[3]
|-
| colspan="13" |13
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
|[[1L 3s]]
|13:6
|
|mothra[4]
|-
| colspan="7" |7
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
|[[1L 4s]]
|7:6
|
|mothra[5]
|-
|1
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
|[[5L 1s]]
|6:1
|machinoid
|mothra[6]
|-
|1
|1
| colspan="5" |5
|1
| colspan="5" |5
|1
| colspan="5" |5
|1
| colspan="5" |5
|1
| colspan="5" |5
|[[5L 6s]]
|5:1
|
|mothra[11]
|-
|1
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|[[5L 11s]]
|4:1
|
|mothra[16]
|-
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|[[5L 16s]]
|3:1
|
|mothra[21]
|-
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 24\31 and 7\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="24" |24
| colspan="7" |7
|[[1L 1s]]
|24:7
|
|
|-
| colspan="17" |17
| colspan="7" |7
| colspan="7" |7
|[[1L 2s]]
|17:7
|
|orwell[3]
|-
| colspan="10" |10
| colspan="7" |7
| colspan="7" |7
| colspan="7" |7
|[[1L 3s]]
|10:7
|
|orwell[4]
|-
| colspan="3" |3
| colspan="7" |7
| colspan="7" |7
| colspan="7" |7
| colspan="7" |7
|[[4L 1s]]
|7:3
|manic
|orwell[5]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
|[[4L 5s]]
|4:3
|orwelloid
|orwell[9]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
| colspan="3" |3
|1
|[[9L 4s]]
|3:1
|
|orwell[13]
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 23\31 and 8\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="23" |23
| colspan="8" |8
|[[1L 1s]]
|23:8
|
|
|-
| colspan="15" |15
| colspan="8" |8
| colspan="8" |8
|[[1L 2s]]
|15:8
|
|myna[3]
|-
| colspan="7" |7
| colspan="8" |8
| colspan="8" |8
| colspan="8" |8
|[[3L 1s]]
|8:7
|
|myna[4]
|-
| colspan="7" |7
| colspan="7" |7
|1
| colspan="7" |7
|1
| colspan="7" |7
|1
|[[4L 3s]]
|7:1
|smitonic
|myna[7]
|-
| colspan="6" |6
|1
| colspan="6" |6
|1
|1
| colspan="6" |6
|1
|1
| colspan="6" |6
|1
|1
|[[4L 7s]]
|6:1
|kleistonic
|myna[11]
|-
| colspan="5" |5
|1
|1
| colspan="5" |5
|1
|1
|1
| colspan="5" |5
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|[[4L 11s]]
|5:1
|
|myna[15]
|-
| colspan="4" |4
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|[[4L 15s]]
|4:1
|
|myna[19]
|-
| colspan="3" |3
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|[[4L 19s]]
|3:1
|
|myna[23]
|-
| colspan="2" |2
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 22\31 and 9\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="22" |22
| colspan="9" |9
|[[1L 1s]]
|22:9
|
|
|-
| colspan="13" |13
| colspan="9" |9
| colspan="9" |9
|[[1L 2s]]
|13:9
|
|mohajira[3]
|-
| colspan="4" |4
| colspan="9" |9
| colspan="9" |9
| colspan="9" |9
|[[3L 1s]]
|9:4
|
|mohajira[4]
|-
| colspan="4" |4
| colspan="4" |4
| colspan="5" |5
| colspan="4" |4
| colspan="5" |5
| colspan="4" |4
| colspan="5" |5
|[[3L 4s]]
|5:4
|mosh
|mohajira[7]
|-
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|1
| colspan="4" |4
| colspan="4" |4
|1
| colspan="4" |4
| colspan="4" |4
|1
|[[7L 3s]]
|4:1
|dicotonic
|mohajira[10]
|-
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|1
|[[7L 10s]]
|3:1
|
|mohajira[17]
|-
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 21\31 and 10\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="21" |21
| colspan="10" |10
|[[1L 1s]]
|21:10
|
|
|-
| colspan="11" |11
| colspan="10" |10
| colspan="10" |10
|[[1L 2s]]
|11:10
|
|würschmidt[3]
|-
|1
| colspan="10" |10
| colspan="10" |10
| colspan="10" |10
|[[3L 1s]]
|10:1
|
|würschmidt[4]
|-
|1
|1
| colspan="9" |9
|1
| colspan="9" |9
|1
| colspan="9" |9
|[[3L 4s]]
|9:1
|mosh
|würschmidt[7]
|-
|1
|1
|1
| colspan="8" |8
|1
|1
| colspan="8" |8
|1
|1
| colspan="8" |8
|[[3L 7s]]
|8:1
|sephiroid
|würschmidt[10]
|-
|1
|1
|1
|1
| colspan="7" |7
|1
|1
|1
| colspan="7" |7
|1
|1
|1
| colspan="7" |7
|[[3L 10s]]
|7:1
|
|würschmidt[13]
|-
|1
|1
|1
|1
|1
| colspan="6" |6
|1
|1
|1
|1
| colspan="6" |6
|1
|1
|1
|1
| colspan="6" |6
|[[3L 13s]]
|6:1
|
|würschmidt[16]
|-
|1
|1
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|1
|1
| colspan="5" |5
|[[3L 16s]]
|5:1
|
|würschmidt[19]
|-
|1
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|[[3L 19s]]
|4:1
|
|würschmidt[22]
|-
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|[[3L 22s]]
|3:1
|
|würschmidt[25]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 20\31 and 11\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="20" |20
| colspan="11" |11
|[[1L 1s]]
|20:11
|
|
|-
| colspan="9" |9
| colspan="11" |11
| colspan="11" |11
|[[2L 1s]]
|11:9
|
|squares[3]
|-
| colspan="9" |9
| colspan="9" |9
| colspan="2" |2
| colspan="9" |9
| colspan="2" |2
|[[3L 2s]]
|9:2
|antipentic
|squares[5]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
|[[3L 5s]]
|7:2
|sensoid
|squares[8]
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[3L 8s]]
|5:2
|
|squares[11]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[3L 11s]]
|3:2
|
|squares[14]
|-
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="31" |Steps for  Generators 19\31 and 12\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="19" |19
| colspan="12" |12
|[[1L 1s]]
|19:12
|
|
|-
| colspan="7" |7
| colspan="12" |12
| colspan="12" |12
|[[2L 1s]]
|12:7
|
|semisept[3]
|-
| colspan="7" |7
| colspan="7" |7
| colspan="5" |5
| colspan="7" |7
| colspan="5" |5
|[[3L 2s]]
|7:5
|antipentic
|semisept[5]
|-
| colspan="2" |2
| colspan="5" |5
| colspan="2" |2
| colspan="5" |5
| colspan="5" |5
| colspan="2" |2
| colspan="5" |5
| colspan="5" |5
|[[5L 3s]]
|5:2
|oneirotonic
|semisept[8]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|[[5L 8s]]
|3:2
|
|semisept[13]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="31" |Steps for  Generators 18\31 and 13\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="18" |18
| colspan="13" |13
|1L 1s
|18:13
|
|
|-
| colspan="5" |5
| colspan="13" |13
| colspan="13" |13
|[[2L 1s]]
|13:5
|
|meantone[3]
|-
| colspan="5" |5
| colspan="5" |5
| colspan="8" |8
| colspan="5" |5
| colspan="8" |8
|[[2L 3s]]
|8:5
|pentic
|meantone[5]
|-
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| colspan="3" |3
| colspan="5" |5
| colspan="5" |5
| colspan="3" |3
|[[5L 2s]]
|5:3
|diatonic
|meantone[7]
|-
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
|[[7L 5s]]
|3:2
|m-chromatic
|meantone[12]
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |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
|
|
|-
! colspan="31" |Steps for  Generators 17\31 and 14\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="17" |17
| colspan="14" |14
|[[1L 1s]]
|17:14
|
|
|-
| colspan="3" |3
| colspan="14" |14
| colspan="14" |14
|[[2L 1s]]
|14:3
|
|casablanca[3]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="11" |11
| colspan="3" |3
| colspan="11" |11
|[[2L 3s]]
|11:3
|pentic
|casablanca[5]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="8" |8
| colspan="3" |3
| colspan="3" |3
| colspan="8" |8
|[[2L 5s]]
|8:3
|antidiatonic
|casablanca[7]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="5" |5
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="5" |5
|[[2L 7s]]
|5:3
|joanatonic
|casablanca[9]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
|[[9L 2s]]
|3:2
|
|casablanca[11]
|-
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="31" |Steps for  Generators 16\31 and 15\31
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="16" |16
| colspan="15" |15
|[[1L 1s]]
|16:15
|
|
|-
|1
| colspan="15" |15
| colspan="15" |15
|[[2L 1s]]
|15:1
|
|tritonic[3]
|-
|1
|1
| colspan="14" |14
|1
| colspan="14" |14
|[[2L 3s]]
|14:1
|pentic
|tritonic[5]
|-
|1
|1
|1
| colspan="13" |13
|1
|1
| colspan="13" |13
|[[2L 5s]]
|13:1
|antidiatonic
|tritonic[7]
|-
|1
|1
|1
|1
| colspan="12" |12
|1
|1
|1
| colspan="12" |12
|[[2L 7s]]
|12:1
|joanatonic
|tritonic[9]
|-
|1
|1
|1
|1
|1
| colspan="11" |11
|1
|1
|1
|1
| colspan="11" |11
|[[2L 9s]]
|11:1
|
|tritonic[11]
|-
|1
|1
|1
|1
|1
|1
| colspan="10" |10
|1
|1
|1
|1
|1
| colspan="10" |10
|[[2L 11s]]
|10:1
|
|tritonic[13]
|-
|1
|1
|1
|1
|1
|1
|1
| colspan="9" |9
|1
|1
|1
|1
|1
|1
| colspan="9" |9
|[[2L 13s]]
|9:1
|
|tritonic[15]
|-
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="8" |8
|1
|1
|1
|1
|1
|1
|1
| colspan="8" |8
|[[2L 15s]]
|8:1
|
|tritonic[17]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="7" |7
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="7" |7
|[[2L 17s]]
|7:1
|
|tritonic[19]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="6" |6
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="6" |6
|[[2L 19s]]
|6:1
|
|tritonic[21]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |5
|[[2L 21s]]
|5:1
|
|tritonic[23]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|[[2L 23s]]
|4:1
|
|tritonic[25]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|[[2L 25s]]
|3:1
|
|tritonic[27]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |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
 
[[Category:31edo]]
[[Category:31edo]]

Latest revision as of 17:48, 2 April 2025

This page lists all moment of symmetry scales in 31edo.

Single-period MOS scales

Generators 16\31 and 15\31
Step visualization MOS (name) Step sizes Step ratio
├───────────────┼──────────────┤ 1L 1s 16, 15 16:15
├┼──────────────┼──────────────┤ 2L 1s 15, 1 15:1
├┼┼─────────────┼┼─────────────┤ 2L 3s 14, 1 14:1
├┼┼┼────────────┼┼┼────────────┤ 2L 5s (antidiatonic) 13, 1 13:1
├┼┼┼┼───────────┼┼┼┼───────────┤ 2L 7s (balzano) 12, 1 12:1
├┼┼┼┼┼──────────┼┼┼┼┼──────────┤ 2L 9s 11, 1 11:1
├┼┼┼┼┼┼─────────┼┼┼┼┼┼─────────┤ 2L 11s 10, 1 10:1
├┼┼┼┼┼┼┼────────┼┼┼┼┼┼┼────────┤ 2L 13s 9, 1 9:1
├┼┼┼┼┼┼┼┼───────┼┼┼┼┼┼┼┼───────┤ 2L 15s 8, 1 8:1
├┼┼┼┼┼┼┼┼┼──────┼┼┼┼┼┼┼┼┼──────┤ 2L 17s 7, 1 7:1
├┼┼┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┼┼┼─────┤ 2L 19s 6, 1 6:1
├┼┼┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┼┼┼────┤ 2L 21s 5, 1 5:1
├┼┼┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┼┼┼───┤ 2L 23s 4, 1 4:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┼┼┼──┤ 2L 25s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┼┼┼─┤ 2L 27s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 17\31 and 14\31
Step visualization MOS (name) Step sizes Step ratio
├────────────────┼─────────────┤ 1L 1s 17, 14 17:14
├──┼─────────────┼─────────────┤ 2L 1s 14, 3 14:3
├──┼──┼──────────┼──┼──────────┤ 2L 3s 11, 3 11:3
├──┼──┼──┼───────┼──┼──┼───────┤ 2L 5s (antidiatonic) 8, 3 8:3
├──┼──┼──┼──┼────┼──┼──┼──┼────┤ 2L 7s (balzano) 5, 3 5:3
├──┼──┼──┼──┼──┼─┼──┼──┼──┼──┼─┤ 9L 2s 3, 2 3:2
├┼─┼┼─┼┼─┼┼─┼┼─┼─┼┼─┼┼─┼┼─┼┼─┼─┤ 11L 9s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 18\31 and 13\31
Step visualization MOS (name) Step sizes Step ratio
├─────────────────┼────────────┤ 1L 1s 18, 13 18:13
├────┼────────────┼────────────┤ 2L 1s 13, 5 13:5
├────┼────┼───────┼────┼───────┤ 2L 3s 8, 5 8:5
├────┼────┼────┼──┼────┼────┼──┤ 5L 2s (diatonic) 5, 3 5:3
├─┼──┼─┼──┼─┼──┼──┼─┼──┼─┼──┼──┤ 7L 5s 3, 2 3:2
├─┼─┼┼─┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼─┼┼─┼┤ 12L 7s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 19\31 and 12\31
Step visualization MOS (name) Step sizes Step ratio
├──────────────────┼───────────┤ 1L 1s 19, 12 19:12
├──────┼───────────┼───────────┤ 2L 1s 12, 7 12:7
├──────┼──────┼────┼──────┼────┤ 3L 2s 7, 5 7:5
├─┼────┼─┼────┼────┼─┼────┼────┤ 5L 3s (oneirotonic) 5, 2 5:2
├─┼─┼──┼─┼─┼──┼─┼──┼─┼─┼──┼─┼──┤ 5L 8s 3, 2 3:2
├─┼─┼─┼┼─┼─┼─┼┼─┼─┼┼─┼─┼─┼┼─┼─┼┤ 13L 5s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 20\31 and 11\31
Step visualization MOS (name) Step sizes Step ratio
├───────────────────┼──────────┤ 1L 1s 20, 11 20:11
├────────┼──────────┼──────────┤ 2L 1s 11, 9 11:9
├────────┼────────┼─┼────────┼─┤ 3L 2s 9, 2 9:2
├──────┼─┼──────┼─┼─┼──────┼─┼─┤ 3L 5s (checkertonic) 7, 2 7:2
├────┼─┼─┼────┼─┼─┼─┼────┼─┼─┼─┤ 3L 8s 5, 2 5:2
├──┼─┼─┼─┼──┼─┼─┼─┼─┼──┼─┼─┼─┼─┤ 3L 11s 3, 2 3:2
├┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┤ 14L 3s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 21\31 and 10\31
Step visualization MOS (name) Step sizes Step ratio
├────────────────────┼─────────┤ 1L 1s 21, 10 21:10
├──────────┼─────────┼─────────┤ 1L 2s 11, 10 11:10
├┼─────────┼─────────┼─────────┤ 3L 1s 10, 1 10:1
├┼┼────────┼┼────────┼┼────────┤ 3L 4s (mosh) 9, 1 9:1
├┼┼┼───────┼┼┼───────┼┼┼───────┤ 3L 7s (sephiroid) 8, 1 8:1
├┼┼┼┼──────┼┼┼┼──────┼┼┼┼──────┤ 3L 10s 7, 1 7:1
├┼┼┼┼┼─────┼┼┼┼┼─────┼┼┼┼┼─────┤ 3L 13s 6, 1 6:1
├┼┼┼┼┼┼────┼┼┼┼┼┼────┼┼┼┼┼┼────┤ 3L 16s 5, 1 5:1
├┼┼┼┼┼┼┼───┼┼┼┼┼┼┼───┼┼┼┼┼┼┼───┤ 3L 19s 4, 1 4:1
├┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼──┤ 3L 22s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼─┤ 3L 25s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 22\31 and 9\31
Step visualization MOS (name) Step sizes Step ratio
├─────────────────────┼────────┤ 1L 1s 22, 9 22:9
├────────────┼────────┼────────┤ 1L 2s 13, 9 13:9
├───┼────────┼────────┼────────┤ 3L 1s 9, 4 9:4
├───┼───┼────┼───┼────┼───┼────┤ 3L 4s (mosh) 5, 4 5:4
├───┼───┼───┼┼───┼───┼┼───┼───┼┤ 7L 3s (dicoid) 4, 1 4:1
├──┼┼──┼┼──┼┼┼──┼┼──┼┼┼──┼┼──┼┼┤ 7L 10s 3, 1 3:1
├─┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┤ 7L 17s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 23\31 and 8\31
Step visualization MOS (name) Step sizes Step ratio
├──────────────────────┼───────┤ 1L 1s 23, 8 23:8
├──────────────┼───────┼───────┤ 1L 2s 15, 8 15:8
├──────┼───────┼───────┼───────┤ 3L 1s 8, 7 8:7
├──────┼──────┼┼──────┼┼──────┼┤ 4L 3s (smitonic) 7, 1 7:1
├─────┼┼─────┼┼┼─────┼┼┼─────┼┼┤ 4L 7s 6, 1 6:1
├────┼┼┼────┼┼┼┼────┼┼┼┼────┼┼┼┤ 4L 11s 5, 1 5:1
├───┼┼┼┼───┼┼┼┼┼───┼┼┼┼┼───┼┼┼┼┤ 4L 15s 4, 1 4:1
├──┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼┤ 4L 19s 3, 1 3:1
├─┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼┤ 4L 23s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 24\31 and 7\31
Step visualization MOS (name) Step sizes Step ratio
├───────────────────────┼──────┤ 1L 1s 24, 7 24:7
├────────────────┼──────┼──────┤ 1L 2s 17, 7 17:7
├─────────┼──────┼──────┼──────┤ 1L 3s 10, 7 10:7
├──┼──────┼──────┼──────┼──────┤ 4L 1s 7, 3 7:3
├──┼──┼───┼──┼───┼──┼───┼──┼───┤ 4L 5s (gramitonic) 4, 3 4:3
├──┼──┼──┼┼──┼──┼┼──┼──┼┼──┼──┼┤ 9L 4s 3, 1 3:1
├─┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┼┼┤ 9L 13s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 25\31 and 6\31
Step visualization MOS (name) Step sizes Step ratio
├────────────────────────┼─────┤ 1L 1s 25, 6 25:6
├──────────────────┼─────┼─────┤ 1L 2s 19, 6 19:6
├────────────┼─────┼─────┼─────┤ 1L 3s 13, 6 13:6
├──────┼─────┼─────┼─────┼─────┤ 1L 4s 7, 6 7:6
├┼─────┼─────┼─────┼─────┼─────┤ 5L 1s (machinoid) 6, 1 6:1
├┼┼────┼┼────┼┼────┼┼────┼┼────┤ 5L 6s 5, 1 5:1
├┼┼┼───┼┼┼───┼┼┼───┼┼┼───┼┼┼───┤ 5L 11s 4, 1 4:1
├┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┼──┤ 5L 16s 3, 1 3:1
├┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┤ 5L 21s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 26\31 and 5\31
Step visualization MOS (name) Step sizes Step ratio
├─────────────────────────┼────┤ 1L 1s 26, 5 26:5
├────────────────────┼────┼────┤ 1L 2s 21, 5 21:5
├───────────────┼────┼────┼────┤ 1L 3s 16, 5 16:5
├──────────┼────┼────┼────┼────┤ 1L 4s 11, 5 11:5
├─────┼────┼────┼────┼────┼────┤ 1L 5s (antimachinoid) 6, 5 6:5
├┼────┼────┼────┼────┼────┼────┤ 6L 1s (archaeotonic) 5, 1 5:1
├┼┼───┼┼───┼┼───┼┼───┼┼───┼┼───┤ 6L 7s 4, 1 4:1
├┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┤ 6L 13s 3, 1 3:1
├┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┤ 6L 19s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 27\31 and 4\31
Step visualization MOS (name) Step sizes Step ratio
├──────────────────────────┼───┤ 1L 1s 27, 4 27:4
├──────────────────────┼───┼───┤ 1L 2s 23, 4 23:4
├──────────────────┼───┼───┼───┤ 1L 3s 19, 4 19:4
├──────────────┼───┼───┼───┼───┤ 1L 4s 15, 4 15:4
├──────────┼───┼───┼───┼───┼───┤ 1L 5s (antimachinoid) 11, 4 11:4
├──────┼───┼───┼───┼───┼───┼───┤ 1L 6s (onyx) 7, 4 7:4
├──┼───┼───┼───┼───┼───┼───┼───┤ 7L 1s (pine) 4, 3 4:3
├──┼──┼┼──┼┼──┼┼──┼┼──┼┼──┼┼──┼┤ 8L 7s 3, 1 3:1
├─┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ 8L 15s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 28\31 and 3\31
Step visualization MOS (name) Step sizes Step ratio
├───────────────────────────┼──┤ 1L 1s 28, 3 28:3
├────────────────────────┼──┼──┤ 1L 2s 25, 3 25:3
├─────────────────────┼──┼──┼──┤ 1L 3s 22, 3 22:3
├──────────────────┼──┼──┼──┼──┤ 1L 4s 19, 3 19:3
├───────────────┼──┼──┼──┼──┼──┤ 1L 5s (antimachinoid) 16, 3 16:3
├────────────┼──┼──┼──┼──┼──┼──┤ 1L 6s (onyx) 13, 3 13:3
├─────────┼──┼──┼──┼──┼──┼──┼──┤ 1L 7s (antipine) 10, 3 10:3
├──────┼──┼──┼──┼──┼──┼──┼──┼──┤ 1L 8s (antisubneutralic) 7, 3 7:3
├───┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ 1L 9s (antisinatonic) 4, 3 4:3
├┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ 10L 1s 3, 1 3:1
├┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┤ 10L 11s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 29\31 and 2\31
Step visualization MOS (name) Step sizes Step ratio
├────────────────────────────┼─┤ 1L 1s 29, 2 29:2
├──────────────────────────┼─┼─┤ 1L 2s 27, 2 27:2
├────────────────────────┼─┼─┼─┤ 1L 3s 25, 2 25:2
├──────────────────────┼─┼─┼─┼─┤ 1L 4s 23, 2 23:2
├────────────────────┼─┼─┼─┼─┼─┤ 1L 5s (antimachinoid) 21, 2 21:2
├──────────────────┼─┼─┼─┼─┼─┼─┤ 1L 6s (onyx) 19, 2 19:2
├────────────────┼─┼─┼─┼─┼─┼─┼─┤ 1L 7s (antipine) 17, 2 17:2
├──────────────┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 8s (antisubneutralic) 15, 2 15:2
├────────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 9s (antisinatonic) 13, 2 13:2
├──────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 10s 11, 2 11:2
├────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 11s 9, 2 9:2
├──────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 12s 7, 2 7:2
├────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 13s 5, 2 5:2
├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 1L 14s 3, 2 3:2
├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 15L 1s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1
Generators 30\31 and 1\31
Step visualization MOS (name) Step sizes Step ratio
├─────────────────────────────┼┤ 1L 1s 30, 1 30:1
├────────────────────────────┼┼┤ 1L 2s 29, 1 29:1
├───────────────────────────┼┼┼┤ 1L 3s 28, 1 28:1
├──────────────────────────┼┼┼┼┤ 1L 4s 27, 1 27:1
├─────────────────────────┼┼┼┼┼┤ 1L 5s (antimachinoid) 26, 1 26:1
├────────────────────────┼┼┼┼┼┼┤ 1L 6s (onyx) 25, 1 25:1
├───────────────────────┼┼┼┼┼┼┼┤ 1L 7s (antipine) 24, 1 24:1
├──────────────────────┼┼┼┼┼┼┼┼┤ 1L 8s (antisubneutralic) 23, 1 23:1
├─────────────────────┼┼┼┼┼┼┼┼┼┤ 1L 9s (antisinatonic) 22, 1 22:1
├────────────────────┼┼┼┼┼┼┼┼┼┼┤ 1L 10s 21, 1 21:1
├───────────────────┼┼┼┼┼┼┼┼┼┼┼┤ 1L 11s 20, 1 20:1
├──────────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 12s 19, 1 19:1
├─────────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 13s 18, 1 18:1
├────────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 14s 17, 1 17:1
├───────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 15s 16, 1 16:1
├──────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 16s 15, 1 15:1
├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 17s 14, 1 14:1
├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 18s 13, 1 13:1
├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 19s 12, 1 12:1
├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 20s 11, 1 11:1
├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 21s 10, 1 10:1
├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 22s 9, 1 9:1
├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 23s 8, 1 8:1
├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 24s 7, 1 7:1
├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 25s 6, 1 6:1
├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 26s 5, 1 5:1
├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 27s 4, 1 4:1
├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 28s 3, 1 3:1
├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 29s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 31edo 1, 1 1:1

Pergen Names

Temperaments supported by 31edo may also be referred by pergen names.

  • 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)

Gallery

31edo_mos_families.jpg
MOS families of 31edo, with selected MOS scales for each generator.
Retrieved from "https://en.xen.wiki/index.php?title=List_of_MOS_scales_in_31edo&oldid=189618"