List of MOS scales in 31edo: Difference between revisions
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* 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. | * 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. | * 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. | * TAMNAMS names are used wherever possible, excluding names for mosses with 3 or fewer notes and 1L ns scales for tidiness. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
| Line 1,670: | Line 1,670: | ||
|[[4L 1s]] | |[[4L 1s]] | ||
|7:3 | |7:3 | ||
| | |manual | ||
|orwell[5] | |orwell[5] | ||
|- | |- | ||
| Line 1,684: | Line 1,684: | ||
|[[4L 5s]] | |[[4L 5s]] | ||
|4:3 | |4:3 | ||
| | |gramitonic | ||
|orwell[9] | |orwell[9] | ||
|- | |- | ||
| Line 1,795: | Line 1,795: | ||
|[[3L 1s]] | |[[3L 1s]] | ||
|8:7 | |8:7 | ||
| | |tetric | ||
|myna[4] | |myna[4] | ||
|- | |- | ||
| Line 1,823: | Line 1,823: | ||
|[[4L 7s]] | |[[4L 7s]] | ||
|6:1 | |6:1 | ||
| | | | ||
|myna[11] | |myna[11] | ||
|- | |- | ||
| Line 1,993: | Line 1,993: | ||
|[[3L 1s]] | |[[3L 1s]] | ||
|9:4 | |9:4 | ||
| | |tetric | ||
|mohajira[4] | |mohajira[4] | ||
|- | |- | ||
| Line 2,137: | Line 2,137: | ||
|[[3L 1s]] | |[[3L 1s]] | ||
|10:1 | |10:1 | ||
| | |tetric | ||
|würschmidt[4] | |würschmidt[4] | ||
|- | |- | ||
| Line 2,397: | Line 2,397: | ||
|[[3L 5s]] | |[[3L 5s]] | ||
|7:2 | |7:2 | ||
| | |checkertonic | ||
|squares[8] | |squares[8] | ||
|- | |- | ||
| Line 2,671: | Line 2,671: | ||
|[[7L 5s]] | |[[7L 5s]] | ||
|3:2 | |3:2 | ||
| | | | ||
|meantone[12] | |meantone[12] | ||
|- | |- | ||
| Line 2,788: | Line 2,788: | ||
|[[2L 7s]] | |[[2L 7s]] | ||
|5:3 | |5:3 | ||
| | |balzano | ||
|casablanca[9] | |casablanca[9] | ||
|- | |- | ||
| Line 2,922: | Line 2,922: | ||
|[[2L 7s]] | |[[2L 7s]] | ||
|12:1 | |12:1 | ||
| | |balzano | ||
|tritonic[9] | |tritonic[9] | ||
|- | |- | ||
Revision as of 21:54, 18 November 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.
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, excluding names for mosses with 3 or fewer notes and 1L ns scales for tidiness.
| 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 | manual | orwell[5] | ||||||||||||||||||||||||||
| 3 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 4L 5s | 4:3 | gramitonic | 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 | tetric | 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 | tetric | 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 | tetric | 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 | checkertonic | 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 | 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 | balzano | 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 | balzano | 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