User:Ganaram inukshuk/Catalog of MOS Scales

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This is an attempt at rewriting the following page: Catalog of MOS

Mosses by total note count

This section orders mosses by total note count.

Table of mosses (up to 15 notes)
Note count Total number of large steps
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Trivial mosses 1L 1s
1L 2s 2L 1s
Tetratonic mosses 1L 3s 2L 2s 3L 1s
Pentatonic mosses 1L 4s 2L 3s 3L 2s 4L 1s
Hexatonic mosses 1L 5s 2L 4s 3L 3s 4L 2s 5L 1s
Heptatonic mosses 1L 6s 2L 5s 3L 4s 4L 3s 5L 2s 6L 1s
Octatonic mosses 1L 7s 2L 6s 3L 5s 4L 4s 5L 3s 6L 2s 7L 1s
Enneatonic mosses 1L 8s 2L 7s 3L 6s 4L 5s 5L 4s 6L 3s 7L 2s 8L 1s
Decatonic mosses 1L 9s 2L 8s 3L 7s 4L 6s 5L 5s 6L 4s 7L 3s 8L 2s 9L 1s
Hendecatonic mosses 1L 10s 2L 9s 3L 8s 4L 7s 5L 6s 6L 5s 7L 4s 8L 3s 9L 2s 10L 1s
Dodecatonic mosses 1L 11s 2L 10s 3L 9s 4L 8s 5L 7s 6L 6s 7L 5s 8L 4s 9L 3s 10L 2s 11L 1s
Tridecatonic mosses 1L 12s 2L 11s 3L 10s 4L 9s 5L 8s 6L 7s 7L 6s 8L 5s 9L 4s 10L 3s 11L 2s 12L 1s
Tetradecatonic mosses 1L 13s 2L 12s 3L 11s 4L 10s 5L 9s 6L 8s 7L 7s 8L 6s 9L 5s 10L 4s 11L 3s 12L 2s 13L 1s
Pentadecatonic mosses 1L 14s 2L 13s 3L 12s 4L 11s 5L 10s 6L 9s 7L 8s 8L 7s 9L 6s 10L 5s 11L 4s 12L 3s 13L 2s 14L 1s

Mosses by equivalence interval

This section shows mosses arranged as a grid. Since mosses can be generalized to non-octave equaves, 3/1 (tritave) and 3/2 (fifth) equivalent mosses are included here. Cutoffs are determined by whether a row or column after a specific point consists of red links.

Catalog of 2/1-equivalent mosses

2/1-equivalent mosses (up to 31 steps)
Number of small steps Number of large steps
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1L 1s 2L 1s 3L 1s 4L 1s 5L 1s 6L 1s 7L 1s 8L 1s 9L 1s 10L 1s 11L 1s 12L 1s 13L 1s 14L 1s 15L 1s 16L 1s 17L 1s 18L 1s 19L 1s 20L 1s 21L 1s 22L 1s 23L 1s 24L 1s 25L 1s 26L 1s 27L 1s 28L 1s 29L 1s 30L 1s
2 1L 2s 2L 2s 3L 2s 4L 2s 5L 2s 6L 2s 7L 2s 8L 2s 9L 2s 10L 2s 11L 2s 12L 2s 13L 2s 14L 2s 15L 2s 16L 2s 17L 2s 18L 2s 19L 2s 20L 2s 21L 2s 22L 2s 23L 2s 24L 2s 25L 2s 26L 2s 27L 2s 28L 2s 29L 2s
3 1L 3s 2L 3s 3L 3s 4L 3s 5L 3s 6L 3s 7L 3s 8L 3s 9L 3s 10L 3s 11L 3s 12L 3s 13L 3s 14L 3s 15L 3s 16L 3s 17L 3s 18L 3s 19L 3s 20L 3s 21L 3s 22L 3s 23L 3s 24L 3s 25L 3s 26L 3s 27L 3s 28L 3s
4 1L 4s 2L 4s 3L 4s 4L 4s 5L 4s 6L 4s 7L 4s 8L 4s 9L 4s 10L 4s 11L 4s 12L 4s 13L 4s 14L 4s 15L 4s 16L 4s 17L 4s 18L 4s 19L 4s 20L 4s 21L 4s 22L 4s 23L 4s 24L 4s 25L 4s 26L 4s 27L 4s
5 1L 5s 2L 5s 3L 5s 4L 5s 5L 5s 6L 5s 7L 5s 8L 5s 9L 5s 10L 5s 11L 5s 12L 5s 13L 5s 14L 5s 15L 5s 16L 5s 17L 5s 18L 5s 19L 5s 20L 5s 21L 5s 22L 5s 23L 5s 24L 5s 25L 5s 26L 5s
6 1L 6s 2L 6s 3L 6s 4L 6s 5L 6s 6L 6s 7L 6s 8L 6s 9L 6s 10L 6s 11L 6s 12L 6s 13L 6s 14L 6s 15L 6s 16L 6s 17L 6s 18L 6s 19L 6s 20L 6s 21L 6s 22L 6s 23L 6s 24L 6s 25L 6s
7 1L 7s 2L 7s 3L 7s 4L 7s 5L 7s 6L 7s 7L 7s 8L 7s 9L 7s 10L 7s 11L 7s 12L 7s 13L 7s 14L 7s 15L 7s 16L 7s 17L 7s 18L 7s 19L 7s 20L 7s 21L 7s 22L 7s 23L 7s 24L 7s
8 1L 8s 2L 8s 3L 8s 4L 8s 5L 8s 6L 8s 7L 8s 8L 8s 9L 8s 10L 8s 11L 8s 12L 8s 13L 8s 14L 8s 15L 8s 16L 8s 17L 8s 18L 8s 19L 8s 20L 8s 21L 8s 22L 8s 23L 8s
9 1L 9s 2L 9s 3L 9s 4L 9s 5L 9s 6L 9s 7L 9s 8L 9s 9L 9s 10L 9s 11L 9s 12L 9s 13L 9s 14L 9s 15L 9s 16L 9s 17L 9s 18L 9s 19L 9s 20L 9s 21L 9s 22L 9s
10 1L 10s 2L 10s 3L 10s 4L 10s 5L 10s 6L 10s 7L 10s 8L 10s 9L 10s 10L 10s 11L 10s 12L 10s 13L 10s 14L 10s 15L 10s 16L 10s 17L 10s 18L 10s 19L 10s 20L 10s 21L 10s
11 1L 11s 2L 11s 3L 11s 4L 11s 5L 11s 6L 11s 7L 11s 8L 11s 9L 11s 10L 11s 11L 11s 12L 11s 13L 11s 14L 11s 15L 11s 16L 11s 17L 11s 18L 11s 19L 11s 20L 11s
12 1L 12s 2L 12s 3L 12s 4L 12s 5L 12s 6L 12s 7L 12s 8L 12s 9L 12s 10L 12s 11L 12s 12L 12s 13L 12s 14L 12s 15L 12s 16L 12s 17L 12s 18L 12s 19L 12s
13 1L 13s 2L 13s 3L 13s 4L 13s 5L 13s 6L 13s 7L 13s 8L 13s 9L 13s 10L 13s 11L 13s 12L 13s 13L 13s 14L 13s 15L 13s 16L 13s 17L 13s 18L 13s
14 1L 14s 2L 14s 3L 14s 4L 14s 5L 14s 6L 14s 7L 14s 8L 14s 9L 14s 10L 14s 11L 14s 12L 14s 13L 14s 14L 14s 15L 14s 16L 14s 17L 14s
15 1L 15s 2L 15s 3L 15s 4L 15s 5L 15s 6L 15s 7L 15s 8L 15s 9L 15s 10L 15s 11L 15s 12L 15s 13L 15s 14L 15s 15L 15s 16L 15s
16 1L 16s 2L 16s 3L 16s 4L 16s 5L 16s 6L 16s 7L 16s 8L 16s 9L 16s 10L 16s 11L 16s 12L 16s 13L 16s 14L 16s 15L 16s
17 1L 17s 2L 17s 3L 17s 4L 17s 5L 17s 6L 17s 7L 17s 8L 17s 9L 17s 10L 17s 11L 17s 12L 17s 13L 17s 14L 17s
18 1L 18s 2L 18s 3L 18s 4L 18s 5L 18s 6L 18s 7L 18s 8L 18s 9L 18s 10L 18s 11L 18s 12L 18s 13L 18s
19 1L 19s 2L 19s 3L 19s 4L 19s 5L 19s 6L 19s 7L 19s 8L 19s 9L 19s 10L 19s 11L 19s 12L 19s
20 1L 20s 2L 20s 3L 20s 4L 20s 5L 20s 6L 20s 7L 20s 8L 20s 9L 20s 10L 20s 11L 20s
21 1L 21s 2L 21s 3L 21s 4L 21s 5L 21s 6L 21s 7L 21s 8L 21s 9L 21s 10L 21s
22 1L 22s 2L 22s 3L 22s 4L 22s 5L 22s 6L 22s 7L 22s 8L 22s 9L 22s
23 1L 23s 2L 23s 3L 23s 4L 23s 5L 23s 6L 23s 7L 23s 8L 23s
24 1L 24s 2L 24s 3L 24s 4L 24s 5L 24s 6L 24s 7L 24s
25 1L 25s 2L 25s 3L 25s 4L 25s 5L 25s 6L 25s
26 1L 26s 2L 26s 3L 26s 4L 26s 5L 26s
27 1L 27s 2L 27s 3L 27s 4L 27s
28 1L 28s 2L 28s 3L 28s
29 1L 29s 2L 29s
30 1L 30s

Catalog of 3/1-equivalent mosses

3/1-equivalent mosses (up to 19 steps)
Number of small steps Number of large steps
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1L 1s⟨3/1⟩ 2L 1s⟨3/1⟩ 3L 1s⟨3/1⟩ 4L 1s⟨3/1⟩ 5L 1s⟨3/1⟩ 6L 1s⟨3/1⟩ 7L 1s⟨3/1⟩ 8L 1s⟨3/1⟩ 9L 1s⟨3/1⟩ 10L 1s⟨3/1⟩ 11L 1s⟨3/1⟩ 12L 1s⟨3/1⟩ 13L 1s⟨3/1⟩ 14L 1s⟨3/1⟩ 15L 1s⟨3/1⟩ 16L 1s⟨3/1⟩ 17L 1s⟨3/1⟩ 18L 1s⟨3/1⟩
2 1L 2s⟨3/1⟩ 2L 2s⟨3/1⟩ 3L 2s⟨3/1⟩ 4L 2s⟨3/1⟩ 5L 2s⟨3/1⟩ 6L 2s⟨3/1⟩ 7L 2s⟨3/1⟩ 8L 2s⟨3/1⟩ 9L 2s⟨3/1⟩ 10L 2s⟨3/1⟩ 11L 2s⟨3/1⟩ 12L 2s⟨3/1⟩ 13L 2s⟨3/1⟩ 14L 2s⟨3/1⟩ 15L 2s⟨3/1⟩ 16L 2s⟨3/1⟩ 17L 2s⟨3/1⟩
3 1L 3s⟨3/1⟩ 2L 3s⟨3/1⟩ 3L 3s⟨3/1⟩ 4L 3s⟨3/1⟩ 5L 3s⟨3/1⟩ 6L 3s⟨3/1⟩ 7L 3s⟨3/1⟩ 8L 3s⟨3/1⟩ 9L 3s⟨3/1⟩ 10L 3s⟨3/1⟩ 11L 3s⟨3/1⟩ 12L 3s⟨3/1⟩ 13L 3s⟨3/1⟩ 14L 3s⟨3/1⟩ 15L 3s⟨3/1⟩ 16L 3s⟨3/1⟩
4 1L 4s⟨3/1⟩ 2L 4s⟨3/1⟩ 3L 4s⟨3/1⟩ 4L 4s⟨3/1⟩ 5L 4s⟨3/1⟩ 6L 4s⟨3/1⟩ 7L 4s⟨3/1⟩ 8L 4s⟨3/1⟩ 9L 4s⟨3/1⟩ 10L 4s⟨3/1⟩ 11L 4s⟨3/1⟩ 12L 4s⟨3/1⟩ 13L 4s⟨3/1⟩ 14L 4s⟨3/1⟩ 15L 4s⟨3/1⟩
5 1L 5s⟨3/1⟩ 2L 5s⟨3/1⟩ 3L 5s⟨3/1⟩ 4L 5s⟨3/1⟩ 5L 5s⟨3/1⟩ 6L 5s⟨3/1⟩ 7L 5s⟨3/1⟩ 8L 5s⟨3/1⟩ 9L 5s⟨3/1⟩ 10L 5s⟨3/1⟩ 11L 5s⟨3/1⟩ 12L 5s⟨3/1⟩ 13L 5s⟨3/1⟩ 14L 5s⟨3/1⟩
6 1L 6s⟨3/1⟩ 2L 6s⟨3/1⟩ 3L 6s⟨3/1⟩ 4L 6s⟨3/1⟩ 5L 6s⟨3/1⟩ 6L 6s⟨3/1⟩ 7L 6s⟨3/1⟩ 8L 6s⟨3/1⟩ 9L 6s⟨3/1⟩ 10L 6s⟨3/1⟩ 11L 6s⟨3/1⟩ 12L 6s⟨3/1⟩ 13L 6s⟨3/1⟩
7 1L 7s⟨3/1⟩ 2L 7s⟨3/1⟩ 3L 7s⟨3/1⟩ 4L 7s⟨3/1⟩ 5L 7s⟨3/1⟩ 6L 7s⟨3/1⟩ 7L 7s⟨3/1⟩ 8L 7s⟨3/1⟩ 9L 7s⟨3/1⟩ 10L 7s⟨3/1⟩ 11L 7s⟨3/1⟩ 12L 7s⟨3/1⟩
8 1L 8s⟨3/1⟩ 2L 8s⟨3/1⟩ 3L 8s⟨3/1⟩ 4L 8s⟨3/1⟩ 5L 8s⟨3/1⟩ 6L 8s⟨3/1⟩ 7L 8s⟨3/1⟩ 8L 8s⟨3/1⟩ 9L 8s⟨3/1⟩ 10L 8s⟨3/1⟩ 11L 8s⟨3/1⟩
9 1L 9s⟨3/1⟩ 2L 9s⟨3/1⟩ 3L 9s⟨3/1⟩ 4L 9s⟨3/1⟩ 5L 9s⟨3/1⟩ 6L 9s⟨3/1⟩ 7L 9s⟨3/1⟩ 8L 9s⟨3/1⟩ 9L 9s⟨3/1⟩ 10L 9s⟨3/1⟩
10 1L 10s⟨3/1⟩ 2L 10s⟨3/1⟩ 3L 10s⟨3/1⟩ 4L 10s⟨3/1⟩ 5L 10s⟨3/1⟩ 6L 10s⟨3/1⟩ 7L 10s⟨3/1⟩ 8L 10s⟨3/1⟩ 9L 10s⟨3/1⟩
11 1L 11s⟨3/1⟩ 2L 11s⟨3/1⟩ 3L 11s⟨3/1⟩ 4L 11s⟨3/1⟩ 5L 11s⟨3/1⟩ 6L 11s⟨3/1⟩ 7L 11s⟨3/1⟩ 8L 11s⟨3/1⟩
12 1L 12s⟨3/1⟩ 2L 12s⟨3/1⟩ 3L 12s⟨3/1⟩ 4L 12s⟨3/1⟩ 5L 12s⟨3/1⟩ 6L 12s⟨3/1⟩ 7L 12s⟨3/1⟩
13 1L 13s⟨3/1⟩ 2L 13s⟨3/1⟩ 3L 13s⟨3/1⟩ 4L 13s⟨3/1⟩ 5L 13s⟨3/1⟩ 6L 13s⟨3/1⟩
14 1L 14s⟨3/1⟩ 2L 14s⟨3/1⟩ 3L 14s⟨3/1⟩ 4L 14s⟨3/1⟩ 5L 14s⟨3/1⟩
15 1L 15s⟨3/1⟩ 2L 15s⟨3/1⟩ 3L 15s⟨3/1⟩ 4L 15s⟨3/1⟩
16 1L 16s⟨3/1⟩ 2L 16s⟨3/1⟩ 3L 16s⟨3/1⟩
17 1L 17s⟨3/1⟩ 2L 17s⟨3/1⟩
18 1L 18s⟨3/1⟩

Catalog of 3/2-equivalent mosses

3/2-equivalent mosses (up to 6 steps)
Number of small steps Number of large steps
1 2 3 4 5
1 1L 1s⟨3/2⟩ 2L 1s⟨3/2⟩ 3L 1s⟨3/2⟩ 4L 1s⟨3/2⟩ 5L 1s⟨3/2⟩
2 1L 2s⟨3/2⟩ 2L 2s⟨3/2⟩ 3L 2s⟨3/2⟩ 4L 2s⟨3/2⟩
3 1L 3s⟨3/2⟩ 2L 3s⟨3/2⟩ 3L 3s⟨3/2⟩
4 1L 4s⟨3/2⟩ 2L 4s⟨3/2⟩
5 1L 5s⟨3/2⟩
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