User:Ganaram inukshuk/Catalog of MOS Scales

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⟩