9L 3s

↖ 8L 2s	↑ 9L 2s	10L 2s ↗
← 8L 3s	9L 3s	10L 3s →
↙ 8L 4s	↓ 9L 4s	10L 4s ↘

┌╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║│║║║│║║║││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLsLLLsLLLs
sLLLsLLLsLLL

Equave

2/1 (1200.0 ¢)

Period

1\3 (400.0 ¢)

Generator size

Bright

1\12 to 1\9 (100.0 ¢ to 133.3 ¢)

Dark

2\9 to 3\12 (266.7 ¢ to 300.0 ¢)

TAMNAMS information

Related to

3L 6s (tcherepnin)

With tunings

1:1 to 2:1 (soft-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

1\12 (100.0 ¢)

Supersoft (L:s = 4:3)

4\45 (106.7 ¢)

3\33 (109.1 ¢)

5\54 (111.1 ¢)

2\21 (114.3 ¢)

5\51 (117.6 ¢)

3\30 (120.0 ¢)

Superhard (L:s = 4:1)

4\39 (123.1 ¢)

Collapsed (L:s = 1:0)

1\9 (133.3 ¢)

9L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 3 small steps, with a period of 3 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 9L 3s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 100 ¢ to 133.3 ¢, or from 266.7 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.

Modes

Modes of 9L 3s
UDP	Cyclic order	Step pattern
9\|0(3)	1	LLLsLLLsLLLs
6\|3(3)	2	LLsLLLsLLLsL
3\|6(3)	3	LsLLLsLLLsLL
0\|9(3)	4	sLLLsLLLsLLL

Scale tree

1/12		100
5/57		105.263
4/45		106.667
	7/78	107.5385
	10/111	108.108
3/33		109.111
		109.992
	8/87	110.345
		110.557
	5/54	111.111
		111.815
	7/75	112
	9/96	112.5
	11/117	112.8205
	13/138	113.0435
2/21		114.286
	11/114	115.7895
	9/93	116.129
	7/72	116.667
	5/51	117.647
		118.274
	8/81	118.5185
		118.769
	11/111	118.919
	14/141	119.149
3/30		120
		120.543
	7/69	121.739
	11/108	122.222
4/39		123.138
	9/87	124.138
5/48		125
1/9		133.333