9L 12s

↖ 8L 11s	↑ 9L 11s	10L 11s ↗
← 8L 12s	9L 12s	10L 12s →
↙ 8L 13s	↓ 9L 13s	10L 13s ↘

┌╥┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐ │║│║│║││║│║│║││║│║│║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLssLsLsLssLsLsLss ssLsLsLssLsLsLssLsLsL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	2\21 to 1\9 (114.3 ¢ to 133.3 ¢)
Dark	2\9 to 5\21 (266.7 ¢ to 285.7 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	9L 3s
Sister	12L 9s
Daughters	21L 9s, 9L 21s
Neutralized	18L 3s
2-Flought	30L 12s, 9L 33s
Equal tunings
Equalized (L:s = 1:1)	2\21 (114.3 ¢)
Supersoft (L:s = 4:3)	7\72 (116.7 ¢)
Soft (L:s = 3:2)	5\51 (117.6 ¢)
Semisoft (L:s = 5:3)	8\81 (118.5 ¢)
Basic (L:s = 2:1)	3\30 (120.0 ¢)
Semihard (L:s = 5:2)	7\69 (121.7 ¢)
Hard (L:s = 3:1)	4\39 (123.1 ¢)
Superhard (L:s = 4:1)	5\48 (125.0 ¢)
Collapsed (L:s = 1:0)	1\9 (133.3 ¢)

9L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 12 small steps, with a period of 3 large steps and 4 small steps that repeats every 400.0 ¢, or 3 times every octave. 9L 12s is a grandchild scale of 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 114.3 ¢ to 133.3 ¢, or from 266.7 ¢ to 285.7 ¢.

Modes

Modes of 9L 12s

UDP	Cyclic order	Step pattern
18|0(3)	1	LsLsLssLsLsLssLsLsLss
15|3(3)	3	LsLssLsLsLssLsLsLssLs
12|6(3)	5	LssLsLsLssLsLsLssLsLs
9|9(3)	7	sLsLsLssLsLsLssLsLsLs
6|12(3)	2	sLsLssLsLsLssLsLsLssL
3|15(3)	4	sLssLsLsLssLsLsLssLsL
0|18(3)	6	ssLsLsLssLsLsLssLsLsL

Intervals

Intervals of 9L 12s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 57.1 ¢
	Major 1-mosstep	M1ms	L	57.1 ¢ to 133.3 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 114.3 ¢
	Perfect 2-mosstep	P2ms	L + s	114.3 ¢ to 133.3 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	133.3 ¢ to 171.4 ¢
	Major 3-mosstep	M3ms	2L + s	171.4 ¢ to 266.7 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	133.3 ¢ to 228.6 ¢
	Major 4-mosstep	M4ms	2L + 2s	228.6 ¢ to 266.7 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	266.7 ¢ to 285.7 ¢
	Augmented 5-mosstep	A5ms	3L + 2s	285.7 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	266.7 ¢ to 342.9 ¢
	Major 6-mosstep	M6ms	3L + 3s	342.9 ¢ to 400.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	3L + 4s	400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	400.0 ¢ to 457.1 ¢
	Major 8-mosstep	M8ms	4L + 4s	457.1 ¢ to 533.3 ¢
9-mosstep	Diminished 9-mosstep	d9ms	3L + 6s	400.0 ¢ to 514.3 ¢
	Perfect 9-mosstep	P9ms	4L + 5s	514.3 ¢ to 533.3 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	533.3 ¢ to 571.4 ¢
	Major 10-mosstep	M10ms	5L + 5s	571.4 ¢ to 666.7 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	533.3 ¢ to 628.6 ¢
	Major 11-mosstep	M11ms	5L + 6s	628.6 ¢ to 666.7 ¢
12-mosstep	Perfect 12-mosstep	P12ms	5L + 7s	666.7 ¢ to 685.7 ¢
	Augmented 12-mosstep	A12ms	6L + 6s	685.7 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	5L + 8s	666.7 ¢ to 742.9 ¢
	Major 13-mosstep	M13ms	6L + 7s	742.9 ¢ to 800.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	6L + 8s	800.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	800.0 ¢ to 857.1 ¢
	Major 15-mosstep	M15ms	7L + 8s	857.1 ¢ to 933.3 ¢
16-mosstep	Diminished 16-mosstep	d16ms	6L + 10s	800.0 ¢ to 914.3 ¢
	Perfect 16-mosstep	P16ms	7L + 9s	914.3 ¢ to 933.3 ¢
17-mosstep	Minor 17-mosstep	m17ms	7L + 10s	933.3 ¢ to 971.4 ¢
	Major 17-mosstep	M17ms	8L + 9s	971.4 ¢ to 1066.7 ¢
18-mosstep	Minor 18-mosstep	m18ms	7L + 11s	933.3 ¢ to 1028.6 ¢
	Major 18-mosstep	M18ms	8L + 10s	1028.6 ¢ to 1066.7 ¢
19-mosstep	Perfect 19-mosstep	P19ms	8L + 11s	1066.7 ¢ to 1085.7 ¢
	Augmented 19-mosstep	A19ms	9L + 10s	1085.7 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	8L + 12s	1066.7 ¢ to 1142.9 ¢
	Major 20-mosstep	M20ms	9L + 11s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	9L + 12s	1200.0 ¢

Scale tree

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