12L 3s (21/10-equivalent)

↖ 11L 2s⟨21/10⟩	↑ 12L 2s⟨21/10⟩	13L 2s⟨21/10⟩ ↗
← 11L 3s⟨21/10⟩	12L 3s (21/10-equivalent)	13L 3s⟨21/10⟩ →
↙ 11L 4s⟨21/10⟩	↓ 12L 4s⟨21/10⟩	13L 4s⟨21/10⟩ ↘

┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║│║║║║│║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLLsLLLLs sLLLLsLLLLsLLLL
Equave	21/10 (1284.5 ¢)
Period	1\3 (428.2 ¢)
Generator size(ed21/10)
Bright	1\15 to 1\12 (85.6 ¢ to 107.0 ¢)
Dark	3\12 to 4\15 (321.1 ¢ to 342.5 ¢)
Related MOS scales
Parent	3L 9s⟨21/10⟩
Sister	3L 12s⟨21/10⟩
Daughters	15L 12s⟨21/10⟩, 12L 15s⟨21/10⟩
Neutralized	9L 6s⟨21/10⟩
2-Flought	27L 3s⟨21/10⟩, 12L 18s⟨21/10⟩
Equal tunings(ed21/10)
Equalized (L:s = 1:1)	1\15 (85.6 ¢)
Supersoft (L:s = 4:3)	4\57 (90.1 ¢)
Soft (L:s = 3:2)	3\42 (91.7 ¢)
Semisoft (L:s = 5:3)	5\69 (93.1 ¢)
Basic (L:s = 2:1)	2\27 (95.1 ¢)
Semihard (L:s = 5:2)	5\66 (97.3 ¢)
Hard (L:s = 3:1)	3\39 (98.8 ¢)
Superhard (L:s = 4:1)	4\51 (100.7 ¢)
Collapsed (L:s = 1:0)	1\12 (107.0 ¢)

12L 3s⟨21/10⟩ is a 21/10-equivalent (non-octave) moment of symmetry scale containing 12 large steps and 3 small steps, with a period of 4 large steps and 1 small step that repeats every 428.2 ¢, or 3 times every interval of 21/10 (1284.5 ¢). Generators that produce this scale range from 85.6 ¢ to 107 ¢, or from 321.1 ¢ to 342.5 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 12L 3s⟨21/10⟩

UDP	Cyclic order	Step pattern
12|0(3)	1	LLLLsLLLLsLLLLs
9|3(3)	2	LLLsLLLLsLLLLsL
6|6(3)	3	LLsLLLLsLLLLsLL
3|9(3)	4	LsLLLLsLLLLsLLL
0|12(3)	5	sLLLLsLLLLsLLLL

Intervals

Intervals of 12L 3s⟨21/10⟩

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 85.6 ¢
	Perfect 1-mosstep	P1ms	L	85.6 ¢ to 107.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	107.0 ¢ to 171.3 ¢
	Major 2-mosstep	M2ms	2L	171.3 ¢ to 214.1 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	214.1 ¢ to 256.9 ¢
	Major 3-mosstep	M3ms	3L	256.9 ¢ to 321.1 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	321.1 ¢ to 342.5 ¢
	Augmented 4-mosstep	A4ms	4L	342.5 ¢ to 428.2 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	428.2 ¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	428.2 ¢ to 513.8 ¢
	Perfect 6-mosstep	P6ms	5L + s	513.8 ¢ to 535.2 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	535.2 ¢ to 599.4 ¢
	Major 7-mosstep	M7ms	6L + s	599.4 ¢ to 642.2 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	642.2 ¢ to 685.0 ¢
	Major 8-mosstep	M8ms	7L + s	685.0 ¢ to 749.3 ¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	749.3 ¢ to 770.7 ¢
	Augmented 9-mosstep	A9ms	8L + s	770.7 ¢ to 856.3 ¢
10-mosstep	Perfect 10-mosstep	P10ms	8L + 2s	856.3 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	856.3 ¢ to 941.9 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	941.9 ¢ to 963.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	963.4 ¢ to 1027.6 ¢
	Major 12-mosstep	M12ms	10L + 2s	1027.6 ¢ to 1070.4 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	1070.4 ¢ to 1113.2 ¢
	Major 13-mosstep	M13ms	11L + 2s	1113.2 ¢ to 1177.4 ¢
14-mosstep	Perfect 14-mosstep	P14ms	11L + 3s	1177.4 ¢ to 1198.8 ¢
	Augmented 14-mosstep	A14ms	12L + 2s	1198.8 ¢ to 1284.5 ¢
15-mosstep	Perfect 15-mosstep	P15ms	12L + 3s	1284.5 ¢

Scale tree

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