12L 3s

↖ 11L 2s	↑ 12L 2s	13L 2s ↗
← 11L 3s	12L 3s	13L 3s →
↙ 11L 4s	↓ 12L 4s	13L 4s ↘

┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║│║║║║│║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLLsLLLLs sLLLLsLLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\15 to 1\12 (80.0 ¢ to 100.0 ¢)
Dark	3\12 to 4\15 (300.0 ¢ to 320.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	3L 9s
Sister	3L 12s
Daughters	15L 12s, 12L 15s
Neutralized	9L 6s
2-Flought	27L 3s, 12L 18s
Equal tunings
Equalized (L:s = 1:1)	1\15 (80.0 ¢)
Supersoft (L:s = 4:3)	4\57 (84.2 ¢)
Soft (L:s = 3:2)	3\42 (85.7 ¢)
Semisoft (L:s = 5:3)	5\69 (87.0 ¢)
Basic (L:s = 2:1)	2\27 (88.9 ¢)
Semihard (L:s = 5:2)	5\66 (90.9 ¢)
Hard (L:s = 3:1)	3\39 (92.3 ¢)
Superhard (L:s = 4:1)	4\51 (94.1 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)

12L 3s is a 2/1-equivalent (octave-equivalent) 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 400.0 ¢, or 3 times every octave. 12L 3s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 80 ¢ to 100 ¢, or from 300 ¢ to 320 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].

Modes

Modes of 12L 3s

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

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 80.0 ¢
	Perfect 1-mosstep	P1ms	L	80.0 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	2L	160.0 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	3L	240.0 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	300.0 ¢ to 320.0 ¢
	Augmented 4-mosstep	A4ms	4L	320.0 ¢ to 400.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	400.0 ¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	400.0 ¢ to 480.0 ¢
	Perfect 6-mosstep	P6ms	5L + s	480.0 ¢ to 500.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	500.0 ¢ to 560.0 ¢
	Major 7-mosstep	M7ms	6L + s	560.0 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	600.0 ¢ to 640.0 ¢
	Major 8-mosstep	M8ms	7L + s	640.0 ¢ to 700.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	700.0 ¢ to 720.0 ¢
	Augmented 9-mosstep	A9ms	8L + s	720.0 ¢ to 800.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	8L + 2s	800.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	800.0 ¢ to 880.0 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	880.0 ¢ to 900.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	900.0 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	10L + 2s	960.0 ¢ to 1000.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	1000.0 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	11L + 2s	1040.0 ¢ to 1100.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	11L + 3s	1100.0 ¢ to 1120.0 ¢
	Augmented 14-mosstep	A14ms	12L + 2s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	12L + 3s	1200.0 ¢