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].

Scale tree

1/15							80
						7\102	82.353
					6\87		82.759
				5/72			83.333
			4/57				84.2105
				7/99			84.8485
		3/42					85.714
							86.27
				8/111			86.4865
							86.617
			5/69				86.9565
				7/96			87.5
	2/27						88.889
						11/147	89.796
					9/120		90
				7/93			90.323
			5/66				90.909
							91.283
				8/105			91.429
							91.578
		3/39					92.308
							92.629
				7/90			93.333
			4/51				94.118
				5/63			95.238
					6/75		96
						7/87	96.552
1/12							100