12L 4s

↖ 11L 3s	↑ 12L 3s	13L 3s ↗
← 11L 4s	12L 4s	13L 4s →
↙ 11L 5s	↓ 12L 5s	13L 5s ↘

┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║│║║║││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	1\16 to 1\12 (75.0 ¢ to 100.0 ¢)
Dark	2\12 to 3\16 (200.0 ¢ to 225.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	4L 8s
Sister	4L 12s
Daughters	16L 12s, 12L 16s
Neutralized	8L 8s
2-Flought	28L 4s, 12L 20s
Equal tunings
Equalized (L:s = 1:1)	1\16 (75.0 ¢)
Supersoft (L:s = 4:3)	4\60 (80.0 ¢)
Soft (L:s = 3:2)	3\44 (81.8 ¢)
Semisoft (L:s = 5:3)	5\72 (83.3 ¢)
Basic (L:s = 2:1)	2\28 (85.7 ¢)
Semihard (L:s = 5:2)	5\68 (88.2 ¢)
Hard (L:s = 3:1)	3\40 (90.0 ¢)
Superhard (L:s = 4:1)	4\52 (92.3 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)

12L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 4 small steps, with a period of 3 large steps and 1 small step that repeats every 300.0 ¢, or 4 times every octave. 12L 4s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 75 ¢ to 100 ¢, or from 200 ¢ to 225 ¢. 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 4s

UDP	Cyclic order	Step pattern
12|0(4)	1	LLLsLLLsLLLsLLLs
8|4(4)	2	LLsLLLsLLLsLLLsL
4|8(4)	3	LsLLLsLLLsLLLsLL
0|12(4)	4	sLLLsLLLsLLLsLLL

Intervals

Intervals of 12L 4s

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 75.0 ¢
	Perfect 1-mosstep	P1ms	L	75.0 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 200.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	200.0 ¢ to 225.0 ¢
	Augmented 3-mosstep	A3ms	3L	225.0 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	300.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	300.0 ¢ to 375.0 ¢
	Perfect 5-mosstep	P5ms	4L + s	375.0 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	400.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	5L + s	450.0 ¢ to 500.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	500.0 ¢ to 525.0 ¢
	Augmented 7-mosstep	A7ms	6L + s	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	6L + 2s	600.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	6L + 3s	600.0 ¢ to 675.0 ¢
	Perfect 9-mosstep	P9ms	7L + 2s	675.0 ¢ to 700.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	700.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	750.0 ¢ to 800.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	800.0 ¢ to 825.0 ¢
	Augmented 11-mosstep	A11ms	9L + 2s	825.0 ¢ to 900.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	9L + 3s	900.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	9L + 4s	900.0 ¢ to 975.0 ¢
	Perfect 13-mosstep	P13ms	10L + 3s	975.0 ¢ to 1000.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	1000.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	1050.0 ¢ to 1100.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	11L + 4s	1100.0 ¢ to 1125.0 ¢
	Augmented 15-mosstep	A15ms	12L + 3s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	12L + 4s	1200.0 ¢

Scale tree

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