4L 12s

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

Scale structure
Step pattern	LsssLsssLsssLsss sssLsssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	3\16 to 1\4 (225.0 ¢ to 300.0 ¢)
Dark	0\4 to 1\16 (0.0 ¢ to 75.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	4L 8s
Sister	12L 4s
Daughters	16L 4s, 4L 16s
Neutralized	8L 8s
2-Flought	20L 12s, 4L 28s
Equal tunings
Equalized (L:s = 1:1)	3\16 (225.0 ¢)
Supersoft (L:s = 4:3)	10\52 (230.8 ¢)
Soft (L:s = 3:2)	7\36 (233.3 ¢)
Semisoft (L:s = 5:3)	11\56 (235.7 ¢)
Basic (L:s = 2:1)	4\20 (240.0 ¢)
Semihard (L:s = 5:2)	9\44 (245.5 ¢)
Hard (L:s = 3:1)	5\24 (250.0 ¢)
Superhard (L:s = 4:1)	6\28 (257.1 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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4L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 12 small steps, with a period of 1 large step and 3 small steps that repeats every 300.0 ¢, or 4 times every octave. 4L 12s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 225 ¢ to 300 ¢, or from 0 ¢ to 75 ¢.

Modes

Modes of 4L 12s

UDP	Cyclic order	Step pattern
12|0(4)	1	LsssLsssLsssLsss
8|4(4)	4	sLsssLsssLsssLss
4|8(4)	3	ssLsssLsssLsssLs
0|12(4)	2	sssLsssLsssLsssL

Intervals

Intervals of 4L 12s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 75.0 ¢
	Augmented 1-mosstep	A1ms	L	75.0 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	L + s	150.0 ¢ to 300.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 225.0 ¢
	Perfect 3-mosstep	P3ms	L + 2s	225.0 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	300.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	300.0 ¢ to 375.0 ¢
	Augmented 5-mosstep	A5ms	2L + 3s	375.0 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	2L + 4s	450.0 ¢ to 600.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	300.0 ¢ to 525.0 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	2L + 6s	600.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	2L + 7s	600.0 ¢ to 675.0 ¢
	Augmented 9-mosstep	A9ms	3L + 6s	675.0 ¢ to 900.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	600.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	3L + 7s	750.0 ¢ to 900.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	2L + 9s	600.0 ¢ to 825.0 ¢
	Perfect 11-mosstep	P11ms	3L + 8s	825.0 ¢ to 900.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	3L + 9s	900.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	3L + 10s	900.0 ¢ to 975.0 ¢
	Augmented 13-mosstep	A13ms	4L + 9s	975.0 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	900.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	4L + 10s	1050.0 ¢ to 1200.0 ¢
15-mosstep	Diminished 15-mosstep	d15ms	3L + 12s	900.0 ¢ to 1125.0 ¢
	Perfect 15-mosstep	P15ms	4L + 11s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	4L + 12s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 4L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\16						225.000	75.000	1:1	1.000	Equalized 4L 12s
					16\84	228.571	71.429	6:5	1.200
				13\68		229.412	70.588	5:4	1.250
					23\120	230.000	70.000	9:7	1.286
			10\52			230.769	69.231	4:3	1.333	Supersoft 4L 12s
					27\140	231.429	68.571	11:8	1.375
				17\88		231.818	68.182	7:5	1.400
					24\124	232.258	67.742	10:7	1.429
		7\36				233.333	66.667	3:2	1.500	Soft 4L 12s
					25\128	234.375	65.625	11:7	1.571
				18\92		234.783	65.217	8:5	1.600
					29\148	235.135	64.865	13:8	1.625
			11\56			235.714	64.286	5:3	1.667	Semisoft 4L 12s
					26\132	236.364	63.636	12:7	1.714
				15\76		236.842	63.158	7:4	1.750
					19\96	237.500	62.500	9:5	1.800
	4\20					240.000	60.000	2:1	2.000	Basic 4L 12s Scales with tunings softer than this are proper
					17\84	242.857	57.143	9:4	2.250
				13\64		243.750	56.250	7:3	2.333
					22\108	244.444	55.556	12:5	2.400
			9\44			245.455	54.545	5:2	2.500	Semihard 4L 12s
					23\112	246.429	53.571	13:5	2.600
				14\68		247.059	52.941	8:3	2.667
					19\92	247.826	52.174	11:4	2.750
		5\24				250.000	50.000	3:1	3.000	Hard 4L 12s
					16\76	252.632	47.368	10:3	3.333
				11\52		253.846	46.154	7:2	3.500
					17\80	255.000	45.000	11:3	3.667
			6\28			257.143	42.857	4:1	4.000	Superhard 4L 12s
					13\60	260.000	40.000	9:2	4.500
				7\32		262.500	37.500	5:1	5.000
					8\36	266.667	33.333	6:1	6.000
1\4						300.000	0.000	1:0	→ ∞	Collapsed 4L 12s

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