3L 12s

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

Scale structure
Step pattern	LssssLssssLssss ssssLssssLssssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	4\15 to 1\3 (320.0 ¢ to 400.0 ¢)
Dark	0\3 to 1\15 (0.0 ¢ to 80.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	3L 9s
Sister	12L 3s
Daughters	15L 3s, 3L 15s
Neutralized	6L 9s
2-Flought	18L 12s, 3L 27s
Equal tunings
Equalized (L:s = 1:1)	4\15 (320.0 ¢)
Supersoft (L:s = 4:3)	13\48 (325.0 ¢)
Soft (L:s = 3:2)	9\33 (327.3 ¢)
Semisoft (L:s = 5:3)	14\51 (329.4 ¢)
Basic (L:s = 2:1)	5\18 (333.3 ¢)
Semihard (L:s = 5:2)	11\39 (338.5 ¢)
Hard (L:s = 3:1)	6\21 (342.9 ¢)
Superhard (L:s = 4:1)	7\24 (350.0 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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3L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 12 small steps, with a period of 1 large step and 4 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 12s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 320 ¢ to 400 ¢, or from 0 ¢ to 80 ¢.

It is the MOS of Inflated[15].

Modes

Modes of 3L 12s

UDP	Cyclic order	Step pattern
12|0(3)	1	LssssLssssLssss
9|3(3)	5	sLssssLssssLsss
6|6(3)	4	ssLssssLssssLss
3|9(3)	3	sssLssssLssssLs
0|12(3)	2	ssssLssssLssssL

Intervals

Intervals of 3L 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 80.0 ¢
	Augmented 1-mosstep	A1ms	L	80.0 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	L + s	160.0 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	L + 2s	240.0 ¢ to 400.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0 ¢ to 320.0 ¢
	Perfect 4-mosstep	P4ms	L + 3s	320.0 ¢ to 400.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	400.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	400.0 ¢ to 480.0 ¢
	Augmented 6-mosstep	A6ms	2L + 4s	480.0 ¢ to 800.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	400.0 ¢ to 560.0 ¢
	Major 7-mosstep	M7ms	2L + 5s	560.0 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0 ¢ to 640.0 ¢
	Major 8-mosstep	M8ms	2L + 6s	640.0 ¢ to 800.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	L + 8s	400.0 ¢ to 720.0 ¢
	Perfect 9-mosstep	P9ms	2L + 7s	720.0 ¢ to 800.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	2L + 8s	800.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	2L + 9s	800.0 ¢ to 880.0 ¢
	Augmented 11-mosstep	A11ms	3L + 8s	880.0 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	800.0 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	3L + 9s	960.0 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	800.0 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	3L + 10s	1040.0 ¢ to 1200.0 ¢
14-mosstep	Diminished 14-mosstep	d14ms	2L + 12s	800.0 ¢ to 1120.0 ¢
	Perfect 14-mosstep	P14ms	3L + 11s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	3L + 12s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 3L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\15						320.000	80.000	1:1	1.000	Equalized 3L 12s
					21\78	323.077	76.923	6:5	1.200
				17\63		323.810	76.190	5:4	1.250
					30\111	324.324	75.676	9:7	1.286
			13\48			325.000	75.000	4:3	1.333	Supersoft 3L 12s
					35\129	325.581	74.419	11:8	1.375
				22\81		325.926	74.074	7:5	1.400
					31\114	326.316	73.684	10:7	1.429
		9\33				327.273	72.727	3:2	1.500	Soft 3L 12s
					32\117	328.205	71.795	11:7	1.571
				23\84		328.571	71.429	8:5	1.600
					37\135	328.889	71.111	13:8	1.625
			14\51			329.412	70.588	5:3	1.667	Semisoft 3L 12s
					33\120	330.000	70.000	12:7	1.714
				19\69		330.435	69.565	7:4	1.750
					24\87	331.034	68.966	9:5	1.800
	5\18					333.333	66.667	2:1	2.000	Basic 3L 12s Scales with tunings softer than this are proper
					21\75	336.000	64.000	9:4	2.250
				16\57		336.842	63.158	7:3	2.333
					27\96	337.500	62.500	12:5	2.400
			11\39			338.462	61.538	5:2	2.500	Semihard 3L 12s
					28\99	339.394	60.606	13:5	2.600
				17\60		340.000	60.000	8:3	2.667
					23\81	340.741	59.259	11:4	2.750
		6\21				342.857	57.143	3:1	3.000	Hard 3L 12s
					19\66	345.455	54.545	10:3	3.333
				13\45		346.667	53.333	7:2	3.500
					20\69	347.826	52.174	11:3	3.667
			7\24			350.000	50.000	4:1	4.000	Superhard 3L 12s
					15\51	352.941	47.059	9:2	4.500
				8\27		355.556	44.444	5:1	5.000
					9\30	360.000	40.000	6:1	6.000
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 12s

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