15L 3s

↖ 14L 2s	↑ 15L 2s	16L 2s ↗
← 14L 3s	15L 3s	16L 3s →
↙ 14L 4s	↓ 15L 4s	16L 4s ↘

Scale structure
Step pattern	LLLLLsLLLLLsLLLLLs sLLLLLsLLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\18 to 1\15 (66.7 ¢ to 80.0 ¢)
Dark	4\15 to 5\18 (320.0 ¢ to 333.3 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	3L 12s
Sister	3L 15s
Daughters	18L 15s, 15L 18s
Neutralized	12L 6s
2-Flought	33L 3s, 15L 21s
Equal tunings
Equalized (L:s = 1:1)	1\18 (66.7 ¢)
Supersoft (L:s = 4:3)	4\69 (69.6 ¢)
Soft (L:s = 3:2)	3\51 (70.6 ¢)
Semisoft (L:s = 5:3)	5\84 (71.4 ¢)
Basic (L:s = 2:1)	2\33 (72.7 ¢)
Semihard (L:s = 5:2)	5\81 (74.1 ¢)
Hard (L:s = 3:1)	3\48 (75.0 ¢)
Superhard (L:s = 4:1)	4\63 (76.2 ¢)
Collapsed (L:s = 1:0)	1\15 (80.0 ¢)
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15L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 3 small steps, with a period of 5 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 15L 3s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 66.7 ¢ to 80 ¢, or from 320 ¢ to 333.3 ¢. 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 15L 3s

UDP	Cyclic order	Step pattern
15|0(3)	1	LLLLLsLLLLLsLLLLLs
12|3(3)	2	LLLLsLLLLLsLLLLLsL
9|6(3)	3	LLLsLLLLLsLLLLLsLL
6|9(3)	4	LLsLLLLLsLLLLLsLLL
3|12(3)	5	LsLLLLLsLLLLLsLLLL
0|15(3)	6	sLLLLLsLLLLLsLLLLL

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 15L 3s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\18						66.667	333.333	1:1	1.000	Equalized 15L 3s
					6\105	68.571	331.429	6:5	1.200
				5\87		68.966	331.034	5:4	1.250
					9\156	69.231	330.769	9:7	1.286
			4\69			69.565	330.435	4:3	1.333	Supersoft 15L 3s
					11\189	69.841	330.159	11:8	1.375
				7\120		70.000	330.000	7:5	1.400
					10\171	70.175	329.825	10:7	1.429
		3\51				70.588	329.412	3:2	1.500	Soft 15L 3s
					11\186	70.968	329.032	11:7	1.571
				8\135		71.111	328.889	8:5	1.600
					13\219	71.233	328.767	13:8	1.625
			5\84			71.429	328.571	5:3	1.667	Semisoft 15L 3s
					12\201	71.642	328.358	12:7	1.714
				7\117		71.795	328.205	7:4	1.750
					9\150	72.000	328.000	9:5	1.800
	2\33					72.727	327.273	2:1	2.000	Basic 15L 3s
					9\147	73.469	326.531	9:4	2.250
				7\114		73.684	326.316	7:3	2.333
					12\195	73.846	326.154	12:5	2.400
			5\81			74.074	325.926	5:2	2.500	Semihard 15L 3s
					13\210	74.286	325.714	13:5	2.600
				8\129		74.419	325.581	8:3	2.667
					11\177	74.576	325.424	11:4	2.750
		3\48				75.000	325.000	3:1	3.000	Hard 15L 3s
					10\159	75.472	324.528	10:3	3.333
				7\111		75.676	324.324	7:2	3.500
					11\174	75.862	324.138	11:3	3.667
			4\63			76.190	323.810	4:1	4.000	Superhard 15L 3s
					9\141	76.596	323.404	9:2	4.500
				5\78		76.923	323.077	5:1	5.000
					6\93	77.419	322.581	6:1	6.000
1\15						80.000	320.000	1:0	→ ∞	Collapsed 15L 3s