3L 15s

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

┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║│││││║│││││║││││││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssssLsssssLsssss sssssLsssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	5\18 to 1\3 (333.3 ¢ to 400.0 ¢)
Dark	0\3 to 1\18 (0.0 ¢ to 66.7 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 12s
Sister	15L 3s
Daughters	18L 3s, 3L 18s
Neutralized	6L 12s
2-Flought	21L 15s, 3L 33s
Equal tunings
Equalized (L:s = 1:1)	5\18 (333.3 ¢)
Supersoft (L:s = 4:3)	16\57 (336.8 ¢)
Soft (L:s = 3:2)	11\39 (338.5 ¢)
Semisoft (L:s = 5:3)	17\60 (340.0 ¢)
Basic (L:s = 2:1)	6\21 (342.9 ¢)
Semihard (L:s = 5:2)	13\45 (346.7 ¢)
Hard (L:s = 3:1)	7\24 (350.0 ¢)
Superhard (L:s = 4:1)	8\27 (355.6 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)

3L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 15 small steps, with a period of 1 large step and 5 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 15s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 333.3 ¢ to 400 ¢, or from 0 ¢ to 66.7 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 3L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\18						333.333	66.667	1:1	1.000	Equalized 3L 15s
					26\93	335.484	64.516	6:5	1.200
				21\75		336.000	64.000	5:4	1.250
					37\132	336.364	63.636	9:7	1.286
			16\57			336.842	63.158	4:3	1.333	Supersoft 3L 15s
					43\153	337.255	62.745	11:8	1.375
				27\96		337.500	62.500	7:5	1.400
					38\135	337.778	62.222	10:7	1.429
		11\39				338.462	61.538	3:2	1.500	Soft 3L 15s
					39\138	339.130	60.870	11:7	1.571
				28\99		339.394	60.606	8:5	1.600
					45\159	339.623	60.377	13:8	1.625
			17\60			340.000	60.000	5:3	1.667	Semisoft 3L 15s
					40\141	340.426	59.574	12:7	1.714
				23\81		340.741	59.259	7:4	1.750
					29\102	341.176	58.824	9:5	1.800
	6\21					342.857	57.143	2:1	2.000	Basic 3L 15s Scales with tunings softer than this are proper
					25\87	344.828	55.172	9:4	2.250
				19\66		345.455	54.545	7:3	2.333
					32\111	345.946	54.054	12:5	2.400
			13\45			346.667	53.333	5:2	2.500	Semihard 3L 15s
					33\114	347.368	52.632	13:5	2.600
				20\69		347.826	52.174	8:3	2.667
					27\93	348.387	51.613	11:4	2.750
		7\24				350.000	50.000	3:1	3.000	Hard 3L 15s
					22\75	352.000	48.000	10:3	3.333
				15\51		352.941	47.059	7:2	3.500
					23\78	353.846	46.154	11:3	3.667
			8\27			355.556	44.444	4:1	4.000	Superhard 3L 15s
					17\57	357.895	42.105	9:2	4.500
				9\30		360.000	40.000	5:1	5.000
					10\33	363.636	36.364	6:1	6.000
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 15s

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