15L 4s

15L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 4 small steps, repeating every octave. 15L 4s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 315.8 ¢ to 320 ¢, or from 880 ¢ to 884.2 ¢.

↖ 14L 3s	↑ 15L 3s	16L 3s ↗
← 14L 4s	15L 4s	16L 4s →
↙ 14L 5s	↓ 15L 5s	16L 5s ↘

Scale structure
Step pattern	LLLLsLLLLsLLLLsLLLs sLLLsLLLLsLLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\19 to 4\15 (315.8 ¢ to 320.0 ¢)
Dark	11\15 to 14\19 (880.0 ¢ to 884.2 ¢)
TAMNAMS information
Related to	4L 3s (smitonic)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	4L 11s
Sister	4L 15s
Daughters	19L 15s, 15L 19s
Neutralized	11L 8s
2-Flought	34L 4s, 15L 23s
Equal tunings
Equalized (L:s = 1:1)	5\19 (315.8 ¢)
Supersoft (L:s = 4:3)	19\72 (316.7 ¢)
Soft (L:s = 3:2)	14\53 (317.0 ¢)
Semisoft (L:s = 5:3)	23\87 (317.2 ¢)
Basic (L:s = 2:1)	9\34 (317.6 ¢)
Semihard (L:s = 5:2)	22\83 (318.1 ¢)
Hard (L:s = 3:1)	13\49 (318.4 ¢)
Superhard (L:s = 4:1)	17\64 (318.8 ¢)
Collapsed (L:s = 1:0)	4\15 (320.0 ¢)
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It is notable as the MOS scale of Catakleismic[19].

Scale tree

Generator						Bright gen.	Dark gen.	L	s	L/s	Comments
5\19						315.789	884.211	1	1	1.000	Equalized 15L 4s (Degenerate case)
					29\110	316.364	883.636	6	5	1.200
				24\91		316.484	883.516	5	4	1.250
					43\163	316.564	883.436	9	7	1.286
			19\72			316.667	883.333	4	3	1.333	Supersoft 15L 4s
					52\197	316.751	883.249	11	8	1.375
				33\125		316.800	883.200	7	5	1.400
					47\178	316.854	883.146	10	7	1.429
		14\53				316.981	883.019	3	2	1.500	Monosoft 15L 4s
					51\193	317.098	882.902	11	7	1.571
				37\140		317.143	882.857	8	5	1.600
					60\227	317.181	882.819	13	8	1.625	Golden 15L 4s sequence can be found here
			23\87			317.241	882.759	5	3	1.667	Semisoft 15L 4s
					55\208	317.308	882.692	12	7	1.714
				32\121		317.355	882.645	7	4	1.750
					41\155	317.419	882.581	9	5	1.800
	9\34					317.647	882.353	2	1	2.000	Basic 15L 4s (Generators smaller than this are proper)
					40\151	317.881	882.119	9	4	2.250
				31\117		317.949	882.051	7	3	2.333
					53\200	318.000	882.000	12	5	2.400
			22\83			318.072	881.928	5	2	2.500	Semihard 15L 4s
					57\215	318.140	881.860	13	5	2.600
				35\132		318.182	881.818	8	3	2.667
					48\181	318.232	881.768	11	4	2.750
		13\49				318.367	881.633	3	1	3.000	Monohard 15L 4s
					43\162	318.519	881.481	10	3	3.333
				30\113		318.584	881.416	7	2	3.500
					47\177	318.644	881.356	11	3	3.667
			17\64			318.750	881.250	4	1	4.000	Superhard 15L 4s
					38\143	318.881	881.119	9	2	4.500
				21\79		318.987	881.013	5	1	5.000
					25\94	319.149	880.851	6	1	6.000
4\15						320.000	880.000	1	0	→ inf	Collapsed 15L 4s (Degenerate case)