15L 4s

↖ 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
Descends from	4L 3s (smitonic)
Ancestor's step ratio range	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¢)

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¢.

It is notable as the MOS scale of Kleismic[19].

Modes

Modes of 15L 4s

UDP	Cyclic order	Step pattern
18|0	1	LLLLsLLLLsLLLLsLLLs
17|1	6	LLLLsLLLLsLLLsLLLLs
16|2	11	LLLLsLLLsLLLLsLLLLs
15|3	16	LLLsLLLLsLLLLsLLLLs
14|4	2	LLLsLLLLsLLLLsLLLsL
13|5	7	LLLsLLLLsLLLsLLLLsL
12|6	12	LLLsLLLsLLLLsLLLLsL
11|7	17	LLsLLLLsLLLLsLLLLsL
10|8	3	LLsLLLLsLLLLsLLLsLL
9|9	8	LLsLLLLsLLLsLLLLsLL
8|10	13	LLsLLLsLLLLsLLLLsLL
7|11	18	LsLLLLsLLLLsLLLLsLL
6|12	4	LsLLLLsLLLLsLLLsLLL
5|13	9	LsLLLLsLLLsLLLLsLLL
4|14	14	LsLLLsLLLLsLLLLsLLL
3|15	19	sLLLLsLLLLsLLLLsLLL
2|16	5	sLLLLsLLLLsLLLsLLLL
1|17	10	sLLLLsLLLsLLLLsLLLL
0|18	15	sLLLsLLLLsLLLLsLLLL

Intervals

Intervals of 15L 4s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0¢ to 63.2¢
	Major 1-mosstep	M1ms	L	63.2¢ to 80.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0¢ to 126.3¢
	Major 2-mosstep	M2ms	2L	126.3¢ to 160.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	160.0¢ to 189.5¢
	Major 3-mosstep	M3ms	3L	189.5¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	240.0¢ to 252.6¢
	Major 4-mosstep	M4ms	4L	252.6¢ to 320.0¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	240.0¢ to 315.8¢
	Perfect 5-mosstep	P5ms	4L + s	315.8¢ to 320.0¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	320.0¢ to 378.9¢
	Major 6-mosstep	M6ms	5L + s	378.9¢ to 400.0¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	400.0¢ to 442.1¢
	Major 7-mosstep	M7ms	6L + s	442.1¢ to 480.0¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	480.0¢ to 505.3¢
	Major 8-mosstep	M8ms	7L + s	505.3¢ to 560.0¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	560.0¢ to 568.4¢
	Major 9-mosstep	M9ms	8L + s	568.4¢ to 640.0¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	560.0¢ to 631.6¢
	Major 10-mosstep	M10ms	8L + 2s	631.6¢ to 640.0¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	640.0¢ to 694.7¢
	Major 11-mosstep	M11ms	9L + 2s	694.7¢ to 720.0¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	720.0¢ to 757.9¢
	Major 12-mosstep	M12ms	10L + 2s	757.9¢ to 800.0¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	800.0¢ to 821.1¢
	Major 13-mosstep	M13ms	11L + 2s	821.1¢ to 880.0¢
14-mosstep	Perfect 14-mosstep	P14ms	11L + 3s	880.0¢ to 884.2¢
	Augmented 14-mosstep	A14ms	12L + 2s	884.2¢ to 960.0¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	880.0¢ to 947.4¢
	Major 15-mosstep	M15ms	12L + 3s	947.4¢ to 960.0¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	960.0¢ to 1010.5¢
	Major 16-mosstep	M16ms	13L + 3s	1010.5¢ to 1040.0¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	1040.0¢ to 1073.7¢
	Major 17-mosstep	M17ms	14L + 3s	1073.7¢ to 1120.0¢
18-mosstep	Minor 18-mosstep	m18ms	14L + 4s	1120.0¢ to 1136.8¢
	Major 18-mosstep	M18ms	15L + 3s	1136.8¢ to 1200.0¢
19-mosstep	Perfect 19-mosstep	P19ms	15L + 4s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 15L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\19						315.789	884.211	1:1	1.000	Equalized 15L 4s
					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	Catakleismic
				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	Soft 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
			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 Scales with tunings softer 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	Hard 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	→ ∞	Collapsed 15L 4s

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