1L 15s

	↑ 1L 14s	2L 14s ↗
	1L 15s	2L 15s →
	↓ 1L 16s	2L 16s ↘

┌╥┬┬┬┬┬┬┬┬┬┬┬┬┬┬┬┐ │║││││││││││││││││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	Lsssssssssssssss sssssssssssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	15\16 to 1\1 (1125.0¢ to 1200.0¢)
Dark	0\1 to 1\16 (0.0¢ to 75.0¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Ancestor's step ratio range	7:1 to 1:0
Related MOS scales
Parent	1L 14s
Sister	15L 1s
Daughters	16L 1s, 1L 16s
Neutralized	2L 14s
2-Flought	17L 15s, 1L 31s
Equal tunings
Equalized (L:s = 1:1)	15\16 (1125.0¢)
Supersoft (L:s = 4:3)	46\49 (1126.5¢)
Soft (L:s = 3:2)	31\33 (1127.3¢)
Semisoft (L:s = 5:3)	47\50 (1128.0¢)
Basic (L:s = 2:1)	16\17 (1129.4¢)
Semihard (L:s = 5:2)	33\35 (1131.4¢)
Hard (L:s = 3:1)	17\18 (1133.3¢)
Superhard (L:s = 4:1)	18\19 (1136.8¢)
Collapsed (L:s = 1:0)	1\1 (1200.0¢)

1L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 15 small steps, repeating every octave. 1L 15s is related to 1L 9s, expanding it by 6 tones. Generators that produce this scale range from 1125¢ to 1200¢, or from 0¢ to 75¢.

Modes

Modes of 1L 15s

UDP	Cyclic order	Step pattern
15|0	1	Lsssssssssssssss
14|1	16	sLssssssssssssss
13|2	15	ssLsssssssssssss
12|3	14	sssLssssssssssss
11|4	13	ssssLsssssssssss
10|5	12	sssssLssssssssss
9|6	11	ssssssLsssssssss
8|7	10	sssssssLssssssss
7|8	9	ssssssssLsssssss
6|9	8	sssssssssLssssss
5|10	7	ssssssssssLsssss
4|11	6	sssssssssssLssss
3|12	5	ssssssssssssLsss
2|13	4	sssssssssssssLss
1|14	3	ssssssssssssssLs
0|15	2	sssssssssssssssL

Intervals

Intervals of 1L 15s

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 75.0¢
	Augmented 1-mosstep	A1ms	L	75.0¢ to 1200.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 150.0¢
	Major 2-mosstep	M2ms	L + s	150.0¢ to 1200.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 225.0¢
	Major 3-mosstep	M3ms	L + 2s	225.0¢ to 1200.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 300.0¢
	Major 4-mosstep	M4ms	L + 3s	300.0¢ to 1200.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 375.0¢
	Major 5-mosstep	M5ms	L + 4s	375.0¢ to 1200.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 450.0¢
	Major 6-mosstep	M6ms	L + 5s	450.0¢ to 1200.0¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0¢ to 525.0¢
	Major 7-mosstep	M7ms	L + 6s	525.0¢ to 1200.0¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0¢ to 600.0¢
	Major 8-mosstep	M8ms	L + 7s	600.0¢ to 1200.0¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0¢ to 675.0¢
	Major 9-mosstep	M9ms	L + 8s	675.0¢ to 1200.0¢
10-mosstep	Minor 10-mosstep	m10ms	10s	0.0¢ to 750.0¢
	Major 10-mosstep	M10ms	L + 9s	750.0¢ to 1200.0¢
11-mosstep	Minor 11-mosstep	m11ms	11s	0.0¢ to 825.0¢
	Major 11-mosstep	M11ms	L + 10s	825.0¢ to 1200.0¢
12-mosstep	Minor 12-mosstep	m12ms	12s	0.0¢ to 900.0¢
	Major 12-mosstep	M12ms	L + 11s	900.0¢ to 1200.0¢
13-mosstep	Minor 13-mosstep	m13ms	13s	0.0¢ to 975.0¢
	Major 13-mosstep	M13ms	L + 12s	975.0¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	14s	0.0¢ to 1050.0¢
	Major 14-mosstep	M14ms	L + 13s	1050.0¢ to 1200.0¢
15-mosstep	Diminished 15-mosstep	d15ms	15s	0.0¢ to 1125.0¢
	Perfect 15-mosstep	P15ms	L + 14s	1125.0¢ to 1200.0¢
16-mosstep	Perfect 16-mosstep	P16ms	L + 15s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 1L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
15\16						1125.000	75.000	1:1	1.000	Equalized 1L 15s
					76\81	1125.926	74.074	6:5	1.200
				61\65		1126.154	73.846	5:4	1.250
					107\114	1126.316	73.684	9:7	1.286
			46\49			1126.531	73.469	4:3	1.333	Supersoft 1L 15s
					123\131	1126.718	73.282	11:8	1.375
				77\82		1126.829	73.171	7:5	1.400
					108\115	1126.957	73.043	10:7	1.429
		31\33				1127.273	72.727	3:2	1.500	Soft 1L 15s
					109\116	1127.586	72.414	11:7	1.571
				78\83		1127.711	72.289	8:5	1.600
					125\133	1127.820	72.180	13:8	1.625	Unnamed golden tuning
			47\50			1128.000	72.000	5:3	1.667	Semisoft 1L 15s
					110\117	1128.205	71.795	12:7	1.714
				63\67		1128.358	71.642	7:4	1.750
					79\84	1128.571	71.429	9:5	1.800
	16\17					1129.412	70.588	2:1	2.000	Basic 1L 15s Scales with tunings softer than this are proper
					65\69	1130.435	69.565	9:4	2.250
				49\52		1130.769	69.231	7:3	2.333
					82\87	1131.034	68.966	12:5	2.400
			33\35			1131.429	68.571	5:2	2.500	Semihard 1L 15s
					83\88	1131.818	68.182	13:5	2.600	Unnamed golden tuning
				50\53		1132.075	67.925	8:3	2.667
					67\71	1132.394	67.606	11:4	2.750
		17\18				1133.333	66.667	3:1	3.000	Hard 1L 15s
					52\55	1134.545	65.455	10:3	3.333
				35\37		1135.135	64.865	7:2	3.500
					53\56	1135.714	64.286	11:3	3.667	Sycamore, betic
			18\19			1136.842	63.158	4:1	4.000	Superhard 1L 15s Rhinoceros
					37\39	1138.462	61.538	9:2	4.500	Unicorn
				19\20		1140.000	60.000	5:1	5.000	Hemimiracle
					20\21	1142.857	57.143	6:1	6.000	Hemimiracle, ↓escapade
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 15s

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