15L 8s

15L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 8 small steps, repeating every octave. 15L 8s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 156.5 ¢ to 160 ¢, or from 1040 ¢ to 1043.5 ¢.

↖ 14L 7s	↑ 15L 7s	16L 7s ↗
← 14L 8s	15L 8s	16L 8s →
↙ 14L 9s	↓ 15L 9s	16L 9s ↘

Scale structure
Step pattern	LLsLLsLLsLLsLLsLLsLLsLs sLsLLsLLsLLsLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\23 to 2\15 (156.5 ¢ to 160.0 ¢)
Dark	13\15 to 20\23 (1040.0 ¢ to 1043.5 ¢)
TAMNAMS information
Related to	7L 1s (pine)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	8L 7s
Sister	8L 15s
Daughters	23L 15s, 15L 23s
Neutralized	7L 16s
2-Flought	38L 8s, 15L 31s
Equal tunings
Equalized (L:s = 1:1)	3\23 (156.5 ¢)
Supersoft (L:s = 4:3)	11\84 (157.1 ¢)
Soft (L:s = 3:2)	8\61 (157.4 ¢)
Semisoft (L:s = 5:3)	13\99 (157.6 ¢)
Basic (L:s = 2:1)	5\38 (157.9 ¢)
Semihard (L:s = 5:2)	12\91 (158.2 ¢)
Hard (L:s = 3:1)	7\53 (158.5 ¢)
Superhard (L:s = 4:1)	9\68 (158.8 ¢)
Collapsed (L:s = 1:0)	2\15 (160.0 ¢)
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It is the quarter tone scale of Hemikleismic temperament, generated by a 'neutral whole tone'.

Modes

Modes of 15L 8s

UDP	Cyclic order	Step pattern
22|0	1	LLsLLsLLsLLsLLsLLsLLsLs
21|1	4	LLsLLsLLsLLsLLsLLsLsLLs
20|2	7	LLsLLsLLsLLsLLsLsLLsLLs
19|3	10	LLsLLsLLsLLsLsLLsLLsLLs
18|4	13	LLsLLsLLsLsLLsLLsLLsLLs
17|5	16	LLsLLsLsLLsLLsLLsLLsLLs
16|6	19	LLsLsLLsLLsLLsLLsLLsLLs
15|7	22	LsLLsLLsLLsLLsLLsLLsLLs
14|8	2	LsLLsLLsLLsLLsLLsLLsLsL
13|9	5	LsLLsLLsLLsLLsLLsLsLLsL
12|10	8	LsLLsLLsLLsLLsLsLLsLLsL
11|11	11	LsLLsLLsLLsLsLLsLLsLLsL
10|12	14	LsLLsLLsLsLLsLLsLLsLLsL
9|13	17	LsLLsLsLLsLLsLLsLLsLLsL
8|14	20	LsLsLLsLLsLLsLLsLLsLLsL
7|15	23	sLLsLLsLLsLLsLLsLLsLLsL
6|16	3	sLLsLLsLLsLLsLLsLLsLsLL
5|17	6	sLLsLLsLLsLLsLLsLsLLsLL
4|18	9	sLLsLLsLLsLLsLsLLsLLsLL
3|19	12	sLLsLLsLLsLsLLsLLsLLsLL
2|20	15	sLLsLLsLsLLsLLsLLsLLsLL
1|21	18	sLLsLsLLsLLsLLsLLsLLsLL
0|22	21	sLsLLsLLsLLsLLsLLsLLsLL

Intervals

Intervals of 15L 8s

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 52.2 ¢
	Major 1-mosstep	M1ms	L	52.2 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0 ¢ to 104.3 ¢
	Major 2-mosstep	M2ms	2L	104.3 ¢ to 160.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	80.0 ¢ to 156.5 ¢
	Perfect 3-mosstep	P3ms	2L + s	156.5 ¢ to 160.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	160.0 ¢ to 208.7 ¢
	Major 4-mosstep	M4ms	3L + s	208.7 ¢ to 240.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	240.0 ¢ to 260.9 ¢
	Major 5-mosstep	M5ms	4L + s	260.9 ¢ to 320.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	240.0 ¢ to 313.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	313.0 ¢ to 320.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	320.0 ¢ to 365.2 ¢
	Major 7-mosstep	M7ms	5L + 2s	365.2 ¢ to 400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	400.0 ¢ to 417.4 ¢
	Major 8-mosstep	M8ms	6L + 2s	417.4 ¢ to 480.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	400.0 ¢ to 469.6 ¢
	Major 9-mosstep	M9ms	6L + 3s	469.6 ¢ to 480.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	480.0 ¢ to 521.7 ¢
	Major 10-mosstep	M10ms	7L + 3s	521.7 ¢ to 560.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	560.0 ¢ to 573.9 ¢
	Major 11-mosstep	M11ms	8L + 3s	573.9 ¢ to 640.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	560.0 ¢ to 626.1 ¢
	Major 12-mosstep	M12ms	8L + 4s	626.1 ¢ to 640.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	640.0 ¢ to 678.3 ¢
	Major 13-mosstep	M13ms	9L + 4s	678.3 ¢ to 720.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	720.0 ¢ to 730.4 ¢
	Major 14-mosstep	M14ms	10L + 4s	730.4 ¢ to 800.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	9L + 6s	720.0 ¢ to 782.6 ¢
	Major 15-mosstep	M15ms	10L + 5s	782.6 ¢ to 800.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	10L + 6s	800.0 ¢ to 834.8 ¢
	Major 16-mosstep	M16ms	11L + 5s	834.8 ¢ to 880.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	11L + 6s	880.0 ¢ to 887.0 ¢
	Major 17-mosstep	M17ms	12L + 5s	887.0 ¢ to 960.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	11L + 7s	880.0 ¢ to 939.1 ¢
	Major 18-mosstep	M18ms	12L + 6s	939.1 ¢ to 960.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	12L + 7s	960.0 ¢ to 991.3 ¢
	Major 19-mosstep	M19ms	13L + 6s	991.3 ¢ to 1040.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	13L + 7s	1040.0 ¢ to 1043.5 ¢
	Augmented 20-mosstep	A20ms	14L + 6s	1043.5 ¢ to 1120.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	13L + 8s	1040.0 ¢ to 1095.7 ¢
	Major 21-mosstep	M21ms	14L + 7s	1095.7 ¢ to 1120.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	14L + 8s	1120.0 ¢ to 1147.8 ¢
	Major 22-mosstep	M22ms	15L + 7s	1147.8 ¢ to 1200.0 ¢
23-mosstep	Perfect 23-mosstep	P23ms	15L + 8s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 15L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\23						156.522	1043.478	1:1	1.000	Equalized 15L 8s
					17\130	156.923	1043.077	6:5	1.200
				14\107		157.009	1042.991	5:4	1.250
					25\191	157.068	1042.932	9:7	1.286
			11\84			157.143	1042.857	4:3	1.333	Supersoft 15L 8s
					30\229	157.205	1042.795	11:8	1.375
				19\145		157.241	1042.759	7:5	1.400
					27\206	157.282	1042.718	10:7	1.429
		8\61				157.377	1042.623	3:2	1.500	Soft 15L 8s
					29\221	157.466	1042.534	11:7	1.571
				21\160		157.500	1042.500	8:5	1.600
					34\259	157.529	1042.471	13:8	1.625
			13\99			157.576	1042.424	5:3	1.667	Semisoft 15L 8s
					31\236	157.627	1042.373	12:7	1.714
				18\137		157.664	1042.336	7:4	1.750
					23\175	157.714	1042.286	9:5	1.800
	5\38					157.895	1042.105	2:1	2.000	Basic 15L 8s Scales with tunings softer than this are proper
					22\167	158.084	1041.916	9:4	2.250
				17\129		158.140	1041.860	7:3	2.333
					29\220	158.182	1041.818	12:5	2.400
			12\91			158.242	1041.758	5:2	2.500	Semihard 15L 8s
					31\235	158.298	1041.702	13:5	2.600
				19\144		158.333	1041.667	8:3	2.667
					26\197	158.376	1041.624	11:4	2.750
		7\53				158.491	1041.509	3:1	3.000	Hard 15L 8s
					23\174	158.621	1041.379	10:3	3.333
				16\121		158.678	1041.322	7:2	3.500	Hemikleismic (includes 38edo and 53edo)
					25\189	158.730	1041.270	11:3	3.667
			9\68			158.824	1041.176	4:1	4.000	Superhard 15L 8s
					20\151	158.940	1041.060	9:2	4.500
				11\83		159.036	1040.964	5:1	5.000
					13\98	159.184	1040.816	6:1	6.000
2\15						160.000	1040.000	1:0	→ ∞	Collapsed 15L 8s