8L 15s

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

┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║││║││║││║││║│││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLssLssLssLssLssLss ssLssLssLssLssLssLssLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	20\23 to 7\8 (1043.5¢ to 1050.0¢)
Dark	1\8 to 3\23 (150.0¢ to 156.5¢)
TAMNAMS information
Descends from	7L 1s (pine)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 7s
Sister	15L 8s
Daughters	23L 8s, 8L 23s
Neutralized	16L 7s
2-Flought	31L 15s, 8L 38s
Equal tunings
Equalized (L:s = 1:1)	20\23 (1043.5¢)
Supersoft (L:s = 4:3)	67\77 (1044.2¢)
Soft (L:s = 3:2)	47\54 (1044.4¢)
Semisoft (L:s = 5:3)	74\85 (1044.7¢)
Basic (L:s = 2:1)	27\31 (1045.2¢)
Semihard (L:s = 5:2)	61\70 (1045.7¢)
Hard (L:s = 3:1)	34\39 (1046.2¢)
Superhard (L:s = 4:1)	41\47 (1046.8¢)
Collapsed (L:s = 1:0)	7\8 (1050.0¢)

8L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 15 small steps, repeating every octave. 8L 15s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 1043.5¢ to 1050¢, or from 150¢ to 156.5¢.

Modes

Modes of 8L 15s

UDP	Cyclic order	Step pattern
22|0	1	LsLssLssLssLssLssLssLss
21|1	21	LssLsLssLssLssLssLssLss
20|2	18	LssLssLsLssLssLssLssLss
19|3	15	LssLssLssLsLssLssLssLss
18|4	12	LssLssLssLssLsLssLssLss
17|5	9	LssLssLssLssLssLsLssLss
16|6	6	LssLssLssLssLssLssLsLss
15|7	3	LssLssLssLssLssLssLssLs
14|8	23	sLsLssLssLssLssLssLssLs
13|9	20	sLssLsLssLssLssLssLssLs
12|10	17	sLssLssLsLssLssLssLssLs
11|11	14	sLssLssLssLsLssLssLssLs
10|12	11	sLssLssLssLssLsLssLssLs
9|13	8	sLssLssLssLssLssLsLssLs
8|14	5	sLssLssLssLssLssLssLsLs
7|15	2	sLssLssLssLssLssLssLssL
6|16	22	ssLsLssLssLssLssLssLssL
5|17	19	ssLssLsLssLssLssLssLssL
4|18	16	ssLssLssLsLssLssLssLssL
3|19	13	ssLssLssLssLsLssLssLssL
2|20	10	ssLssLssLssLssLsLssLssL
1|21	7	ssLssLssLssLssLssLsLssL
0|22	4	ssLssLssLssLssLssLssLsL

Intervals

Intervals of 8L 15s

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 150.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 104.3¢
	Major 2-mosstep	M2ms	L + s	104.3¢ to 150.0¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	150.0¢ to 156.5¢
	Augmented 3-mosstep	A3ms	2L + s	156.5¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	150.0¢ to 208.7¢
	Major 4-mosstep	M4ms	2L + 2s	208.7¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	150.0¢ to 260.9¢
	Major 5-mosstep	M5ms	2L + 3s	260.9¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	300.0¢ to 313.0¢
	Major 6-mosstep	M6ms	3L + 3s	313.0¢ to 450.0¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	300.0¢ to 365.2¢
	Major 7-mosstep	M7ms	3L + 4s	365.2¢ to 450.0¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	300.0¢ to 417.4¢
	Major 8-mosstep	M8ms	3L + 5s	417.4¢ to 450.0¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	450.0¢ to 469.6¢
	Major 9-mosstep	M9ms	4L + 5s	469.6¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	450.0¢ to 521.7¢
	Major 10-mosstep	M10ms	4L + 6s	521.7¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	450.0¢ to 573.9¢
	Major 11-mosstep	M11ms	4L + 7s	573.9¢ to 600.0¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	600.0¢ to 626.1¢
	Major 12-mosstep	M12ms	5L + 7s	626.1¢ to 750.0¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	600.0¢ to 678.3¢
	Major 13-mosstep	M13ms	5L + 8s	678.3¢ to 750.0¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	600.0¢ to 730.4¢
	Major 14-mosstep	M14ms	5L + 9s	730.4¢ to 750.0¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	750.0¢ to 782.6¢
	Major 15-mosstep	M15ms	6L + 9s	782.6¢ to 900.0¢
16-mosstep	Minor 16-mosstep	m16ms	5L + 11s	750.0¢ to 834.8¢
	Major 16-mosstep	M16ms	6L + 10s	834.8¢ to 900.0¢
17-mosstep	Minor 17-mosstep	m17ms	5L + 12s	750.0¢ to 887.0¢
	Major 17-mosstep	M17ms	6L + 11s	887.0¢ to 900.0¢
18-mosstep	Minor 18-mosstep	m18ms	6L + 12s	900.0¢ to 939.1¢
	Major 18-mosstep	M18ms	7L + 11s	939.1¢ to 1050.0¢
19-mosstep	Minor 19-mosstep	m19ms	6L + 13s	900.0¢ to 991.3¢
	Major 19-mosstep	M19ms	7L + 12s	991.3¢ to 1050.0¢
20-mosstep	Diminished 20-mosstep	d20ms	6L + 14s	900.0¢ to 1043.5¢
	Perfect 20-mosstep	P20ms	7L + 13s	1043.5¢ to 1050.0¢
21-mosstep	Minor 21-mosstep	m21ms	7L + 14s	1050.0¢ to 1095.7¢
	Major 21-mosstep	M21ms	8L + 13s	1095.7¢ to 1200.0¢
22-mosstep	Minor 22-mosstep	m22ms	7L + 15s	1050.0¢ to 1147.8¢
	Major 22-mosstep	M22ms	8L + 14s	1147.8¢ to 1200.0¢
23-mosstep	Perfect 23-mosstep	P23ms	8L + 15s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 8L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
20\23						1043.478	156.522	1:1	1.000	Equalized 8L 15s
					107\123	1043.902	156.098	6:5	1.200
				87\100		1044.000	156.000	5:4	1.250
					154\177	1044.068	155.932	9:7	1.286
			67\77			1044.156	155.844	4:3	1.333	Supersoft 8L 15s
					181\208	1044.231	155.769	11:8	1.375
				114\131		1044.275	155.725	7:5	1.400
					161\185	1044.324	155.676	10:7	1.429
		47\54				1044.444	155.556	3:2	1.500	Soft 8L 15s
					168\193	1044.560	155.440	11:7	1.571
				121\139		1044.604	155.396	8:5	1.600
					195\224	1044.643	155.357	13:8	1.625
			74\85			1044.706	155.294	5:3	1.667	Semisoft 8L 15s
					175\201	1044.776	155.224	12:7	1.714
				101\116		1044.828	155.172	7:4	1.750
					128\147	1044.898	155.102	9:5	1.800
	27\31					1045.161	154.839	2:1	2.000	Basic 8L 15s Scales with tunings softer than this are proper
					115\132	1045.455	154.545	9:4	2.250
				88\101		1045.545	154.455	7:3	2.333
					149\171	1045.614	154.386	12:5	2.400
			61\70			1045.714	154.286	5:2	2.500	Semihard 8L 15s
					156\179	1045.810	154.190	13:5	2.600
				95\109		1045.872	154.128	8:3	2.667
					129\148	1045.946	154.054	11:4	2.750
		34\39				1046.154	153.846	3:1	3.000	Hard 8L 15s
					109\125	1046.400	153.600	10:3	3.333
				75\86		1046.512	153.488	7:2	3.500
					116\133	1046.617	153.383	11:3	3.667
			41\47			1046.809	153.191	4:1	4.000	Superhard 8L 15s
					89\102	1047.059	152.941	9:2	4.500
				48\55		1047.273	152.727	5:1	5.000
					55\63	1047.619	152.381	6:1	6.000
7\8						1050.000	150.000	1:0	→ ∞	Collapsed 8L 15s

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