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)
Required step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 7s
Sister	15L 8s
Daughters	23L 8s 8L 23s
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	Rotational 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

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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