13L 8s

↖ 12L 7s	↑ 13L 7s	14L 7s ↗
← 12L 8s	13L 8s	14L 8s →
↙ 12L 9s	↓ 13L 9s	14L 9s ↘

┌╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║║│║│║║│║║│║│║║│║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLsLLsLLsLsLLsLs sLsLLsLsLLsLLsLsLLsLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	8\21 to 5\13 (457.1¢ to 461.5¢)
Dark	8\13 to 13\21 (738.5¢ to 742.9¢)
TAMNAMS information
Descends from	5L 3s (oneirotonic)
Ancestor's step ratio range	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	8L 5s
Sister	8L 13s
Daughters	21L 13s, 13L 21s
Neutralized	5L 16s
2-Flought	34L 8s, 13L 29s
Equal tunings
Equalized (L:s = 1:1)	8\21 (457.1¢)
Supersoft (L:s = 4:3)	29\76 (457.9¢)
Soft (L:s = 3:2)	21\55 (458.2¢)
Semisoft (L:s = 5:3)	34\89 (458.4¢)
Basic (L:s = 2:1)	13\34 (458.8¢)
Semihard (L:s = 5:2)	31\81 (459.3¢)
Hard (L:s = 3:1)	18\47 (459.6¢)
Superhard (L:s = 4:1)	23\60 (460.0¢)
Collapsed (L:s = 1:0)	5\13 (461.5¢)

13L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 8 small steps, repeating every octave. 13L 8s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 457.1¢ to 461.5¢, or from 738.5¢ to 742.9¢.

Modes

Modes of 13L 8s

UDP	Cyclic order	Step pattern
20|0	1	LLsLLsLsLLsLLsLsLLsLs
19|1	9	LLsLLsLsLLsLsLLsLLsLs
18|2	17	LLsLsLLsLLsLsLLsLLsLs
17|3	4	LLsLsLLsLLsLsLLsLsLLs
16|4	12	LLsLsLLsLsLLsLLsLsLLs
15|5	20	LsLLsLLsLsLLsLLsLsLLs
14|6	7	LsLLsLLsLsLLsLsLLsLLs
13|7	15	LsLLsLsLLsLLsLsLLsLLs
12|8	2	LsLLsLsLLsLLsLsLLsLsL
11|9	10	LsLLsLsLLsLsLLsLLsLsL
10|10	18	LsLsLLsLLsLsLLsLLsLsL
9|11	5	LsLsLLsLLsLsLLsLsLLsL
8|12	13	LsLsLLsLsLLsLLsLsLLsL
7|13	21	sLLsLLsLsLLsLLsLsLLsL
6|14	8	sLLsLLsLsLLsLsLLsLLsL
5|15	16	sLLsLsLLsLLsLsLLsLLsL
4|16	3	sLLsLsLLsLLsLsLLsLsLL
3|17	11	sLLsLsLLsLsLLsLLsLsLL
2|18	19	sLsLLsLLsLsLLsLLsLsLL
1|19	6	sLsLLsLLsLsLLsLsLLsLL
0|20	14	sLsLLsLsLLsLLsLsLLsLL

Scale tree

Scale Tree and Tuning Spectrum of 13L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\21						457.143	742.857	1:1	1.000	Equalized 13L 8s
					45\118	457.627	742.373	6:5	1.200
				37\97		457.732	742.268	5:4	1.250
					66\173	457.803	742.197	9:7	1.286
			29\76			457.895	742.105	4:3	1.333	Supersoft 13L 8s
					79\207	457.971	742.029	11:8	1.375
				50\131		458.015	741.985	7:5	1.400
					71\186	458.065	741.935	10:7	1.429
		21\55				458.182	741.818	3:2	1.500	Soft 13L 8s
					76\199	458.291	741.709	11:7	1.571
				55\144		458.333	741.667	8:5	1.600
					89\233	458.369	741.631	13:8	1.625
			34\89			458.427	741.573	5:3	1.667	Semisoft 13L 8s
					81\212	458.491	741.509	12:7	1.714
				47\123		458.537	741.463	7:4	1.750
					60\157	458.599	741.401	9:5	1.800
	13\34					458.824	741.176	2:1	2.000	Basic 13L 8s Scales with tunings softer than this are proper
					57\149	459.060	740.940	9:4	2.250
				44\115		459.130	740.870	7:3	2.333
					75\196	459.184	740.816	12:5	2.400
			31\81			459.259	740.741	5:2	2.500	Semihard 13L 8s
					80\209	459.330	740.670	13:5	2.600
				49\128		459.375	740.625	8:3	2.667
					67\175	459.429	740.571	11:4	2.750
		18\47				459.574	740.426	3:1	3.000	Hard 13L 8s
					59\154	459.740	740.260	10:3	3.333
				41\107		459.813	740.187	7:2	3.500
					64\167	459.880	740.120	11:3	3.667
			23\60			460.000	740.000	4:1	4.000	Superhard 13L 8s
					51\133	460.150	739.850	9:2	4.500
				28\73		460.274	739.726	5:1	5.000
					33\86	460.465	739.535	6:1	6.000
5\13						461.538	738.462	1:0	→ ∞	Collapsed 13L 8s

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