8L 5s

↖ 7L 4s	↑ 8L 4s	9L 4s ↗
← 7L 5s	8L 5s	9L 5s →
↙ 7L 6s	↓ 8L 6s	9L 6s ↘

┌╥╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║║│║│║║│║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLsLLsLs sLsLLsLsLLsLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	8\13 to 5\8 (738.5¢ to 750.0¢)
Dark	3\8 to 5\13 (450.0¢ to 461.5¢)
TAMNAMS information
Descends from	5L 3s (oneirotonic)
Ancestor's step ratio range	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 3s
Sister	5L 8s
Daughters	13L 8s, 8L 13s
Neutralized	3L 10s
2-Flought	21L 5s, 8L 18s
Equal tunings
Equalized (L:s = 1:1)	8\13 (738.5¢)
Supersoft (L:s = 4:3)	29\47 (740.4¢)
Soft (L:s = 3:2)	21\34 (741.2¢)
Semisoft (L:s = 5:3)	34\55 (741.8¢)
Basic (L:s = 2:1)	13\21 (742.9¢)
Semihard (L:s = 5:2)	31\50 (744.0¢)
Hard (L:s = 3:1)	18\29 (744.8¢)
Superhard (L:s = 4:1)	23\37 (745.9¢)
Collapsed (L:s = 1:0)	5\8 (750.0¢)

8L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 5 small steps, repeating every octave. 8L 5s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 738.5¢ to 750¢, or from 450¢ to 461.5¢. 8L 5s represents the chromatic scale of Semidim, Tridec, Ammonite and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 semisixth, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to logarithmic phi, or even logarithmic phi itself.

Modes

Modes of 8L 5s

UDP	Cyclic order	Step pattern
12|0	1	LLsLLsLsLLsLs
11|1	9	LLsLsLLsLLsLs
10|2	4	LLsLsLLsLsLLs
9|3	12	LsLLsLLsLsLLs
8|4	7	LsLLsLsLLsLLs
7|5	2	LsLLsLsLLsLsL
6|6	10	LsLsLLsLLsLsL
5|7	5	LsLsLLsLsLLsL
4|8	13	sLLsLLsLsLLsL
3|9	8	sLLsLsLLsLLsL
2|10	3	sLLsLsLLsLsLL
1|11	11	sLsLLsLLsLsLL
0|12	6	sLsLLsLsLLsLL

Scale tree

Scale Tree and Tuning Spectrum of 8L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\13						738.462	461.538	1:1	1.000	Equalized 8L 5s
					45\73	739.726	460.274	6:5	1.200
				37\60		740.000	460.000	5:4	1.250
					66\107	740.187	459.813	9:7	1.286
			29\47			740.426	459.574	4:3	1.333	Supersoft 8L 5s
					79\128	740.625	459.375	11:8	1.375
				50\81		740.741	459.259	7:5	1.400
					71\115	740.870	459.130	10:7	1.429
		21\34				741.176	458.824	3:2	1.500	Soft 8L 5s
					76\123	741.463	458.537	11:7	1.571
				55\89		741.573	458.427	8:5	1.600
					89\144	741.667	458.333	13:8	1.625
			34\55			741.818	458.182	5:3	1.667	Semisoft 8L 5s
					81\131	741.985	458.015	12:7	1.714
				47\76		742.105	457.895	7:4	1.750
					60\97	742.268	457.732	9:5	1.800
	13\21					742.857	457.143	2:1	2.000	Basic 8L 5s Scales with tunings softer than this are proper
					57\92	743.478	456.522	9:4	2.250
				44\71		743.662	456.338	7:3	2.333
					75\121	743.802	456.198	12:5	2.400
			31\50			744.000	456.000	5:2	2.500	Semihard 8L 5s
					80\129	744.186	455.814	13:5	2.600
				49\79		744.304	455.696	8:3	2.667
					67\108	744.444	455.556	11:4	2.750
		18\29				744.828	455.172	3:1	3.000	Hard 8L 5s
					59\95	745.263	454.737	10:3	3.333
				41\66		745.455	454.545	7:2	3.500
					64\103	745.631	454.369	11:3	3.667
			23\37			745.946	454.054	4:1	4.000	Superhard 8L 5s
					51\82	746.341	453.659	9:2	4.500
				28\45		746.667	453.333	5:1	5.000
					33\53	747.170	452.830	6:1	6.000
5\8						750.000	450.000	1:0	→ ∞	Collapsed 8L 5s