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
Related to	5L 3s (oneirotonic)
With tunings	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 is a scale pattern that expands on oneirotonic (5L 3s). This MOS is 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

		cents	2g
3/8		450	900
17/45		453.333	906.667
	31/82	453.512	907.024
14/37		454.054	908.108
	25/66	454.5455	909.091
		454.978	909.956
11/29		455.172	910.345
		455.608	911.825
	30/79	455.696	911.392
		455.782	911.563
	19/50	456	912
	27/71	456.338	912.676
	35/92	456.522	913.043
8/21		457.143	914.286
	29/76	457.684	915.368
		457.955	915.91
	21/55	458.182	916.364
		458.359	916.718
	34/89	458.427	916.854
		458.539	917.078
13/34		458.8235	917.647
	31/81	459.259	918.5185
18/47		459.5745	919.149
23/60		460	920
5/13		461.5385	923.077