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 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