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

Intervals

Intervals of 8L 5s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	150.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 300.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	150.0 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	2L + s	276.9 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	300.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	3L + s	369.2 ¢ to 450.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	450.0 ¢ to 461.5 ¢
	Augmented 5-mosstep	A5ms	4L + s	461.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	450.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	4L + 2s	553.8 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	600.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	5L + 2s	646.2 ¢ to 750.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	4L + 4s	600.0 ¢ to 738.5 ¢
	Perfect 8-mosstep	P8ms	5L + 3s	738.5 ¢ to 750.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	750.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	6L + 3s	830.8 ¢ to 900.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	900.0 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	7L + 3s	923.1 ¢ to 1050.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	900.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	7L + 4s	1015.4 ¢ to 1050.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	1050.0 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	8L + 4s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	8L + 5s	1200.0 ¢