9L 5s

Todo: confirm Verify temperaments that correspond with 9L 5s

↖ 8L 4s	↑ 9L 4s	10L 4s ↗
← 8L 5s	9L 5s	10L 5s →
↙ 8L 6s	↓ 9L 6s	10L 6s ↘

┌╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║║│║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLLsLLsLs sLsLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\14 to 2\9 (257.1 ¢ to 266.7 ¢)
Dark	7\9 to 11\14 (933.3 ¢ to 942.9 ¢)
TAMNAMS information
Related to	5L 4s (semiquartal)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 4s
Sister	5L 9s
Daughters	14L 9s, 9L 14s
Neutralized	4L 10s
2-Flought	23L 5s, 9L 19s
Equal tunings
Equalized (L:s = 1:1)	3\14 (257.1 ¢)
Supersoft (L:s = 4:3)	11\51 (258.8 ¢)
Soft (L:s = 3:2)	8\37 (259.5 ¢)
Semisoft (L:s = 5:3)	13\60 (260.0 ¢)
Basic (L:s = 2:1)	5\23 (260.9 ¢)
Semihard (L:s = 5:2)	12\55 (261.8 ¢)
Hard (L:s = 3:1)	7\32 (262.5 ¢)
Superhard (L:s = 4:1)	9\41 (263.4 ¢)
Collapsed (L:s = 1:0)	2\9 (266.7 ¢)

9L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 5 small steps, repeating every octave. 9L 5s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 257.1 ¢ to 266.7 ¢, or from 933.3 ¢ to 942.9 ¢. The generator can be said to approximate 7/6, but just 7/6 is larger than 2\9edo, so it cannot be used as a generator. The simplest just interval that works as a generator is 36/31. Two generators are said to create a fourth like Godzilla, but in reality it is closer to 27/20, if that is considered a consonance. 9L5s is third smallest MOS of Semiphore.

Modes

Modes of 9L 5s

UDP	Cyclic order	Step pattern
13|0	1	LLsLLsLLsLLsLs
12|1	4	LLsLLsLLsLsLLs
11|2	7	LLsLLsLsLLsLLs
10|3	10	LLsLsLLsLLsLLs
9|4	13	LsLLsLLsLLsLLs
8|5	2	LsLLsLLsLLsLsL
7|6	5	LsLLsLLsLsLLsL
6|7	8	LsLLsLsLLsLLsL
5|8	11	LsLsLLsLLsLLsL
4|9	14	sLLsLLsLLsLLsL
3|10	3	sLLsLLsLLsLsLL
2|11	6	sLLsLLsLsLLsLL
1|12	9	sLLsLsLLsLLsLL
0|13	12	sLsLLsLLsLLsLL

Intervals

Intervals of 9L 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 85.7 ¢
	Major 1-mosstep	M1ms	L	85.7 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	2L	171.4 ¢ to 266.7 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	133.3 ¢ to 257.1 ¢
	Perfect 3-mosstep	P3ms	2L + s	257.1 ¢ to 266.7 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	266.7 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	3L + s	342.9 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	400.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	4L + s	428.6 ¢ to 533.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	400.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	4L + 2s	514.3 ¢ to 533.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	533.3 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	5L + 2s	600.0 ¢ to 666.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	666.7 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	6L + 2s	685.7 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	666.7 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	6L + 3s	771.4 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	800.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	7L + 3s	857.1 ¢ to 933.3 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	933.3 ¢ to 942.9 ¢
	Augmented 11-mosstep	A11ms	8L + 3s	942.9 ¢ to 1066.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	933.3 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	8L + 4s	1028.6 ¢ to 1066.7 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	1066.7 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	9L + 4s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	9L + 5s	1200.0 ¢