9L 13s

↖ 8L 12s	↑ 9L 12s	10L 12s ↗
← 8L 13s	9L 13s	10L 13s →
↙ 8L 14s	↓ 9L 14s	10L 14s ↘

┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║││║│║││║│║│││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLssLsLssLsLssLsLss ssLsLssLsLssLsLssLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	17\22 to 7\9 (927.3 ¢ to 933.3 ¢)
Dark	2\9 to 5\22 (266.7 ¢ to 272.7 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	9L 4s
Sister	13L 9s
Daughters	22L 9s, 9L 22s
Neutralized	18L 4s
2-Flought	31L 13s, 9L 35s
Equal tunings
Equalized (L:s = 1:1)	17\22 (927.3 ¢)
Supersoft (L:s = 4:3)	58\75 (928.0 ¢)
Soft (L:s = 3:2)	41\53 (928.3 ¢)
Semisoft (L:s = 5:3)	65\84 (928.6 ¢)
Basic (L:s = 2:1)	24\31 (929.0 ¢)
Semihard (L:s = 5:2)	55\71 (929.6 ¢)
Hard (L:s = 3:1)	31\40 (930.0 ¢)
Superhard (L:s = 4:1)	38\49 (930.6 ¢)
Collapsed (L:s = 1:0)	7\9 (933.3 ¢)

9L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 13 small steps, repeating every octave. 9L 13s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 927.3 ¢ to 933.3 ¢, or from 266.7 ¢ to 272.7 ¢.

Modes

Modes of 9L 13s

UDP	Cyclic order	Step pattern
21|0	1	LsLsLssLsLssLsLssLsLss
20|1	18	LsLssLsLsLssLsLssLsLss
19|2	13	LsLssLsLssLsLsLssLsLss
18|3	8	LsLssLsLssLsLssLsLsLss
17|4	3	LsLssLsLssLsLssLsLssLs
16|5	20	LssLsLsLssLsLssLsLssLs
15|6	15	LssLsLssLsLsLssLsLssLs
14|7	10	LssLsLssLsLssLsLsLssLs
13|8	5	LssLsLssLsLssLsLssLsLs
12|9	22	sLsLsLssLsLssLsLssLsLs
11|10	17	sLsLssLsLsLssLsLssLsLs
10|11	12	sLsLssLsLssLsLsLssLsLs
9|12	7	sLsLssLsLssLsLssLsLsLs
8|13	2	sLsLssLsLssLsLssLsLssL
7|14	19	sLssLsLsLssLsLssLsLssL
6|15	14	sLssLsLssLsLsLssLsLssL
5|16	9	sLssLsLssLsLssLsLsLssL
4|17	4	sLssLsLssLsLssLsLssLsL
3|18	21	ssLsLsLssLsLssLsLssLsL
2|19	16	ssLsLssLsLsLssLsLssLsL
1|20	11	ssLsLssLsLssLsLsLssLsL
0|21	6	ssLsLssLsLssLsLssLsLsL

Intervals

Intervals of 9L 13s

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 54.5 ¢
	Major 1-mosstep	M1ms	L	54.5 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 109.1 ¢
	Major 2-mosstep	M2ms	L + s	109.1 ¢ to 133.3 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	133.3 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	2L + s	163.6 ¢ to 266.7 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	133.3 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	218.2 ¢ to 266.7 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	266.7 ¢ to 272.7 ¢
	Augmented 5-mosstep	A5ms	3L + 2s	272.7 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	266.7 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	3L + 3s	327.3 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	266.7 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	3L + 4s	381.8 ¢ to 400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	400.0 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	4L + 4s	436.4 ¢ to 533.3 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	400.0 ¢ to 490.9 ¢
	Major 9-mosstep	M9ms	4L + 5s	490.9 ¢ to 533.3 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	533.3 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	5L + 5s	545.5 ¢ to 666.7 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	533.3 ¢ to 600.0 ¢
	Major 11-mosstep	M11ms	5L + 6s	600.0 ¢ to 666.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	533.3 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	5L + 7s	654.5 ¢ to 666.7 ¢
13-mosstep	Minor 13-mosstep	m13ms	5L + 8s	666.7 ¢ to 709.1 ¢
	Major 13-mosstep	M13ms	6L + 7s	709.1 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	666.7 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	6L + 8s	763.6 ¢ to 800.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	800.0 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	7L + 8s	818.2 ¢ to 933.3 ¢
16-mosstep	Minor 16-mosstep	m16ms	6L + 10s	800.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	7L + 9s	872.7 ¢ to 933.3 ¢
17-mosstep	Diminished 17-mosstep	d17ms	6L + 11s	800.0 ¢ to 927.3 ¢
	Perfect 17-mosstep	P17ms	7L + 10s	927.3 ¢ to 933.3 ¢
18-mosstep	Minor 18-mosstep	m18ms	7L + 11s	933.3 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	8L + 10s	981.8 ¢ to 1066.7 ¢
19-mosstep	Minor 19-mosstep	m19ms	7L + 12s	933.3 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	8L + 11s	1036.4 ¢ to 1066.7 ¢
20-mosstep	Minor 20-mosstep	m20ms	8L + 12s	1066.7 ¢ to 1090.9 ¢
	Major 20-mosstep	M20ms	9L + 11s	1090.9 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	8L + 13s	1066.7 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	9L + 12s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	9L + 13s	1200.0 ¢

Scale tree

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