5L 13s

↖ 4L 12s	↑ 5L 12s	6L 12s ↗
← 4L 13s	5L 13s	6L 13s →
↙ 4L 14s	↓ 5L 14s	6L 14s ↘

┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬┬┐ │║││║│││║││║│││║││││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLsssLssLsssLsss sssLsssLssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\18 to 2\5 (466.7 ¢ to 480.0 ¢)
Dark	3\5 to 11\18 (720.0 ¢ to 733.3 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	5L 8s
Sister	13L 5s
Daughters	18L 5s, 5L 18s
Neutralized	10L 8s
2-Flought	23L 13s, 5L 31s
Equal tunings
Equalized (L:s = 1:1)	7\18 (466.7 ¢)
Supersoft (L:s = 4:3)	23\59 (467.8 ¢)
Soft (L:s = 3:2)	16\41 (468.3 ¢)
Semisoft (L:s = 5:3)	25\64 (468.8 ¢)
Basic (L:s = 2:1)	9\23 (469.6 ¢)
Semihard (L:s = 5:2)	20\51 (470.6 ¢)
Hard (L:s = 3:1)	11\28 (471.4 ¢)
Superhard (L:s = 4:1)	13\33 (472.7 ¢)
Collapsed (L:s = 1:0)	2\5 (480.0 ¢)

5L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 13 small steps, repeating every octave. 5L 13s is a grandchild scale of 5L 3s, expanding it by 10 tones. Generators that produce this scale range from 466.7 ¢ to 480 ¢, or from 720 ¢ to 733.3 ¢.

Modes

Modes of 5L 13s

UDP	Cyclic order	Step pattern
17|0	1	LssLsssLssLsssLsss
16|1	8	LssLsssLsssLssLsss
15|2	15	LsssLssLsssLssLsss
14|3	4	LsssLssLsssLsssLss
13|4	11	LsssLsssLssLsssLss
12|5	18	sLssLsssLssLsssLss
11|6	7	sLssLsssLsssLssLss
10|7	14	sLsssLssLsssLssLss
9|8	3	sLsssLssLsssLsssLs
8|9	10	sLsssLsssLssLsssLs
7|10	17	ssLssLsssLssLsssLs
6|11	6	ssLssLsssLsssLssLs
5|12	13	ssLsssLssLsssLssLs
4|13	2	ssLsssLssLsssLsssL
3|14	9	ssLsssLsssLssLsssL
2|15	16	sssLssLsssLssLsssL
1|16	5	sssLssLsssLsssLssL
0|17	12	sssLsssLssLsssLssL

Intervals

Intervals of 5L 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 66.7 ¢
	Major 1-mosstep	M1ms	L	66.7 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 133.3 ¢
	Major 2-mosstep	M2ms	L + s	133.3 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 200.0 ¢
	Major 3-mosstep	M3ms	L + 2s	200.0 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 266.7 ¢
	Major 4-mosstep	M4ms	2L + 2s	266.7 ¢ to 480.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 333.3 ¢
	Major 5-mosstep	M5ms	2L + 3s	333.3 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 400.0 ¢
	Major 6-mosstep	M6ms	2L + 4s	400.0 ¢ to 480.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	240.0 ¢ to 466.7 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	466.7 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	480.0 ¢ to 533.3 ¢
	Major 8-mosstep	M8ms	3L + 5s	533.3 ¢ to 720.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	480.0 ¢ to 600.0 ¢
	Major 9-mosstep	M9ms	3L + 6s	600.0 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	480.0 ¢ to 666.7 ¢
	Major 10-mosstep	M10ms	3L + 7s	666.7 ¢ to 720.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	720.0 ¢ to 733.3 ¢
	Augmented 11-mosstep	A11ms	4L + 7s	733.3 ¢ to 960.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	720.0 ¢ to 800.0 ¢
	Major 12-mosstep	M12ms	4L + 8s	800.0 ¢ to 960.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	720.0 ¢ to 866.7 ¢
	Major 13-mosstep	M13ms	4L + 9s	866.7 ¢ to 960.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	720.0 ¢ to 933.3 ¢
	Major 14-mosstep	M14ms	4L + 10s	933.3 ¢ to 960.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	960.0 ¢ to 1000.0 ¢
	Major 15-mosstep	M15ms	5L + 10s	1000.0 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	960.0 ¢ to 1066.7 ¢
	Major 16-mosstep	M16ms	5L + 11s	1066.7 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	4L + 13s	960.0 ¢ to 1133.3 ¢
	Major 17-mosstep	M17ms	5L + 12s	1133.3 ¢ to 1200.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	5L + 13s	1200.0 ¢

Scale tree

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