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
Descends from	5L 3s (oneirotonic)
Ancestor's step ratio range	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

Scale tree

Scale Tree and Tuning Spectrum of 5L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\18						466.667	733.333	1:1	1.000	Equalized 5L 13s
					37\95	467.368	732.632	6:5	1.200
				30\77		467.532	732.468	5:4	1.250
					53\136	467.647	732.353	9:7	1.286
			23\59			467.797	732.203	4:3	1.333	Supersoft 5L 13s
					62\159	467.925	732.075	11:8	1.375
				39\100		468.000	732.000	7:5	1.400
					55\141	468.085	731.915	10:7	1.429
		16\41				468.293	731.707	3:2	1.500	Soft 5L 13s
					57\146	468.493	731.507	11:7	1.571
				41\105		468.571	731.429	8:5	1.600
					66\169	468.639	731.361	13:8	1.625
			25\64			468.750	731.250	5:3	1.667	Semisoft 5L 13s
					59\151	468.874	731.126	12:7	1.714
				34\87		468.966	731.034	7:4	1.750
					43\110	469.091	730.909	9:5	1.800
	9\23					469.565	730.435	2:1	2.000	Basic 5L 13s Scales with tunings softer than this are proper
					38\97	470.103	729.897	9:4	2.250
				29\74		470.270	729.730	7:3	2.333
					49\125	470.400	729.600	12:5	2.400
			20\51			470.588	729.412	5:2	2.500	Semihard 5L 13s
					51\130	470.769	729.231	13:5	2.600
				31\79		470.886	729.114	8:3	2.667
					42\107	471.028	728.972	11:4	2.750
		11\28				471.429	728.571	3:1	3.000	Hard 5L 13s
					35\89	471.910	728.090	10:3	3.333
				24\61		472.131	727.869	7:2	3.500
					37\94	472.340	727.660	11:3	3.667
			13\33			472.727	727.273	4:1	4.000	Superhard 5L 13s
					28\71	473.239	726.761	9:2	4.500
				15\38		473.684	726.316	5:1	5.000
					17\43	474.419	725.581	6:1	6.000
2\5						480.000	720.000	1:0	→ ∞	Collapsed 5L 13s

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