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

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

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

This page is a stub. You can help the Xenharmonic Wiki by expanding it.