5L 21s

↖ 4L 20s	↑ 5L 20s	6L 20s ↗
← 4L 21s	5L 21s	6L 21s →
↙ 4L 22s	↓ 5L 22s	6L 22s ↘

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││║││││║││││││ ││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLssssLssssLsssss sssssLssssLssssLssssLssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	5\26 to 1\5 (230.8¢ to 240.0¢)
Dark	4\5 to 21\26 (960.0¢ to 969.2¢)
TAMNAMS information
Descends from	5L 1s (machinoid)
Ancestor's step ratio range	5:1 to 1:0
Related MOS scales
Parent	5L 16s
Sister	21L 5s
Daughters	26L 5s, 5L 26s
Neutralized	10L 16s
2-Flought	31L 21s, 5L 47s
Equal tunings
Equalized (L:s = 1:1)	5\26 (230.8¢)
Supersoft (L:s = 4:3)	16\83 (231.3¢)
Soft (L:s = 3:2)	11\57 (231.6¢)
Semisoft (L:s = 5:3)	17\88 (231.8¢)
Basic (L:s = 2:1)	6\31 (232.3¢)
Semihard (L:s = 5:2)	13\67 (232.8¢)
Hard (L:s = 3:1)	7\36 (233.3¢)
Superhard (L:s = 4:1)	8\41 (234.1¢)
Collapsed (L:s = 1:0)	1\5 (240.0¢)

5L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 21 small steps, repeating every octave. 5L 21s is related to 5L 1s, expanding it by 20 tones. Generators that produce this scale range from 230.8¢ to 240¢, or from 960¢ to 969.2¢.

Modes

Modes of 5L 21s

UDP	Cyclic order	Step pattern
25|0	1	LssssLssssLssssLssssLsssss
24|1	6	LssssLssssLssssLsssssLssss
23|2	11	LssssLssssLsssssLssssLssss
22|3	16	LssssLsssssLssssLssssLssss
21|4	21	LsssssLssssLssssLssssLssss
20|5	26	sLssssLssssLssssLssssLssss
19|6	5	sLssssLssssLssssLsssssLsss
18|7	10	sLssssLssssLsssssLssssLsss
17|8	15	sLssssLsssssLssssLssssLsss
16|9	20	sLsssssLssssLssssLssssLsss
15|10	25	ssLssssLssssLssssLssssLsss
14|11	4	ssLssssLssssLssssLsssssLss
13|12	9	ssLssssLssssLsssssLssssLss
12|13	14	ssLssssLsssssLssssLssssLss
11|14	19	ssLsssssLssssLssssLssssLss
10|15	24	sssLssssLssssLssssLssssLss
9|16	3	sssLssssLssssLssssLsssssLs
8|17	8	sssLssssLssssLsssssLssssLs
7|18	13	sssLssssLsssssLssssLssssLs
6|19	18	sssLsssssLssssLssssLssssLs
5|20	23	ssssLssssLssssLssssLssssLs
4|21	2	ssssLssssLssssLssssLsssssL
3|22	7	ssssLssssLssssLsssssLssssL
2|23	12	ssssLssssLsssssLssssLssssL
1|24	17	ssssLsssssLssssLssssLssssL
0|25	22	sssssLssssLssssLssssLssssL

Intervals

Intervals of 5L 21s

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 46.2¢
	Major 1-mosstep	M1ms	L	46.2¢ to 240.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 92.3¢
	Major 2-mosstep	M2ms	L + s	92.3¢ to 240.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 138.5¢
	Major 3-mosstep	M3ms	L + 2s	138.5¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 184.6¢
	Major 4-mosstep	M4ms	L + 3s	184.6¢ to 240.0¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0¢ to 230.8¢
	Perfect 5-mosstep	P5ms	L + 4s	230.8¢ to 240.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0¢ to 276.9¢
	Major 6-mosstep	M6ms	2L + 4s	276.9¢ to 480.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0¢ to 323.1¢
	Major 7-mosstep	M7ms	2L + 5s	323.1¢ to 480.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0¢ to 369.2¢
	Major 8-mosstep	M8ms	2L + 6s	369.2¢ to 480.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	240.0¢ to 415.4¢
	Major 9-mosstep	M9ms	2L + 7s	415.4¢ to 480.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	240.0¢ to 461.5¢
	Major 10-mosstep	M10ms	2L + 8s	461.5¢ to 480.0¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	480.0¢ to 507.7¢
	Major 11-mosstep	M11ms	3L + 8s	507.7¢ to 720.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0¢ to 553.8¢
	Major 12-mosstep	M12ms	3L + 9s	553.8¢ to 720.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	480.0¢ to 600.0¢
	Major 13-mosstep	M13ms	3L + 10s	600.0¢ to 720.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	480.0¢ to 646.2¢
	Major 14-mosstep	M14ms	3L + 11s	646.2¢ to 720.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	480.0¢ to 692.3¢
	Major 15-mosstep	M15ms	3L + 12s	692.3¢ to 720.0¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	720.0¢ to 738.5¢
	Major 16-mosstep	M16ms	4L + 12s	738.5¢ to 960.0¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	720.0¢ to 784.6¢
	Major 17-mosstep	M17ms	4L + 13s	784.6¢ to 960.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	720.0¢ to 830.8¢
	Major 18-mosstep	M18ms	4L + 14s	830.8¢ to 960.0¢
19-mosstep	Minor 19-mosstep	m19ms	3L + 16s	720.0¢ to 876.9¢
	Major 19-mosstep	M19ms	4L + 15s	876.9¢ to 960.0¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	720.0¢ to 923.1¢
	Major 20-mosstep	M20ms	4L + 16s	923.1¢ to 960.0¢
21-mosstep	Perfect 21-mosstep	P21ms	4L + 17s	960.0¢ to 969.2¢
	Augmented 21-mosstep	A21ms	5L + 16s	969.2¢ to 1200.0¢
22-mosstep	Minor 22-mosstep	m22ms	4L + 18s	960.0¢ to 1015.4¢
	Major 22-mosstep	M22ms	5L + 17s	1015.4¢ to 1200.0¢
23-mosstep	Minor 23-mosstep	m23ms	4L + 19s	960.0¢ to 1061.5¢
	Major 23-mosstep	M23ms	5L + 18s	1061.5¢ to 1200.0¢
24-mosstep	Minor 24-mosstep	m24ms	4L + 20s	960.0¢ to 1107.7¢
	Major 24-mosstep	M24ms	5L + 19s	1107.7¢ to 1200.0¢
25-mosstep	Minor 25-mosstep	m25ms	4L + 21s	960.0¢ to 1153.8¢
	Major 25-mosstep	M25ms	5L + 20s	1153.8¢ to 1200.0¢
26-mosstep	Perfect 26-mosstep	P26ms	5L + 21s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 21s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\26						230.769	969.231	1:1	1.000	Equalized 5L 21s
					26\135	231.111	968.889	6:5	1.200
				21\109		231.193	968.807	5:4	1.250
					37\192	231.250	968.750	9:7	1.286
			16\83			231.325	968.675	4:3	1.333	Supersoft 5L 21s
					43\223	231.390	968.610	11:8	1.375
				27\140		231.429	968.571	7:5	1.400
					38\197	231.472	968.528	10:7	1.429
		11\57				231.579	968.421	3:2	1.500	Soft 5L 21s
					39\202	231.683	968.317	11:7	1.571
				28\145		231.724	968.276	8:5	1.600
					45\233	231.760	968.240	13:8	1.625
			17\88			231.818	968.182	5:3	1.667	Semisoft 5L 21s
					40\207	231.884	968.116	12:7	1.714
				23\119		231.933	968.067	7:4	1.750
					29\150	232.000	968.000	9:5	1.800
	6\31					232.258	967.742	2:1	2.000	Basic 5L 21s Scales with tunings softer than this are proper
					25\129	232.558	967.442	9:4	2.250
				19\98		232.653	967.347	7:3	2.333
					32\165	232.727	967.273	12:5	2.400
			13\67			232.836	967.164	5:2	2.500	Semihard 5L 21s
					33\170	232.941	967.059	13:5	2.600
				20\103		233.010	966.990	8:3	2.667
					27\139	233.094	966.906	11:4	2.750
		7\36				233.333	966.667	3:1	3.000	Hard 5L 21s
					22\113	233.628	966.372	10:3	3.333
				15\77		233.766	966.234	7:2	3.500
					23\118	233.898	966.102	11:3	3.667
			8\41			234.146	965.854	4:1	4.000	Superhard 5L 21s
					17\87	234.483	965.517	9:2	4.500
				9\46		234.783	965.217	5:1	5.000
					10\51	235.294	964.706	6:1	6.000
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 21s

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