5L 22s

↖ 4L 21s	↑ 5L 21s	6L 21s ↗
← 4L 22s	5L 22s	6L 22s →
↙ 4L 23s	↓ 5L 23s	6L 23s ↘

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║│││││║││││║││││││ │││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLsssssLssssLsssss sssssLssssLsssssLssssLssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	16\27 to 3\5 (711.1¢ to 720.0¢)
Dark	2\5 to 11\27 (480.0¢ to 488.9¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Ancestor's step ratio range	5:1 to 1:0
Related MOS scales
Parent	5L 17s
Sister	22L 5s
Daughters	27L 5s, 5L 27s
Neutralized	10L 17s
2-Flought	32L 22s, 5L 49s
Equal tunings
Equalized (L:s = 1:1)	16\27 (711.1¢)
Supersoft (L:s = 4:3)	51\86 (711.6¢)
Soft (L:s = 3:2)	35\59 (711.9¢)
Semisoft (L:s = 5:3)	54\91 (712.1¢)
Basic (L:s = 2:1)	19\32 (712.5¢)
Semihard (L:s = 5:2)	41\69 (713.0¢)
Hard (L:s = 3:1)	22\37 (713.5¢)
Superhard (L:s = 4:1)	25\42 (714.3¢)
Collapsed (L:s = 1:0)	3\5 (720.0¢)

5L 22s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 22 small steps, repeating every octave. 5L 22s is related to 5L 2s, expanding it by 20 tones. Generators that produce this scale range from 711.1¢ to 720¢, or from 480¢ to 488.9¢.

Modes

Modes of 5L 22s

UDP	Cyclic order	Step pattern
26|0	1	LssssLssssLsssssLssssLsssss
25|1	17	LssssLsssssLssssLssssLsssss
24|2	6	LssssLsssssLssssLsssssLssss
23|3	22	LsssssLssssLssssLsssssLssss
22|4	11	LsssssLssssLsssssLssssLssss
21|5	27	sLssssLssssLsssssLssssLssss
20|6	16	sLssssLsssssLssssLssssLssss
19|7	5	sLssssLsssssLssssLsssssLsss
18|8	21	sLsssssLssssLssssLsssssLsss
17|9	10	sLsssssLssssLsssssLssssLsss
16|10	26	ssLssssLssssLsssssLssssLsss
15|11	15	ssLssssLsssssLssssLssssLsss
14|12	4	ssLssssLsssssLssssLsssssLss
13|13	20	ssLsssssLssssLssssLsssssLss
12|14	9	ssLsssssLssssLsssssLssssLss
11|15	25	sssLssssLssssLsssssLssssLss
10|16	14	sssLssssLsssssLssssLssssLss
9|17	3	sssLssssLsssssLssssLsssssLs
8|18	19	sssLsssssLssssLssssLsssssLs
7|19	8	sssLsssssLssssLsssssLssssLs
6|20	24	ssssLssssLssssLsssssLssssLs
5|21	13	ssssLssssLsssssLssssLssssLs
4|22	2	ssssLssssLsssssLssssLsssssL
3|23	18	ssssLsssssLssssLssssLsssssL
2|24	7	ssssLsssssLssssLsssssLssssL
1|25	23	sssssLssssLssssLsssssLssssL
0|26	12	sssssLssssLsssssLssssLssssL

Intervals

Intervals of 5L 22s

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 44.4¢
	Major 1-mosstep	M1ms	L	44.4¢ to 240.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 88.9¢
	Major 2-mosstep	M2ms	L + s	88.9¢ to 240.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 133.3¢
	Major 3-mosstep	M3ms	L + 2s	133.3¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 177.8¢
	Major 4-mosstep	M4ms	L + 3s	177.8¢ to 240.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 222.2¢
	Major 5-mosstep	M5ms	L + 4s	222.2¢ to 240.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0¢ to 266.7¢
	Major 6-mosstep	M6ms	2L + 4s	266.7¢ to 480.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0¢ to 311.1¢
	Major 7-mosstep	M7ms	2L + 5s	311.1¢ to 480.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0¢ to 355.6¢
	Major 8-mosstep	M8ms	2L + 6s	355.6¢ to 480.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	240.0¢ to 400.0¢
	Major 9-mosstep	M9ms	2L + 7s	400.0¢ to 480.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	240.0¢ to 444.4¢
	Major 10-mosstep	M10ms	2L + 8s	444.4¢ to 480.0¢
11-mosstep	Perfect 11-mosstep	P11ms	2L + 9s	480.0¢ to 488.9¢
	Augmented 11-mosstep	A11ms	3L + 8s	488.9¢ to 720.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0¢ to 533.3¢
	Major 12-mosstep	M12ms	3L + 9s	533.3¢ to 720.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	480.0¢ to 577.8¢
	Major 13-mosstep	M13ms	3L + 10s	577.8¢ to 720.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	480.0¢ to 622.2¢
	Major 14-mosstep	M14ms	3L + 11s	622.2¢ to 720.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	480.0¢ to 666.7¢
	Major 15-mosstep	M15ms	3L + 12s	666.7¢ to 720.0¢
16-mosstep	Diminished 16-mosstep	d16ms	2L + 14s	480.0¢ to 711.1¢
	Perfect 16-mosstep	P16ms	3L + 13s	711.1¢ to 720.0¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	720.0¢ to 755.6¢
	Major 17-mosstep	M17ms	4L + 13s	755.6¢ to 960.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	720.0¢ to 800.0¢
	Major 18-mosstep	M18ms	4L + 14s	800.0¢ to 960.0¢
19-mosstep	Minor 19-mosstep	m19ms	3L + 16s	720.0¢ to 844.4¢
	Major 19-mosstep	M19ms	4L + 15s	844.4¢ to 960.0¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	720.0¢ to 888.9¢
	Major 20-mosstep	M20ms	4L + 16s	888.9¢ to 960.0¢
21-mosstep	Minor 21-mosstep	m21ms	3L + 18s	720.0¢ to 933.3¢
	Major 21-mosstep	M21ms	4L + 17s	933.3¢ to 960.0¢
22-mosstep	Minor 22-mosstep	m22ms	4L + 18s	960.0¢ to 977.8¢
	Major 22-mosstep	M22ms	5L + 17s	977.8¢ to 1200.0¢
23-mosstep	Minor 23-mosstep	m23ms	4L + 19s	960.0¢ to 1022.2¢
	Major 23-mosstep	M23ms	5L + 18s	1022.2¢ to 1200.0¢
24-mosstep	Minor 24-mosstep	m24ms	4L + 20s	960.0¢ to 1066.7¢
	Major 24-mosstep	M24ms	5L + 19s	1066.7¢ to 1200.0¢
25-mosstep	Minor 25-mosstep	m25ms	4L + 21s	960.0¢ to 1111.1¢
	Major 25-mosstep	M25ms	5L + 20s	1111.1¢ to 1200.0¢
26-mosstep	Minor 26-mosstep	m26ms	4L + 22s	960.0¢ to 1155.6¢
	Major 26-mosstep	M26ms	5L + 21s	1155.6¢ to 1200.0¢
27-mosstep	Perfect 27-mosstep	P27ms	5L + 22s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 22s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
16\27						711.111	488.889	1:1	1.000	Equalized 5L 22s
					83\140	711.429	488.571	6:5	1.200
				67\113		711.504	488.496	5:4	1.250
					118\199	711.558	488.442	9:7	1.286
			51\86			711.628	488.372	4:3	1.333	Supersoft 5L 22s
					137\231	711.688	488.312	11:8	1.375
				86\145		711.724	488.276	7:5	1.400
					121\204	711.765	488.235	10:7	1.429
		35\59				711.864	488.136	3:2	1.500	Soft 5L 22s
					124\209	711.962	488.038	11:7	1.571
				89\150		712.000	488.000	8:5	1.600
					143\241	712.033	487.967	13:8	1.625
			54\91			712.088	487.912	5:3	1.667	Semisoft 5L 22s
					127\214	712.150	487.850	12:7	1.714
				73\123		712.195	487.805	7:4	1.750
					92\155	712.258	487.742	9:5	1.800
	19\32					712.500	487.500	2:1	2.000	Basic 5L 22s Scales with tunings softer than this are proper
					79\133	712.782	487.218	9:4	2.250
				60\101		712.871	487.129	7:3	2.333
					101\170	712.941	487.059	12:5	2.400
			41\69			713.043	486.957	5:2	2.500	Semihard 5L 22s
					104\175	713.143	486.857	13:5	2.600
				63\106		713.208	486.792	8:3	2.667
					85\143	713.287	486.713	11:4	2.750
		22\37				713.514	486.486	3:1	3.000	Hard 5L 22s
					69\116	713.793	486.207	10:3	3.333
				47\79		713.924	486.076	7:2	3.500
					72\121	714.050	485.950	11:3	3.667
			25\42			714.286	485.714	4:1	4.000	Superhard 5L 22s
					53\89	714.607	485.393	9:2	4.500
				28\47		714.894	485.106	5:1	5.000
					31\52	715.385	484.615	6:1	6.000
3\5						720.000	480.000	1:0	→ ∞	Collapsed 5L 22s

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