22L 5s

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

┌╥╥╥╥╥┬╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║│║║║║║│║║║║│║║║║││ │││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLsLLLLsLLLLLsLLLLsLLLLs sLLLLsLLLLsLLLLLsLLLLsLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	11\27 to 9\22 (488.9¢ to 490.9¢)
Dark	13\22 to 16\27 (709.1¢ to 711.1¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Required step ratio range	4:1 to 5:1
Related MOS scales
Parent	5L 17s
Sister	5L 22s
Daughters	27L 22s 22L 27s
Equal tunings
Equalized (L:s = 1:1)	11\27 (488.9¢)
Supersoft (L:s = 4:3)	42\103 (489.3¢)
Soft (L:s = 3:2)	31\76 (489.5¢)
Semisoft (L:s = 5:3)	51\125 (489.6¢)
Basic (L:s = 2:1)	20\49 (489.8¢)
Semihard (L:s = 5:2)	49\120 (490.0¢)
Hard (L:s = 3:1)	29\71 (490.1¢)
Superhard (L:s = 4:1)	38\93 (490.3¢)
Collapsed (L:s = 1:0)	9\22 (490.9¢)

22L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 22 large steps and 5 small steps, repeating every octave. 22L 5s is related to 5L 2s, expanding it by 20 tones. Generators that produce this scale range from 488.9¢ to 490.9¢, or from 709.1¢ to 711.1¢.

Modes

Modes of 22L 5s

UDP	Rotational order	Step pattern
26|0	1	LLLLLsLLLLsLLLLLsLLLLsLLLLs
25|1	12	LLLLLsLLLLsLLLLsLLLLLsLLLLs
24|2	23	LLLLsLLLLLsLLLLsLLLLLsLLLLs
23|3	7	LLLLsLLLLLsLLLLsLLLLsLLLLLs
22|4	18	LLLLsLLLLsLLLLLsLLLLsLLLLLs
21|5	2	LLLLsLLLLsLLLLLsLLLLsLLLLsL
20|6	13	LLLLsLLLLsLLLLsLLLLLsLLLLsL
19|7	24	LLLsLLLLLsLLLLsLLLLLsLLLLsL
18|8	8	LLLsLLLLLsLLLLsLLLLsLLLLLsL
17|9	19	LLLsLLLLsLLLLLsLLLLsLLLLLsL
16|10	3	LLLsLLLLsLLLLLsLLLLsLLLLsLL
15|11	14	LLLsLLLLsLLLLsLLLLLsLLLLsLL
14|12	25	LLsLLLLLsLLLLsLLLLLsLLLLsLL
13|13	9	LLsLLLLLsLLLLsLLLLsLLLLLsLL
12|14	20	LLsLLLLsLLLLLsLLLLsLLLLLsLL
11|15	4	LLsLLLLsLLLLLsLLLLsLLLLsLLL
10|16	15	LLsLLLLsLLLLsLLLLLsLLLLsLLL
9|17	26	LsLLLLLsLLLLsLLLLLsLLLLsLLL
8|18	10	LsLLLLLsLLLLsLLLLsLLLLLsLLL
7|19	21	LsLLLLsLLLLLsLLLLsLLLLLsLLL
6|20	5	LsLLLLsLLLLLsLLLLsLLLLsLLLL
5|21	16	LsLLLLsLLLLsLLLLLsLLLLsLLLL
4|22	27	sLLLLLsLLLLsLLLLLsLLLLsLLLL
3|23	11	sLLLLLsLLLLsLLLLsLLLLLsLLLL
2|24	22	sLLLLsLLLLLsLLLLsLLLLLsLLLL
1|25	6	sLLLLsLLLLLsLLLLsLLLLsLLLLL
0|26	17	sLLLLsLLLLsLLLLLsLLLLsLLLLL

Scale tree

Scale tree and tuning spectrum of 22L 5s

Generator (edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\27						488.889	711.111	1:1	1.000	Equalized 22L 5s
					64\157	489.172	710.828	6:5	1.200
				53\130		489.231	710.769	5:4	1.250
					95\233	489.270	710.730	9:7	1.286
			42\103			489.320	710.680	4:3	1.333	Supersoft 22L 5s
					115\282	489.362	710.638	11:8	1.375
				73\179		489.385	710.615	7:5	1.400
					104\255	489.412	710.588	10:7	1.429
		31\76				489.474	710.526	3:2	1.500	Soft 22L 5s
					113\277	489.531	710.469	11:7	1.571
				82\201		489.552	710.448	8:5	1.600
					133\326	489.571	710.429	13:8	1.625
			51\125			489.600	710.400	5:3	1.667	Semisoft 22L 5s
					122\299	489.632	710.368	12:7	1.714
				71\174		489.655	710.345	7:4	1.750
					91\223	489.686	710.314	9:5	1.800
	20\49					489.796	710.204	2:1	2.000	Basic 22L 5s Scales with tunings softer than this are proper
					89\218	489.908	710.092	9:4	2.250
				69\169		489.941	710.059	7:3	2.333
					118\289	489.965	710.035	12:5	2.400
			49\120			490.000	710.000	5:2	2.500	Semihard 22L 5s
					127\311	490.032	709.968	13:5	2.600
				78\191		490.052	709.948	8:3	2.667
					107\262	490.076	709.924	11:4	2.750
		29\71				490.141	709.859	3:1	3.000	Hard 22L 5s
					96\235	490.213	709.787	10:3	3.333
				67\164		490.244	709.756	7:2	3.500
					105\257	490.272	709.728	11:3	3.667
			38\93			490.323	709.677	4:1	4.000	Superhard 22L 5s
					85\208	490.385	709.615	9:2	4.500
				47\115		490.435	709.565	5:1	5.000
					56\137	490.511	709.489	6:1	6.000
9\22						490.909	709.091	1:0	→ ∞	Collapsed 22L 5s

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