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
Related to	5L 2s (diatonic)
With tunings	4:1 to 5:1
Related MOS scales
Parent	5L 17s
Sister	5L 22s
Daughters	27L 22s, 22L 27s
Neutralized	17L 10s
2-Flought	49L 5s, 22L 32s
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 ¢)
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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 ¢.

This scale corresponds to the 27-note MOS of superpyth temperament, and it's tuning range is the same as the tuning rannge of 11-limit superpyth. 22edo can be considered a collapsed version of this scale, while 27edo is an equalized version of this scale. The basic tuning of this scale is 49edo, which is more optimized for superpyth temperament.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 22L 5s

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 54.5 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	54.5 ¢ to 88.9 ¢
	Major 2-mosstep	M2ms	2L	88.9 ¢ to 109.1 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	109.1 ¢ to 133.3 ¢
	Major 3-mosstep	M3ms	3L	133.3 ¢ to 163.6 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	163.6 ¢ to 177.8 ¢
	Major 4-mosstep	M4ms	4L	177.8 ¢ to 218.2 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	218.2 ¢ to 222.2 ¢
	Major 5-mosstep	M5ms	5L	222.2 ¢ to 272.7 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	218.2 ¢ to 266.7 ¢
	Major 6-mosstep	M6ms	5L + s	266.7 ¢ to 272.7 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	272.7 ¢ to 311.1 ¢
	Major 7-mosstep	M7ms	6L + s	311.1 ¢ to 327.3 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	327.3 ¢ to 355.6 ¢
	Major 8-mosstep	M8ms	7L + s	355.6 ¢ to 381.8 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	381.8 ¢ to 400.0 ¢
	Major 9-mosstep	M9ms	8L + s	400.0 ¢ to 436.4 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	436.4 ¢ to 444.4 ¢
	Major 10-mosstep	M10ms	9L + s	444.4 ¢ to 490.9 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	436.4 ¢ to 488.9 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	488.9 ¢ to 490.9 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	490.9 ¢ to 533.3 ¢
	Major 12-mosstep	M12ms	10L + 2s	533.3 ¢ to 545.5 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	545.5 ¢ to 577.8 ¢
	Major 13-mosstep	M13ms	11L + 2s	577.8 ¢ to 600.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	600.0 ¢ to 622.2 ¢
	Major 14-mosstep	M14ms	12L + 2s	622.2 ¢ to 654.5 ¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	654.5 ¢ to 666.7 ¢
	Major 15-mosstep	M15ms	13L + 2s	666.7 ¢ to 709.1 ¢
16-mosstep	Perfect 16-mosstep	P16ms	13L + 3s	709.1 ¢ to 711.1 ¢
	Augmented 16-mosstep	A16ms	14L + 2s	711.1 ¢ to 763.6 ¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	709.1 ¢ to 755.6 ¢
	Major 17-mosstep	M17ms	14L + 3s	755.6 ¢ to 763.6 ¢
18-mosstep	Minor 18-mosstep	m18ms	14L + 4s	763.6 ¢ to 800.0 ¢
	Major 18-mosstep	M18ms	15L + 3s	800.0 ¢ to 818.2 ¢
19-mosstep	Minor 19-mosstep	m19ms	15L + 4s	818.2 ¢ to 844.4 ¢
	Major 19-mosstep	M19ms	16L + 3s	844.4 ¢ to 872.7 ¢
20-mosstep	Minor 20-mosstep	m20ms	16L + 4s	872.7 ¢ to 888.9 ¢
	Major 20-mosstep	M20ms	17L + 3s	888.9 ¢ to 927.3 ¢
21-mosstep	Minor 21-mosstep	m21ms	17L + 4s	927.3 ¢ to 933.3 ¢
	Major 21-mosstep	M21ms	18L + 3s	933.3 ¢ to 981.8 ¢
22-mosstep	Minor 22-mosstep	m22ms	17L + 5s	927.3 ¢ to 977.8 ¢
	Major 22-mosstep	M22ms	18L + 4s	977.8 ¢ to 981.8 ¢
23-mosstep	Minor 23-mosstep	m23ms	18L + 5s	981.8 ¢ to 1022.2 ¢
	Major 23-mosstep	M23ms	19L + 4s	1022.2 ¢ to 1036.4 ¢
24-mosstep	Minor 24-mosstep	m24ms	19L + 5s	1036.4 ¢ to 1066.7 ¢
	Major 24-mosstep	M24ms	20L + 4s	1066.7 ¢ to 1090.9 ¢
25-mosstep	Minor 25-mosstep	m25ms	20L + 5s	1090.9 ¢ to 1111.1 ¢
	Major 25-mosstep	M25ms	21L + 4s	1111.1 ¢ to 1145.5 ¢
26-mosstep	Minor 26-mosstep	m26ms	21L + 5s	1145.5 ¢ to 1155.6 ¢
	Major 26-mosstep	M26ms	22L + 4s	1155.6 ¢ to 1200.0 ¢
27-mosstep	Perfect 27-mosstep	P27ms	22L + 5s	1200.0 ¢

Generator chain

Generator chain of 22L 5s

Bright gens	Scale degree	Abbrev.
48	Augmented 15-mosdegree	A15md
47	Augmented 4-mosdegree	A4md
46	Augmented 20-mosdegree	A20md
45	Augmented 9-mosdegree	A9md
44	Augmented 25-mosdegree	A25md
43	Augmented 14-mosdegree	A14md
42	Augmented 3-mosdegree	A3md
41	Augmented 19-mosdegree	A19md
40	Augmented 8-mosdegree	A8md
39	Augmented 24-mosdegree	A24md
38	Augmented 13-mosdegree	A13md
37	Augmented 2-mosdegree	A2md
36	Augmented 18-mosdegree	A18md
35	Augmented 7-mosdegree	A7md
34	Augmented 23-mosdegree	A23md
33	Augmented 12-mosdegree	A12md
32	Augmented 1-mosdegree	A1md
31	Augmented 17-mosdegree	A17md
30	Augmented 6-mosdegree	A6md
29	Augmented 22-mosdegree	A22md
28	Augmented 11-mosdegree	A11md
27	Augmented 0-mosdegree	A0md
26	Augmented 16-mosdegree	A16md
25	Major 5-mosdegree	M5md
24	Major 21-mosdegree	M21md
23	Major 10-mosdegree	M10md
22	Major 26-mosdegree	M26md
21	Major 15-mosdegree	M15md
20	Major 4-mosdegree	M4md
19	Major 20-mosdegree	M20md
18	Major 9-mosdegree	M9md
17	Major 25-mosdegree	M25md
16	Major 14-mosdegree	M14md
15	Major 3-mosdegree	M3md
14	Major 19-mosdegree	M19md
13	Major 8-mosdegree	M8md
12	Major 24-mosdegree	M24md
11	Major 13-mosdegree	M13md
10	Major 2-mosdegree	M2md
9	Major 18-mosdegree	M18md
8	Major 7-mosdegree	M7md
7	Major 23-mosdegree	M23md
6	Major 12-mosdegree	M12md
5	Major 1-mosdegree	M1md
4	Major 17-mosdegree	M17md
3	Major 6-mosdegree	M6md
2	Major 22-mosdegree	M22md
1	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 27-mosdegree	P0md P27md
−1	Perfect 16-mosdegree	P16md
−2	Minor 5-mosdegree	m5md
−3	Minor 21-mosdegree	m21md
−4	Minor 10-mosdegree	m10md
−5	Minor 26-mosdegree	m26md
−6	Minor 15-mosdegree	m15md
−7	Minor 4-mosdegree	m4md
−8	Minor 20-mosdegree	m20md
−9	Minor 9-mosdegree	m9md
−10	Minor 25-mosdegree	m25md
−11	Minor 14-mosdegree	m14md
−12	Minor 3-mosdegree	m3md
−13	Minor 19-mosdegree	m19md
−14	Minor 8-mosdegree	m8md
−15	Minor 24-mosdegree	m24md
−16	Minor 13-mosdegree	m13md
−17	Minor 2-mosdegree	m2md
−18	Minor 18-mosdegree	m18md
−19	Minor 7-mosdegree	m7md
−20	Minor 23-mosdegree	m23md
−21	Minor 12-mosdegree	m12md
−22	Minor 1-mosdegree	m1md
−23	Minor 17-mosdegree	m17md
−24	Minor 6-mosdegree	m6md
−25	Minor 22-mosdegree	m22md
−26	Diminished 11-mosdegree	d11md
−27	Diminished 27-mosdegree	d27md
−28	Diminished 16-mosdegree	d16md
−29	Diminished 5-mosdegree	d5md
−30	Diminished 21-mosdegree	d21md
−31	Diminished 10-mosdegree	d10md
−32	Diminished 26-mosdegree	d26md
−33	Diminished 15-mosdegree	d15md
−34	Diminished 4-mosdegree	d4md
−35	Diminished 20-mosdegree	d20md
−36	Diminished 9-mosdegree	d9md
−37	Diminished 25-mosdegree	d25md
−38	Diminished 14-mosdegree	d14md
−39	Diminished 3-mosdegree	d3md
−40	Diminished 19-mosdegree	d19md
−41	Diminished 8-mosdegree	d8md
−42	Diminished 24-mosdegree	d24md
−43	Diminished 13-mosdegree	d13md
−44	Diminished 2-mosdegree	d2md
−45	Diminished 18-mosdegree	d18md
−46	Diminished 7-mosdegree	d7md
−47	Diminished 23-mosdegree	d23md
−48	Diminished 12-mosdegree	d12md

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