1L 20s

1L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 20 small steps, repeating every octave. 1L 20s is related to 1L 9s, expanding it by 11 tones. Generators that produce this scale range from 1142.9 ¢ to 1200 ¢, or from 0 ¢ to 57.1 ¢.

	↑ 1L 19s	2L 19s ↗
	1L 20s	2L 20s →
	↓ 1L 21s	2L 21s ↘

Scale structure
Step pattern	Lssssssssssssssssssss ssssssssssssssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	20\21 to 1\1 (1142.9 ¢ to 1200.0 ¢)
Dark	0\1 to 1\21 (0.0 ¢ to 57.1 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	12:1 to 1:0
Related MOS scales
Parent	1L 19s
Sister	20L 1s
Daughters	21L 1s, 1L 21s
Neutralized	2L 19s
2-Flought	22L 20s, 1L 41s
Equal tunings
Equalized (L:s = 1:1)	20\21 (1142.9 ¢)
Supersoft (L:s = 4:3)	61\64 (1143.8 ¢)
Soft (L:s = 3:2)	41\43 (1144.2 ¢)
Semisoft (L:s = 5:3)	62\65 (1144.6 ¢)
Basic (L:s = 2:1)	21\22 (1145.5 ¢)
Semihard (L:s = 5:2)	43\45 (1146.7 ¢)
Hard (L:s = 3:1)	22\23 (1147.8 ¢)
Superhard (L:s = 4:1)	23\24 (1150.0 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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Modes

Modes of 1L 20s

UDP	Cyclic order	Step pattern
20|0	1	Lssssssssssssssssssss
19|1	21	sLsssssssssssssssssss
18|2	20	ssLssssssssssssssssss
17|3	19	sssLsssssssssssssssss
16|4	18	ssssLssssssssssssssss
15|5	17	sssssLsssssssssssssss
14|6	16	ssssssLssssssssssssss
13|7	15	sssssssLsssssssssssss
12|8	14	ssssssssLssssssssssss
11|9	13	sssssssssLsssssssssss
10|10	12	ssssssssssLssssssssss
9|11	11	sssssssssssLsssssssss
8|12	10	ssssssssssssLssssssss
7|13	9	sssssssssssssLsssssss
6|14	8	ssssssssssssssLssssss
5|15	7	sssssssssssssssLsssss
4|16	6	ssssssssssssssssLssss
3|17	5	sssssssssssssssssLsss
2|18	4	ssssssssssssssssssLss
1|19	3	sssssssssssssssssssLs
0|20	2	ssssssssssssssssssssL

Intervals

Intervals of 1L 20s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 57.1 ¢
	Augmented 1-mosstep	A1ms	L	57.1 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 114.3 ¢
	Major 2-mosstep	M2ms	L + s	114.3 ¢ to 1200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 171.4 ¢
	Major 3-mosstep	M3ms	L + 2s	171.4 ¢ to 1200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 228.6 ¢
	Major 4-mosstep	M4ms	L + 3s	228.6 ¢ to 1200.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 285.7 ¢
	Major 5-mosstep	M5ms	L + 4s	285.7 ¢ to 1200.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 342.9 ¢
	Major 6-mosstep	M6ms	L + 5s	342.9 ¢ to 1200.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 400.0 ¢
	Major 7-mosstep	M7ms	L + 6s	400.0 ¢ to 1200.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0 ¢ to 457.1 ¢
	Major 8-mosstep	M8ms	L + 7s	457.1 ¢ to 1200.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0 ¢ to 514.3 ¢
	Major 9-mosstep	M9ms	L + 8s	514.3 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	10s	0.0 ¢ to 571.4 ¢
	Major 10-mosstep	M10ms	L + 9s	571.4 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	11s	0.0 ¢ to 628.6 ¢
	Major 11-mosstep	M11ms	L + 10s	628.6 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	12s	0.0 ¢ to 685.7 ¢
	Major 12-mosstep	M12ms	L + 11s	685.7 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	13s	0.0 ¢ to 742.9 ¢
	Major 13-mosstep	M13ms	L + 12s	742.9 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	14s	0.0 ¢ to 800.0 ¢
	Major 14-mosstep	M14ms	L + 13s	800.0 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	15s	0.0 ¢ to 857.1 ¢
	Major 15-mosstep	M15ms	L + 14s	857.1 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	16s	0.0 ¢ to 914.3 ¢
	Major 16-mosstep	M16ms	L + 15s	914.3 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	17s	0.0 ¢ to 971.4 ¢
	Major 17-mosstep	M17ms	L + 16s	971.4 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	18s	0.0 ¢ to 1028.6 ¢
	Major 18-mosstep	M18ms	L + 17s	1028.6 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	19s	0.0 ¢ to 1085.7 ¢
	Major 19-mosstep	M19ms	L + 18s	1085.7 ¢ to 1200.0 ¢
20-mosstep	Diminished 20-mosstep	d20ms	20s	0.0 ¢ to 1142.9 ¢
	Perfect 20-mosstep	P20ms	L + 19s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	L + 20s	1200.0 ¢

Scale tree

1L 20s is generated by the 22&43 temperament, which is available in 22edo and 43edo, both of which are quite popular among xenharmonic composers for their ‘smooth’ or ‘rounded’ sound and strong JI approximations — 22edo as a zeta peak and the smallest full 11-limit edo, 43edo as the optimal tuning of meantone by some metrics and a compromise option between 12edo and 31edo. This temperament might appeal to those who like both those tunings. It also occurs in 65edo and 87edo (both unusually accurate tunings) and 152edo (another zeta peak like 22).

Scale tree and tuning spectrum of 1L 20s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
20\21						1142.857	57.143	1:1	1.000	Equalized 1L 20s
					101\106	1143.396	56.604	6:5	1.200
				81\85		1143.529	56.471	5:4	1.250
					142\149	1143.624	56.376	9:7	1.286
			61\64			1143.750	56.250	4:3	1.333	Supersoft 1L 20s
					163\171	1143.860	56.140	11:8	1.375
				102\107		1143.925	56.075	7:5	1.400
					143\150	1144.000	56.000	10:7	1.429
		41\43				1144.186	55.814	3:2	1.500	Soft 1L 20s
					144\151	1144.371	55.629	11:7	1.571
				103\108		1144.444	55.556	8:5	1.600
					165\173	1144.509	55.491	13:8	1.625
			62\65			1144.615	55.385	5:3	1.667	Semisoft 1L 20s
					145\152	1144.737	55.263	12:7	1.714
				83\87		1144.828	55.172	7:4	1.750
					104\109	1144.954	55.046	9:5	1.800
	21\22					1145.455	54.545	2:1	2.000	Basic 1L 20s Scales with tunings softer than this are proper
					85\89	1146.067	53.933	9:4	2.250
				64\67		1146.269	53.731	7:3	2.333
					107\112	1146.429	53.571	12:5	2.400
			43\45			1146.667	53.333	5:2	2.500	Semihard 1L 20s
					108\113	1146.903	53.097	13:5	2.600
				65\68		1147.059	52.941	8:3	2.667
					87\91	1147.253	52.747	11:4	2.750
		22\23				1147.826	52.174	3:1	3.000	Hard 1L 20s
					67\70	1148.571	51.429	10:3	3.333
				45\47		1148.936	51.064	7:2	3.500
					68\71	1149.296	50.704	11:3	3.667
			23\24			1150.000	50.000	4:1	4.000	Superhard 1L 20s
					47\49	1151.020	48.980	9:2	4.500
				24\25		1152.000	48.000	5:1	5.000
					25\26	1153.846	46.154	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 20s

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