1L 20s

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↑ 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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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 ¢.

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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