4L 20s

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↖ 3L 19s ↑ 4L 19s 5L 19s ↗
← 3L 20s 4L 20s 5L 20s →
↙ 3L 21s ↓ 4L 21s 5L 21s ↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLsssssLsssssLsssss
sssssLsssssLsssssLsssssL
Equave 2/1 (1200.0¢)
Period 1\4 (300.0¢)
Generator size
Bright 5\24 to 1\4 (250.0¢ to 300.0¢)
Dark 0\4 to 1\24 (0.0¢ to 50.0¢)
TAMNAMS information
Descends from 4L 4s (tetrawood)
Ancestor's step ratio range 5:1 to 1:0
Related MOS scales
Parent 4L 16s
Sister 20L 4s
Daughters 24L 4s, 4L 24s
Neutralized 8L 16s
2-Flought 28L 20s, 4L 44s
Equal tunings
Equalized (L:s = 1:1) 5\24 (250.0¢)
Supersoft (L:s = 4:3) 16\76 (252.6¢)
Soft (L:s = 3:2) 11\52 (253.8¢)
Semisoft (L:s = 5:3) 17\80 (255.0¢)
Basic (L:s = 2:1) 6\28 (257.1¢)
Semihard (L:s = 5:2) 13\60 (260.0¢)
Hard (L:s = 3:1) 7\32 (262.5¢)
Superhard (L:s = 4:1) 8\36 (266.7¢)
Collapsed (L:s = 1:0) 1\4 (300.0¢)

4L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 20 small steps, with a period of 1 large step and 5 small steps that repeats every 300.0¢, or 4 times every octave. 4L 20s is related to 4L 4s, expanding it by 16 tones. Generators that produce this scale range from 250¢ to 300¢, or from 0¢ to 50¢.

Modes

Modes of 4L 20s
UDP Cyclic
order
Step
pattern
20|0(4) 1 LsssssLsssssLsssssLsssss
16|4(4) 6 sLsssssLsssssLsssssLssss
12|8(4) 5 ssLsssssLsssssLsssssLsss
8|12(4) 4 sssLsssssLsssssLsssssLss
4|16(4) 3 ssssLsssssLsssssLsssssLs
0|20(4) 2 sssssLsssssLsssssLsssssL

Scale tree

Scale Tree and Tuning Spectrum of 4L 20s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\24 250.000 50.000 1:1 1.000 Equalized 4L 20s
26\124 251.613 48.387 6:5 1.200
21\100 252.000 48.000 5:4 1.250
37\176 252.273 47.727 9:7 1.286
16\76 252.632 47.368 4:3 1.333 Supersoft 4L 20s
43\204 252.941 47.059 11:8 1.375
27\128 253.125 46.875 7:5 1.400
38\180 253.333 46.667 10:7 1.429
11\52 253.846 46.154 3:2 1.500 Soft 4L 20s
39\184 254.348 45.652 11:7 1.571
28\132 254.545 45.455 8:5 1.600
45\212 254.717 45.283 13:8 1.625
17\80 255.000 45.000 5:3 1.667 Semisoft 4L 20s
40\188 255.319 44.681 12:7 1.714
23\108 255.556 44.444 7:4 1.750
29\136 255.882 44.118 9:5 1.800
6\28 257.143 42.857 2:1 2.000 Basic 4L 20s
Scales with tunings softer than this are proper
25\116 258.621 41.379 9:4 2.250
19\88 259.091 40.909 7:3 2.333
32\148 259.459 40.541 12:5 2.400
13\60 260.000 40.000 5:2 2.500 Semihard 4L 20s
33\152 260.526 39.474 13:5 2.600
20\92 260.870 39.130 8:3 2.667
27\124 261.290 38.710 11:4 2.750
7\32 262.500 37.500 3:1 3.000 Hard 4L 20s
22\100 264.000 36.000 10:3 3.333
15\68 264.706 35.294 7:2 3.500
23\104 265.385 34.615 11:3 3.667
8\36 266.667 33.333 4:1 4.000 Superhard 4L 20s
17\76 268.421 31.579 9:2 4.500
9\40 270.000 30.000 5:1 5.000
10\44 272.727 27.273 6:1 6.000
1\4 300.000 0.000 1:0 → ∞ Collapsed 4L 20s