4L 20s

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↖ 3L 19s ↑ 4L 19s 5L 19s ↗
← 3L 20s 4L 20s 5L 20s →
↙ 3L 21s ↓ 4L 21s 5L 21s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐
│║│││││║│││││║│││││║││││││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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

Intervals

Intervals of 4L 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 50.0¢
Augmented 1-mosstep A1ms L 50.0¢ to 300.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 100.0¢
Major 2-mosstep M2ms L + s 100.0¢ to 300.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 150.0¢
Major 3-mosstep M3ms L + 2s 150.0¢ to 300.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 200.0¢
Major 4-mosstep M4ms L + 3s 200.0¢ to 300.0¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0¢ to 250.0¢
Perfect 5-mosstep P5ms L + 4s 250.0¢ to 300.0¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 300.0¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 300.0¢ to 350.0¢
Augmented 7-mosstep A7ms 2L + 5s 350.0¢ to 600.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 300.0¢ to 400.0¢
Major 8-mosstep M8ms 2L + 6s 400.0¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms L + 8s 300.0¢ to 450.0¢
Major 9-mosstep M9ms 2L + 7s 450.0¢ to 600.0¢
10-mosstep Minor 10-mosstep m10ms L + 9s 300.0¢ to 500.0¢
Major 10-mosstep M10ms 2L + 8s 500.0¢ to 600.0¢
11-mosstep Diminished 11-mosstep d11ms L + 10s 300.0¢ to 550.0¢
Perfect 11-mosstep P11ms 2L + 9s 550.0¢ to 600.0¢
12-mosstep Perfect 12-mosstep P12ms 2L + 10s 600.0¢
13-mosstep Perfect 13-mosstep P13ms 2L + 11s 600.0¢ to 650.0¢
Augmented 13-mosstep A13ms 3L + 10s 650.0¢ to 900.0¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 600.0¢ to 700.0¢
Major 14-mosstep M14ms 3L + 11s 700.0¢ to 900.0¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 600.0¢ to 750.0¢
Major 15-mosstep M15ms 3L + 12s 750.0¢ to 900.0¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 600.0¢ to 800.0¢
Major 16-mosstep M16ms 3L + 13s 800.0¢ to 900.0¢
17-mosstep Diminished 17-mosstep d17ms 2L + 15s 600.0¢ to 850.0¢
Perfect 17-mosstep P17ms 3L + 14s 850.0¢ to 900.0¢
18-mosstep Perfect 18-mosstep P18ms 3L + 15s 900.0¢
19-mosstep Perfect 19-mosstep P19ms 3L + 16s 900.0¢ to 950.0¢
Augmented 19-mosstep A19ms 4L + 15s 950.0¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 3L + 17s 900.0¢ to 1000.0¢
Major 20-mosstep M20ms 4L + 16s 1000.0¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 3L + 18s 900.0¢ to 1050.0¢
Major 21-mosstep M21ms 4L + 17s 1050.0¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 3L + 19s 900.0¢ to 1100.0¢
Major 22-mosstep M22ms 4L + 18s 1100.0¢ to 1200.0¢
23-mosstep Diminished 23-mosstep d23ms 3L + 20s 900.0¢ to 1150.0¢
Perfect 23-mosstep P23ms 4L + 19s 1150.0¢ to 1200.0¢
24-mosstep Perfect 24-mosstep P24ms 4L + 20s 1200.0¢

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


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