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