5L 20s
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Scale structure
Step pattern
LssssLssssLssssLssssLssss
ssssLssssLssssLssssLssssL
Equave
2/1 (1200.0¢)
Period
1\5 (240.0¢)
Generator size
Bright
4\25 to 1\5 (192.0¢ to 240.0¢)
Dark
0\5 to 1\25 (0.0¢ to 48.0¢)
TAMNAMS information
Descends from
5L 5s (pentawood)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
5L 15s
Sister
20L 5s
Daughters
25L 5s, 5L 25s
Neutralized
10L 15s
2-Flought
30L 20s, 5L 45s
Equal tunings
Equalized (L:s = 1:1)
4\25 (192.0¢)
Supersoft (L:s = 4:3)
13\80 (195.0¢)
Soft (L:s = 3:2)
9\55 (196.4¢)
Semisoft (L:s = 5:3)
14\85 (197.6¢)
Basic (L:s = 2:1)
5\30 (200.0¢)
Semihard (L:s = 5:2)
11\65 (203.1¢)
Hard (L:s = 3:1)
6\35 (205.7¢)
Superhard (L:s = 4:1)
7\40 (210.0¢)
Collapsed (L:s = 1:0)
1\5 (240.0¢)
| ↖ 4L 19s | ↑ 5L 19s | 6L 19s ↗ |
| ← 4L 20s | 5L 20s | 6L 20s → |
| ↙ 4L 21s | ↓ 5L 21s | 6L 21s ↘ |
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║││││║││││║││││║││││║│││││ │││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLssssLssssLssssLssssL
5L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 20 small steps, with a period of 1 large step and 4 small steps that repeats every 240.0¢, or 5 times every octave. 5L 20s is a great-grandchild scale of 5L 5s, expanding it by 15 tones. Generators that produce this scale range from 192¢ to 240¢, or from 0¢ to 48¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 20|0(5) | 1 | LssssLssssLssssLssssLssss |
| 15|5(5) | 5 | sLssssLssssLssssLssssLsss |
| 10|10(5) | 4 | ssLssssLssssLssssLssssLss |
| 5|15(5) | 3 | sssLssssLssssLssssLssssLs |
| 0|20(5) | 2 | ssssLssssLssssLssssLssssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\25 | 192.000 | 48.000 | 1:1 | 1.000 | Equalized 5L 20s | |||||
| 21\130 | 193.846 | 46.154 | 6:5 | 1.200 | ||||||
| 17\105 | 194.286 | 45.714 | 5:4 | 1.250 | ||||||
| 30\185 | 194.595 | 45.405 | 9:7 | 1.286 | ||||||
| 13\80 | 195.000 | 45.000 | 4:3 | 1.333 | Supersoft 5L 20s | |||||
| 35\215 | 195.349 | 44.651 | 11:8 | 1.375 | ||||||
| 22\135 | 195.556 | 44.444 | 7:5 | 1.400 | ||||||
| 31\190 | 195.789 | 44.211 | 10:7 | 1.429 | ||||||
| 9\55 | 196.364 | 43.636 | 3:2 | 1.500 | Soft 5L 20s | |||||
| 32\195 | 196.923 | 43.077 | 11:7 | 1.571 | ||||||
| 23\140 | 197.143 | 42.857 | 8:5 | 1.600 | ||||||
| 37\225 | 197.333 | 42.667 | 13:8 | 1.625 | ||||||
| 14\85 | 197.647 | 42.353 | 5:3 | 1.667 | Semisoft 5L 20s | |||||
| 33\200 | 198.000 | 42.000 | 12:7 | 1.714 | ||||||
| 19\115 | 198.261 | 41.739 | 7:4 | 1.750 | ||||||
| 24\145 | 198.621 | 41.379 | 9:5 | 1.800 | ||||||
| 5\30 | 200.000 | 40.000 | 2:1 | 2.000 | Basic 5L 20s Scales with tunings softer than this are proper | |||||
| 21\125 | 201.600 | 38.400 | 9:4 | 2.250 | ||||||
| 16\95 | 202.105 | 37.895 | 7:3 | 2.333 | ||||||
| 27\160 | 202.500 | 37.500 | 12:5 | 2.400 | ||||||
| 11\65 | 203.077 | 36.923 | 5:2 | 2.500 | Semihard 5L 20s | |||||
| 28\165 | 203.636 | 36.364 | 13:5 | 2.600 | ||||||
| 17\100 | 204.000 | 36.000 | 8:3 | 2.667 | ||||||
| 23\135 | 204.444 | 35.556 | 11:4 | 2.750 | ||||||
| 6\35 | 205.714 | 34.286 | 3:1 | 3.000 | Hard 5L 20s | |||||
| 19\110 | 207.273 | 32.727 | 10:3 | 3.333 | ||||||
| 13\75 | 208.000 | 32.000 | 7:2 | 3.500 | ||||||
| 20\115 | 208.696 | 31.304 | 11:3 | 3.667 | ||||||
| 7\40 | 210.000 | 30.000 | 4:1 | 4.000 | Superhard 5L 20s | |||||
| 15\85 | 211.765 | 28.235 | 9:2 | 4.500 | ||||||
| 8\45 | 213.333 | 26.667 | 5:1 | 5.000 | ||||||
| 9\50 | 216.000 | 24.000 | 6:1 | 6.000 | ||||||
| 1\5 | 240.000 | 0.000 | 1:0 | → ∞ | Collapsed 5L 20s | |||||