5L 21s
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Scale structure
Step pattern
LssssLssssLssssLssssLsssss
sssssLssssLssssLssssLssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
5\26 to 1\5 (230.8¢ to 240.0¢)
Dark
4\5 to 21\26 (960.0¢ to 969.2¢)
TAMNAMS information
Descends from
5L 1s (machinoid)
Ancestor's step ratio range
5:1 to 1:0
Related MOS scales
Parent
5L 16s
Sister
21L 5s
Daughters
26L 5s, 5L 26s
Neutralized
10L 16s
2-Flought
31L 21s, 5L 47s
Equal tunings
Equalized (L:s = 1:1)
5\26 (230.8¢)
Supersoft (L:s = 4:3)
16\83 (231.3¢)
Soft (L:s = 3:2)
11\57 (231.6¢)
Semisoft (L:s = 5:3)
17\88 (231.8¢)
Basic (L:s = 2:1)
6\31 (232.3¢)
Semihard (L:s = 5:2)
13\67 (232.8¢)
Hard (L:s = 3:1)
7\36 (233.3¢)
Superhard (L:s = 4:1)
8\41 (234.1¢)
Collapsed (L:s = 1:0)
1\5 (240.0¢)
| ↖ 4L 20s | ↑ 5L 20s | 6L 20s ↗ |
| ← 4L 21s | 5L 21s | 6L 21s → |
| ↙ 4L 22s | ↓ 5L 22s | 6L 22s ↘ |
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││║││││║││││││ ││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssLssssLssssLssssLssssL
5L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 21 small steps, repeating every octave. 5L 21s is related to 5L 1s, expanding it by 20 tones. Generators that produce this scale range from 230.8¢ to 240¢, or from 960¢ to 969.2¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 25|0 | 1 | LssssLssssLssssLssssLsssss |
| 24|1 | 6 | LssssLssssLssssLsssssLssss |
| 23|2 | 11 | LssssLssssLsssssLssssLssss |
| 22|3 | 16 | LssssLsssssLssssLssssLssss |
| 21|4 | 21 | LsssssLssssLssssLssssLssss |
| 20|5 | 26 | sLssssLssssLssssLssssLssss |
| 19|6 | 5 | sLssssLssssLssssLsssssLsss |
| 18|7 | 10 | sLssssLssssLsssssLssssLsss |
| 17|8 | 15 | sLssssLsssssLssssLssssLsss |
| 16|9 | 20 | sLsssssLssssLssssLssssLsss |
| 15|10 | 25 | ssLssssLssssLssssLssssLsss |
| 14|11 | 4 | ssLssssLssssLssssLsssssLss |
| 13|12 | 9 | ssLssssLssssLsssssLssssLss |
| 12|13 | 14 | ssLssssLsssssLssssLssssLss |
| 11|14 | 19 | ssLsssssLssssLssssLssssLss |
| 10|15 | 24 | sssLssssLssssLssssLssssLss |
| 9|16 | 3 | sssLssssLssssLssssLsssssLs |
| 8|17 | 8 | sssLssssLssssLsssssLssssLs |
| 7|18 | 13 | sssLssssLsssssLssssLssssLs |
| 6|19 | 18 | sssLsssssLssssLssssLssssLs |
| 5|20 | 23 | ssssLssssLssssLssssLssssLs |
| 4|21 | 2 | ssssLssssLssssLssssLsssssL |
| 3|22 | 7 | ssssLssssLssssLsssssLssssL |
| 2|23 | 12 | ssssLssssLsssssLssssLssssL |
| 1|24 | 17 | ssssLsssssLssssLssssLssssL |
| 0|25 | 22 | sssssLssssLssssLssssLssssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 5\26 | 230.769 | 969.231 | 1:1 | 1.000 | Equalized 5L 21s | |||||
| 26\135 | 231.111 | 968.889 | 6:5 | 1.200 | ||||||
| 21\109 | 231.193 | 968.807 | 5:4 | 1.250 | ||||||
| 37\192 | 231.250 | 968.750 | 9:7 | 1.286 | ||||||
| 16\83 | 231.325 | 968.675 | 4:3 | 1.333 | Supersoft 5L 21s | |||||
| 43\223 | 231.390 | 968.610 | 11:8 | 1.375 | ||||||
| 27\140 | 231.429 | 968.571 | 7:5 | 1.400 | ||||||
| 38\197 | 231.472 | 968.528 | 10:7 | 1.429 | ||||||
| 11\57 | 231.579 | 968.421 | 3:2 | 1.500 | Soft 5L 21s | |||||
| 39\202 | 231.683 | 968.317 | 11:7 | 1.571 | ||||||
| 28\145 | 231.724 | 968.276 | 8:5 | 1.600 | ||||||
| 45\233 | 231.760 | 968.240 | 13:8 | 1.625 | ||||||
| 17\88 | 231.818 | 968.182 | 5:3 | 1.667 | Semisoft 5L 21s | |||||
| 40\207 | 231.884 | 968.116 | 12:7 | 1.714 | ||||||
| 23\119 | 231.933 | 968.067 | 7:4 | 1.750 | ||||||
| 29\150 | 232.000 | 968.000 | 9:5 | 1.800 | ||||||
| 6\31 | 232.258 | 967.742 | 2:1 | 2.000 | Basic 5L 21s Scales with tunings softer than this are proper | |||||
| 25\129 | 232.558 | 967.442 | 9:4 | 2.250 | ||||||
| 19\98 | 232.653 | 967.347 | 7:3 | 2.333 | ||||||
| 32\165 | 232.727 | 967.273 | 12:5 | 2.400 | ||||||
| 13\67 | 232.836 | 967.164 | 5:2 | 2.500 | Semihard 5L 21s | |||||
| 33\170 | 232.941 | 967.059 | 13:5 | 2.600 | ||||||
| 20\103 | 233.010 | 966.990 | 8:3 | 2.667 | ||||||
| 27\139 | 233.094 | 966.906 | 11:4 | 2.750 | ||||||
| 7\36 | 233.333 | 966.667 | 3:1 | 3.000 | Hard 5L 21s | |||||
| 22\113 | 233.628 | 966.372 | 10:3 | 3.333 | ||||||
| 15\77 | 233.766 | 966.234 | 7:2 | 3.500 | ||||||
| 23\118 | 233.898 | 966.102 | 11:3 | 3.667 | ||||||
| 8\41 | 234.146 | 965.854 | 4:1 | 4.000 | Superhard 5L 21s | |||||
| 17\87 | 234.483 | 965.517 | 9:2 | 4.500 | ||||||
| 9\46 | 234.783 | 965.217 | 5:1 | 5.000 | ||||||
| 10\51 | 235.294 | 964.706 | 6:1 | 6.000 | ||||||
| 1\5 | 240.000 | 960.000 | 1:0 | → ∞ | Collapsed 5L 21s | |||||
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