3L 21s
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Scale structure
Step pattern
LsssssssLsssssssLsssssss
sssssssLsssssssLsssssssL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
7\24 to 1\3 (350.0¢ to 400.0¢)
Dark
0\3 to 1\24 (0.0¢ to 50.0¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
6:1 to 1:0
Related MOS scales
Parent
3L 18s
Sister
21L 3s
Daughters
24L 3s, 3L 24s
Neutralized
6L 18s
2-Flought
27L 21s, 3L 45s
Equal tunings
Equalized (L:s = 1:1)
7\24 (350.0¢)
Supersoft (L:s = 4:3)
22\75 (352.0¢)
Soft (L:s = 3:2)
15\51 (352.9¢)
Semisoft (L:s = 5:3)
23\78 (353.8¢)
Basic (L:s = 2:1)
8\27 (355.6¢)
Semihard (L:s = 5:2)
17\57 (357.9¢)
Hard (L:s = 3:1)
9\30 (360.0¢)
Superhard (L:s = 4:1)
10\33 (363.6¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 20s | ↑ 3L 20s | 4L 20s ↗ |
| ← 2L 21s | 3L 21s | 4L 21s → |
| ↙ 2L 22s | ↓ 3L 22s | 4L 22s ↘ |
┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐ │║│││││││║│││││││║││││││││ ││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssssLsssssssLsssssssL
3L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 21 small steps, with a period of 1 large step and 7 small steps that repeats every 400.0¢, or 3 times every octave. 3L 21s is related to 3L 6s, expanding it by 15 tones. Generators that produce this scale range from 350¢ to 400¢, or from 0¢ to 50¢.
Modes
| UDP | Cyclic Order |
Step Pattern |
|---|---|---|
| 21|0(3) | 1 | LsssssssLsssssssLsssssss |
| 18|3(3) | 8 | sLsssssssLsssssssLssssss |
| 15|6(3) | 7 | ssLsssssssLsssssssLsssss |
| 12|9(3) | 6 | sssLsssssssLsssssssLssss |
| 9|12(3) | 5 | ssssLsssssssLsssssssLsss |
| 6|15(3) | 4 | sssssLsssssssLsssssssLss |
| 3|18(3) | 3 | ssssssLsssssssLsssssssLs |
| 0|21(3) | 2 | sssssssLsssssssLsssssssL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\24 | 350.000 | 50.000 | 1:1 | 1.000 | Equalized 3L 21s | |||||
| 36\123 | 351.220 | 48.780 | 6:5 | 1.200 | ||||||
| 29\99 | 351.515 | 48.485 | 5:4 | 1.250 | ||||||
| 51\174 | 351.724 | 48.276 | 9:7 | 1.286 | ||||||
| 22\75 | 352.000 | 48.000 | 4:3 | 1.333 | Supersoft 3L 21s | |||||
| 59\201 | 352.239 | 47.761 | 11:8 | 1.375 | ||||||
| 37\126 | 352.381 | 47.619 | 7:5 | 1.400 | ||||||
| 52\177 | 352.542 | 47.458 | 10:7 | 1.429 | ||||||
| 15\51 | 352.941 | 47.059 | 3:2 | 1.500 | Soft 3L 21s | |||||
| 53\180 | 353.333 | 46.667 | 11:7 | 1.571 | ||||||
| 38\129 | 353.488 | 46.512 | 8:5 | 1.600 | ||||||
| 61\207 | 353.623 | 46.377 | 13:8 | 1.625 | ||||||
| 23\78 | 353.846 | 46.154 | 5:3 | 1.667 | Semisoft 3L 21s | |||||
| 54\183 | 354.098 | 45.902 | 12:7 | 1.714 | ||||||
| 31\105 | 354.286 | 45.714 | 7:4 | 1.750 | ||||||
| 39\132 | 354.545 | 45.455 | 9:5 | 1.800 | ||||||
| 8\27 | 355.556 | 44.444 | 2:1 | 2.000 | Basic 3L 21s Scales with tunings softer than this are proper | |||||
| 33\111 | 356.757 | 43.243 | 9:4 | 2.250 | ||||||
| 25\84 | 357.143 | 42.857 | 7:3 | 2.333 | ||||||
| 42\141 | 357.447 | 42.553 | 12:5 | 2.400 | ||||||
| 17\57 | 357.895 | 42.105 | 5:2 | 2.500 | Semihard 3L 21s | |||||
| 43\144 | 358.333 | 41.667 | 13:5 | 2.600 | ||||||
| 26\87 | 358.621 | 41.379 | 8:3 | 2.667 | ||||||
| 35\117 | 358.974 | 41.026 | 11:4 | 2.750 | ||||||
| 9\30 | 360.000 | 40.000 | 3:1 | 3.000 | Hard 3L 21s | |||||
| 28\93 | 361.290 | 38.710 | 10:3 | 3.333 | ||||||
| 19\63 | 361.905 | 38.095 | 7:2 | 3.500 | ||||||
| 29\96 | 362.500 | 37.500 | 11:3 | 3.667 | ||||||
| 10\33 | 363.636 | 36.364 | 4:1 | 4.000 | Superhard 3L 21s | |||||
| 21\69 | 365.217 | 34.783 | 9:2 | 4.500 | ||||||
| 11\36 | 366.667 | 33.333 | 5:1 | 5.000 | ||||||
| 12\39 | 369.231 | 30.769 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 0.000 | 1:0 | → ∞ | Collapsed 3L 21s | |||||