3L 15s
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Scale structure
Step pattern
LsssssLsssssLsssss
sssssLsssssLsssssL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
5\18 to 1\3 (333.3¢ to 400.0¢)
Dark
0\3 to 1\18 (0.0¢ to 66.7¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
3L 12s
Sister
15L 3s
Daughters
18L 3s, 3L 18s
Neutralized
6L 12s
2-Flought
21L 15s, 3L 33s
Equal tunings
Equalized (L:s = 1:1)
5\18 (333.3¢)
Supersoft (L:s = 4:3)
16\57 (336.8¢)
Soft (L:s = 3:2)
11\39 (338.5¢)
Semisoft (L:s = 5:3)
17\60 (340.0¢)
Basic (L:s = 2:1)
6\21 (342.9¢)
Semihard (L:s = 5:2)
13\45 (346.7¢)
Hard (L:s = 3:1)
7\24 (350.0¢)
Superhard (L:s = 4:1)
8\27 (355.6¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 14s | ↑ 3L 14s | 4L 14s ↗ |
| ← 2L 15s | 3L 15s | 4L 15s → |
| ↙ 2L 16s | ↓ 3L 16s | 4L 16s ↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║│││││║│││││║││││││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssLsssssLsssssL
3L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 15 small steps, with a period of 1 large step and 5 small steps that repeats every 400.0¢, or 3 times every octave. 3L 15s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 333.3¢ to 400¢, or from 0¢ to 66.7¢.
Modes
| UDP | Cyclic Order |
Step Pattern |
|---|---|---|
| 15|0(3) | 1 | LsssssLsssssLsssss |
| 12|3(3) | 6 | sLsssssLsssssLssss |
| 9|6(3) | 5 | ssLsssssLsssssLsss |
| 6|9(3) | 4 | sssLsssssLsssssLss |
| 3|12(3) | 3 | ssssLsssssLsssssLs |
| 0|15(3) | 2 | sssssLsssssLsssssL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 5\18 | 333.333 | 66.667 | 1:1 | 1.000 | Equalized 3L 15s | |||||
| 26\93 | 335.484 | 64.516 | 6:5 | 1.200 | ||||||
| 21\75 | 336.000 | 64.000 | 5:4 | 1.250 | ||||||
| 37\132 | 336.364 | 63.636 | 9:7 | 1.286 | ||||||
| 16\57 | 336.842 | 63.158 | 4:3 | 1.333 | Supersoft 3L 15s | |||||
| 43\153 | 337.255 | 62.745 | 11:8 | 1.375 | ||||||
| 27\96 | 337.500 | 62.500 | 7:5 | 1.400 | ||||||
| 38\135 | 337.778 | 62.222 | 10:7 | 1.429 | ||||||
| 11\39 | 338.462 | 61.538 | 3:2 | 1.500 | Soft 3L 15s | |||||
| 39\138 | 339.130 | 60.870 | 11:7 | 1.571 | ||||||
| 28\99 | 339.394 | 60.606 | 8:5 | 1.600 | ||||||
| 45\159 | 339.623 | 60.377 | 13:8 | 1.625 | ||||||
| 17\60 | 340.000 | 60.000 | 5:3 | 1.667 | Semisoft 3L 15s | |||||
| 40\141 | 340.426 | 59.574 | 12:7 | 1.714 | ||||||
| 23\81 | 340.741 | 59.259 | 7:4 | 1.750 | ||||||
| 29\102 | 341.176 | 58.824 | 9:5 | 1.800 | ||||||
| 6\21 | 342.857 | 57.143 | 2:1 | 2.000 | Basic 3L 15s Scales with tunings softer than this are proper | |||||
| 25\87 | 344.828 | 55.172 | 9:4 | 2.250 | ||||||
| 19\66 | 345.455 | 54.545 | 7:3 | 2.333 | ||||||
| 32\111 | 345.946 | 54.054 | 12:5 | 2.400 | ||||||
| 13\45 | 346.667 | 53.333 | 5:2 | 2.500 | Semihard 3L 15s | |||||
| 33\114 | 347.368 | 52.632 | 13:5 | 2.600 | ||||||
| 20\69 | 347.826 | 52.174 | 8:3 | 2.667 | ||||||
| 27\93 | 348.387 | 51.613 | 11:4 | 2.750 | ||||||
| 7\24 | 350.000 | 50.000 | 3:1 | 3.000 | Hard 3L 15s | |||||
| 22\75 | 352.000 | 48.000 | 10:3 | 3.333 | ||||||
| 15\51 | 352.941 | 47.059 | 7:2 | 3.500 | ||||||
| 23\78 | 353.846 | 46.154 | 11:3 | 3.667 | ||||||
| 8\27 | 355.556 | 44.444 | 4:1 | 4.000 | Superhard 3L 15s | |||||
| 17\57 | 357.895 | 42.105 | 9:2 | 4.500 | ||||||
| 9\30 | 360.000 | 40.000 | 5:1 | 5.000 | ||||||
| 10\33 | 363.636 | 36.364 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 0.000 | 1:0 | → ∞ | Collapsed 3L 15s | |||||