15L 5s
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Scale structure
Step pattern
LLLsLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLsLLL
Equave
2/1 (1200.0¢)
Period
1\5 (240.0¢)
Generator size
Bright
1\20 to 1\15 (60.0¢ to 80.0¢)
Dark
2\15 to 3\20 (160.0¢ to 180.0¢)
TAMNAMS information
Descends from
5L 5s (pentawood)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
5L 10s
Sister
5L 15s
Daughters
20L 15s, 15L 20s
Neutralized
10L 10s
2-Flought
35L 5s, 15L 25s
Equal tunings
Equalized (L:s = 1:1)
1\20 (60.0¢)
Supersoft (L:s = 4:3)
4\75 (64.0¢)
Soft (L:s = 3:2)
3\55 (65.5¢)
Semisoft (L:s = 5:3)
5\90 (66.7¢)
Basic (L:s = 2:1)
2\35 (68.6¢)
Semihard (L:s = 5:2)
5\85 (70.6¢)
Hard (L:s = 3:1)
3\50 (72.0¢)
Superhard (L:s = 4:1)
4\65 (73.8¢)
Collapsed (L:s = 1:0)
1\15 (80.0¢)
| ↖ 14L 4s | ↑ 15L 4s | 16L 4s ↗ |
| ← 14L 5s | 15L 5s | 16L 5s → |
| ↙ 14L 6s | ↓ 15L 6s | 16L 6s ↘ |
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║│║║║│║║║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLsLLLsLLL
15L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 5 small steps, with a period of 3 large steps and 1 small step that repeats every 240.0¢, or 5 times every octave. 15L 5s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 60¢ to 80¢, or from 160¢ to 180¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 15|0(5) | 1 | LLLsLLLsLLLsLLLsLLLs |
| 10|5(5) | 2 | LLsLLLsLLLsLLLsLLLsL |
| 5|10(5) | 3 | LsLLLsLLLsLLLsLLLsLL |
| 0|15(5) | 4 | sLLLsLLLsLLLsLLLsLLL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\20 | 60.000 | 180.000 | 1:1 | 1.000 | Equalized 15L 5s | |||||
| 6\115 | 62.609 | 177.391 | 6:5 | 1.200 | ||||||
| 5\95 | 63.158 | 176.842 | 5:4 | 1.250 | ||||||
| 9\170 | 63.529 | 176.471 | 9:7 | 1.286 | ||||||
| 4\75 | 64.000 | 176.000 | 4:3 | 1.333 | Supersoft 15L 5s | |||||
| 11\205 | 64.390 | 175.610 | 11:8 | 1.375 | ||||||
| 7\130 | 64.615 | 175.385 | 7:5 | 1.400 | ||||||
| 10\185 | 64.865 | 175.135 | 10:7 | 1.429 | ||||||
| 3\55 | 65.455 | 174.545 | 3:2 | 1.500 | Soft 15L 5s | |||||
| 11\200 | 66.000 | 174.000 | 11:7 | 1.571 | ||||||
| 8\145 | 66.207 | 173.793 | 8:5 | 1.600 | ||||||
| 13\235 | 66.383 | 173.617 | 13:8 | 1.625 | ||||||
| 5\90 | 66.667 | 173.333 | 5:3 | 1.667 | Semisoft 15L 5s | |||||
| 12\215 | 66.977 | 173.023 | 12:7 | 1.714 | ||||||
| 7\125 | 67.200 | 172.800 | 7:4 | 1.750 | ||||||
| 9\160 | 67.500 | 172.500 | 9:5 | 1.800 | ||||||
| 2\35 | 68.571 | 171.429 | 2:1 | 2.000 | Basic 15L 5s | |||||
| 9\155 | 69.677 | 170.323 | 9:4 | 2.250 | ||||||
| 7\120 | 70.000 | 170.000 | 7:3 | 2.333 | ||||||
| 12\205 | 70.244 | 169.756 | 12:5 | 2.400 | ||||||
| 5\85 | 70.588 | 169.412 | 5:2 | 2.500 | Semihard 15L 5s | |||||
| 13\220 | 70.909 | 169.091 | 13:5 | 2.600 | ||||||
| 8\135 | 71.111 | 168.889 | 8:3 | 2.667 | ||||||
| 11\185 | 71.351 | 168.649 | 11:4 | 2.750 | ||||||
| 3\50 | 72.000 | 168.000 | 3:1 | 3.000 | Hard 15L 5s | |||||
| 10\165 | 72.727 | 167.273 | 10:3 | 3.333 | ||||||
| 7\115 | 73.043 | 166.957 | 7:2 | 3.500 | ||||||
| 11\180 | 73.333 | 166.667 | 11:3 | 3.667 | ||||||
| 4\65 | 73.846 | 166.154 | 4:1 | 4.000 | Superhard 15L 5s | |||||
| 9\145 | 74.483 | 165.517 | 9:2 | 4.500 | ||||||
| 5\80 | 75.000 | 165.000 | 5:1 | 5.000 | ||||||
| 6\95 | 75.789 | 164.211 | 6:1 | 6.000 | ||||||
| 1\15 | 80.000 | 160.000 | 1:0 | → ∞ | Collapsed 15L 5s | |||||