9L 13s
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Scale structure
Step pattern
LsLsLssLsLssLsLssLsLss
ssLsLssLsLssLsLssLsLsL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
17\22 to 7\9 (927.3¢ to 933.3¢)
Dark
2\9 to 5\22 (266.7¢ to 272.7¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Required step ratio range
1:1 to 3:2 (soft)
Related MOS scales
Parent
9L 4s
Sister
13L 9s
Daughters
22L 9s
9L 22s
Equal tunings
Equalized (L:s = 1:1)
17\22 (927.3¢)
Supersoft (L:s = 4:3)
58\75 (928.0¢)
Soft (L:s = 3:2)
41\53 (928.3¢)
Semisoft (L:s = 5:3)
65\84 (928.6¢)
Basic (L:s = 2:1)
24\31 (929.0¢)
Semihard (L:s = 5:2)
55\71 (929.6¢)
Hard (L:s = 3:1)
31\40 (930.0¢)
Superhard (L:s = 4:1)
38\49 (930.6¢)
Collapsed (L:s = 1:0)
7\9 (933.3¢)
| ↖8L 12s | ↑9L 12s | 10L 12s↗ |
| ←8L 13s | 9L 13s | 10L 13s→ |
| ↙8L 14s | ↓9L 14s | 10L 14s↘ |
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║││║│║││║│║│││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLssLsLssLsLssLsLsL
9L 22s
9L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 13 small steps, repeating every octave. 9L 13s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 927.3¢ to 933.3¢, or from 266.7¢ to 272.7¢.
Scale tree
| Generator (edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 17\22 | 927.273 | 272.727 | 1:1 | 1.000 | Equalized 9L 13s | |||||
| 92\119 | 927.731 | 272.269 | 6:5 | 1.200 | ||||||
| 75\97 | 927.835 | 272.165 | 5:4 | 1.250 | ||||||
| 133\172 | 927.907 | 272.093 | 9:7 | 1.286 | ||||||
| 58\75 | 928.000 | 272.000 | 4:3 | 1.333 | Supersoft 9L 13s | |||||
| 157\203 | 928.079 | 271.921 | 11:8 | 1.375 | ||||||
| 99\128 | 928.125 | 271.875 | 7:5 | 1.400 | ||||||
| 140\181 | 928.177 | 271.823 | 10:7 | 1.429 | ||||||
| 41\53 | 928.302 | 271.698 | 3:2 | 1.500 | Soft 9L 13s | |||||
| 147\190 | 928.421 | 271.579 | 11:7 | 1.571 | ||||||
| 106\137 | 928.467 | 271.533 | 8:5 | 1.600 | ||||||
| 171\221 | 928.507 | 271.493 | 13:8 | 1.625 | ||||||
| 65\84 | 928.571 | 271.429 | 5:3 | 1.667 | Semisoft 9L 13s | |||||
| 154\199 | 928.643 | 271.357 | 12:7 | 1.714 | ||||||
| 89\115 | 928.696 | 271.304 | 7:4 | 1.750 | ||||||
| 113\146 | 928.767 | 271.233 | 9:5 | 1.800 | ||||||
| 24\31 | 929.032 | 270.968 | 2:1 | 2.000 | Basic 9L 13s Scales with tunings softer than this are proper | |||||
| 103\133 | 929.323 | 270.677 | 9:4 | 2.250 | ||||||
| 79\102 | 929.412 | 270.588 | 7:3 | 2.333 | ||||||
| 134\173 | 929.480 | 270.520 | 12:5 | 2.400 | ||||||
| 55\71 | 929.577 | 270.423 | 5:2 | 2.500 | Semihard 9L 13s | |||||
| 141\182 | 929.670 | 270.330 | 13:5 | 2.600 | ||||||
| 86\111 | 929.730 | 270.270 | 8:3 | 2.667 | ||||||
| 117\151 | 929.801 | 270.199 | 11:4 | 2.750 | ||||||
| 31\40 | 930.000 | 270.000 | 3:1 | 3.000 | Hard 9L 13s | |||||
| 100\129 | 930.233 | 269.767 | 10:3 | 3.333 | ||||||
| 69\89 | 930.337 | 269.663 | 7:2 | 3.500 | ||||||
| 107\138 | 930.435 | 269.565 | 11:3 | 3.667 | ||||||
| 38\49 | 930.612 | 269.388 | 4:1 | 4.000 | Superhard 9L 13s | |||||
| 83\107 | 930.841 | 269.159 | 9:2 | 4.500 | ||||||
| 45\58 | 931.034 | 268.966 | 5:1 | 5.000 | ||||||
| 52\67 | 931.343 | 268.657 | 6:1 | 6.000 | ||||||
| 7\9 | 933.333 | 266.667 | 1:0 | → ∞ | Collapsed 9L 13s | |||||
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