9L 12s
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Scale structure
Step pattern
LsLsLssLsLsLssLsLsLss
ssLsLsLssLsLsLssLsLsL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
2\21 to 1\9 (114.3¢ to 133.3¢)
Dark
2\9 to 5\21 (266.7¢ to 285.7¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
1:1 to 3:2 (soft)
Related MOS scales
Parent
9L 3s
Sister
12L 9s
Daughters
21L 9s, 9L 21s
Neutralized
18L 3s
2-Flought
30L 12s, 9L 33s
Equal tunings
Equalized (L:s = 1:1)
2\21 (114.3¢)
Supersoft (L:s = 4:3)
7\72 (116.7¢)
Soft (L:s = 3:2)
5\51 (117.6¢)
Semisoft (L:s = 5:3)
8\81 (118.5¢)
Basic (L:s = 2:1)
3\30 (120.0¢)
Semihard (L:s = 5:2)
7\69 (121.7¢)
Hard (L:s = 3:1)
4\39 (123.1¢)
Superhard (L:s = 4:1)
5\48 (125.0¢)
Collapsed (L:s = 1:0)
1\9 (133.3¢)
| ↖ 8L 11s | ↑ 9L 11s | 10L 11s ↗ |
| ← 8L 12s | 9L 12s | 10L 12s → |
| ↙ 8L 13s | ↓ 9L 13s | 10L 13s ↘ |
┌╥┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐ │║│║│║││║│║│║││║│║│║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLsLssLsLsLssLsLsL
9L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 12 small steps, with a period of 3 large steps and 4 small steps that repeats every 400.0¢, or 3 times every octave. 9L 12s is a grandchild scale of 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 114.3¢ to 133.3¢, or from 266.7¢ to 285.7¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 18|0(3) | 1 | LsLsLssLsLsLssLsLsLss |
| 15|3(3) | 3 | LsLssLsLsLssLsLsLssLs |
| 12|6(3) | 5 | LssLsLsLssLsLsLssLsLs |
| 9|9(3) | 7 | sLsLsLssLsLsLssLsLsLs |
| 6|12(3) | 2 | sLsLssLsLsLssLsLsLssL |
| 3|15(3) | 4 | sLssLsLsLssLsLsLssLsL |
| 0|18(3) | 6 | ssLsLsLssLsLsLssLsLsL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\21 | 114.286 | 285.714 | 1:1 | 1.000 | Equalized 9L 12s | |||||
| 11\114 | 115.789 | 284.211 | 6:5 | 1.200 | ||||||
| 9\93 | 116.129 | 283.871 | 5:4 | 1.250 | ||||||
| 16\165 | 116.364 | 283.636 | 9:7 | 1.286 | ||||||
| 7\72 | 116.667 | 283.333 | 4:3 | 1.333 | Supersoft 9L 12s | |||||
| 19\195 | 116.923 | 283.077 | 11:8 | 1.375 | ||||||
| 12\123 | 117.073 | 282.927 | 7:5 | 1.400 | ||||||
| 17\174 | 117.241 | 282.759 | 10:7 | 1.429 | ||||||
| 5\51 | 117.647 | 282.353 | 3:2 | 1.500 | Soft 9L 12s | |||||
| 18\183 | 118.033 | 281.967 | 11:7 | 1.571 | ||||||
| 13\132 | 118.182 | 281.818 | 8:5 | 1.600 | ||||||
| 21\213 | 118.310 | 281.690 | 13:8 | 1.625 | ||||||
| 8\81 | 118.519 | 281.481 | 5:3 | 1.667 | Semisoft 9L 12s | |||||
| 19\192 | 118.750 | 281.250 | 12:7 | 1.714 | ||||||
| 11\111 | 118.919 | 281.081 | 7:4 | 1.750 | ||||||
| 14\141 | 119.149 | 280.851 | 9:5 | 1.800 | ||||||
| 3\30 | 120.000 | 280.000 | 2:1 | 2.000 | Basic 9L 12s Scales with tunings softer than this are proper | |||||
| 13\129 | 120.930 | 279.070 | 9:4 | 2.250 | ||||||
| 10\99 | 121.212 | 278.788 | 7:3 | 2.333 | ||||||
| 17\168 | 121.429 | 278.571 | 12:5 | 2.400 | ||||||
| 7\69 | 121.739 | 278.261 | 5:2 | 2.500 | Semihard 9L 12s | |||||
| 18\177 | 122.034 | 277.966 | 13:5 | 2.600 | ||||||
| 11\108 | 122.222 | 277.778 | 8:3 | 2.667 | ||||||
| 15\147 | 122.449 | 277.551 | 11:4 | 2.750 | ||||||
| 4\39 | 123.077 | 276.923 | 3:1 | 3.000 | Hard 9L 12s | |||||
| 13\126 | 123.810 | 276.190 | 10:3 | 3.333 | ||||||
| 9\87 | 124.138 | 275.862 | 7:2 | 3.500 | ||||||
| 14\135 | 124.444 | 275.556 | 11:3 | 3.667 | ||||||
| 5\48 | 125.000 | 275.000 | 4:1 | 4.000 | Superhard 9L 12s | |||||
| 11\105 | 125.714 | 274.286 | 9:2 | 4.500 | ||||||
| 6\57 | 126.316 | 273.684 | 5:1 | 5.000 | ||||||
| 7\66 | 127.273 | 272.727 | 6:1 | 6.000 | ||||||
| 1\9 | 133.333 | 266.667 | 1:0 | → ∞ | Collapsed 9L 12s | |||||