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 |
Intervals
Intervals | Steps subtended |
Range in cents | ||
---|---|---|---|---|
Generic | Specific | Abbrev. | ||
0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 57.1¢ |
Major 1-mosstep | M1ms | L | 57.1¢ to 133.3¢ | |
2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0¢ to 114.3¢ |
Perfect 2-mosstep | P2ms | L + s | 114.3¢ to 133.3¢ | |
3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 133.3¢ to 171.4¢ |
Major 3-mosstep | M3ms | 2L + s | 171.4¢ to 266.7¢ | |
4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 133.3¢ to 228.6¢ |
Major 4-mosstep | M4ms | 2L + 2s | 228.6¢ to 266.7¢ | |
5-mosstep | Perfect 5-mosstep | P5ms | 2L + 3s | 266.7¢ to 285.7¢ |
Augmented 5-mosstep | A5ms | 3L + 2s | 285.7¢ to 400.0¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 266.7¢ to 342.9¢ |
Major 6-mosstep | M6ms | 3L + 3s | 342.9¢ to 400.0¢ | |
7-mosstep | Perfect 7-mosstep | P7ms | 3L + 4s | 400.0¢ |
8-mosstep | Minor 8-mosstep | m8ms | 3L + 5s | 400.0¢ to 457.1¢ |
Major 8-mosstep | M8ms | 4L + 4s | 457.1¢ to 533.3¢ | |
9-mosstep | Diminished 9-mosstep | d9ms | 3L + 6s | 400.0¢ to 514.3¢ |
Perfect 9-mosstep | P9ms | 4L + 5s | 514.3¢ to 533.3¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 4L + 6s | 533.3¢ to 571.4¢ |
Major 10-mosstep | M10ms | 5L + 5s | 571.4¢ to 666.7¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 4L + 7s | 533.3¢ to 628.6¢ |
Major 11-mosstep | M11ms | 5L + 6s | 628.6¢ to 666.7¢ | |
12-mosstep | Perfect 12-mosstep | P12ms | 5L + 7s | 666.7¢ to 685.7¢ |
Augmented 12-mosstep | A12ms | 6L + 6s | 685.7¢ to 800.0¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 5L + 8s | 666.7¢ to 742.9¢ |
Major 13-mosstep | M13ms | 6L + 7s | 742.9¢ to 800.0¢ | |
14-mosstep | Perfect 14-mosstep | P14ms | 6L + 8s | 800.0¢ |
15-mosstep | Minor 15-mosstep | m15ms | 6L + 9s | 800.0¢ to 857.1¢ |
Major 15-mosstep | M15ms | 7L + 8s | 857.1¢ to 933.3¢ | |
16-mosstep | Diminished 16-mosstep | d16ms | 6L + 10s | 800.0¢ to 914.3¢ |
Perfect 16-mosstep | P16ms | 7L + 9s | 914.3¢ to 933.3¢ | |
17-mosstep | Minor 17-mosstep | m17ms | 7L + 10s | 933.3¢ to 971.4¢ |
Major 17-mosstep | M17ms | 8L + 9s | 971.4¢ to 1066.7¢ | |
18-mosstep | Minor 18-mosstep | m18ms | 7L + 11s | 933.3¢ to 1028.6¢ |
Major 18-mosstep | M18ms | 8L + 10s | 1028.6¢ to 1066.7¢ | |
19-mosstep | Perfect 19-mosstep | P19ms | 8L + 11s | 1066.7¢ to 1085.7¢ |
Augmented 19-mosstep | A19ms | 9L + 10s | 1085.7¢ to 1200.0¢ | |
20-mosstep | Minor 20-mosstep | m20ms | 8L + 12s | 1066.7¢ to 1142.9¢ |
Major 20-mosstep | M20ms | 9L + 11s | 1142.9¢ to 1200.0¢ | |
21-mosstep | Perfect 21-mosstep | P21ms | 9L + 12s | 1200.0¢ |
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 |
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