9L 12s

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↖ 8L 11s ↑ 9L 11s 10L 11s ↗
← 8L 12s 9L 12s 10L 12s →
↙ 8L 13s ↓ 9L 13s 10L 13s ↘
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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¢)

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

Modes of 9L 12s
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 of 9L 12s
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

Scale Tree and Tuning Spectrum of 9L 12s
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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