12L 3s

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↖ 11L 2s ↑12L 2s 13L 2s ↗
← 11L 3s12L 3s 13L 3s →
↙ 11L 4s ↓12L 4s 13L 4s ↘
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐
│║║║║│║║║║│║║║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 1\15 to 1\12 (80.0¢ to 100.0¢)
Dark 3\12 to 4\15 (300.0¢ to 320.0¢)
TAMNAMS information
Descends from 3L 6s (tcherepnin)
Required step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 3L 9s
Sister 3L 12s
Daughters 15L 12s, 12L 15s
Neutralized 9L 6s
2-Flought 27L 3s, 12L 18s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0¢)
Supersoft (L:s = 4:3) 4\57 (84.2¢)
Soft (L:s = 3:2) 3\42 (85.7¢)
Semisoft (L:s = 5:3) 5\69 (87.0¢)
Basic (L:s = 2:1) 2\27 (88.9¢)
Semihard (L:s = 5:2) 5\66 (90.9¢)
Hard (L:s = 3:1) 3\39 (92.3¢)
Superhard (L:s = 4:1) 4\51 (94.1¢)
Collapsed (L:s = 1:0) 1\12 (100.0¢)

12L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 3 small steps, with a period of 4 large steps and 1 small step that repeats every 400.0¢, or 3 times every octave. 12L 3s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 80¢ to 100¢, or from 300¢ to 320¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].

Scale tree

Scale Tree and Tuning Spectrum of 12L 3s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 320.000 1:1 1.000 Equalized 12L 3s
6\87 82.759 317.241 6:5 1.200
5\72 83.333 316.667 5:4 1.250
9\129 83.721 316.279 9:7 1.286
4\57 84.211 315.789 4:3 1.333 Supersoft 12L 3s
11\156 84.615 315.385 11:8 1.375
7\99 84.848 315.152 7:5 1.400
10\141 85.106 314.894 10:7 1.429
3\42 85.714 314.286 3:2 1.500 Soft 12L 3s
11\153 86.275 313.725 11:7 1.571
8\111 86.486 313.514 8:5 1.600
13\180 86.667 313.333 13:8 1.625
5\69 86.957 313.043 5:3 1.667 Semisoft 12L 3s
12\165 87.273 312.727 12:7 1.714
7\96 87.500 312.500 7:4 1.750
9\123 87.805 312.195 9:5 1.800
2\27 88.889 311.111 2:1 2.000 Basic 12L 3s
9\120 90.000 310.000 9:4 2.250
7\93 90.323 309.677 7:3 2.333
12\159 90.566 309.434 12:5 2.400
5\66 90.909 309.091 5:2 2.500 Semihard 12L 3s
13\171 91.228 308.772 13:5 2.600
8\105 91.429 308.571 8:3 2.667
11\144 91.667 308.333 11:4 2.750
3\39 92.308 307.692 3:1 3.000 Hard 12L 3s
10\129 93.023 306.977 10:3 3.333
7\90 93.333 306.667 7:2 3.500
11\141 93.617 306.383 11:3 3.667
4\51 94.118 305.882 4:1 4.000 Superhard 12L 3s
9\114 94.737 305.263 9:2 4.500
5\63 95.238 304.762 5:1 5.000
6\75 96.000 304.000 6:1 6.000
1\12 100.000 300.000 1:0 → ∞ Collapsed 12L 3s