12L 2s

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↖11L 1s↑12L 1s 13L 1s↗
←11L 2s12L 2s13L 2s→
↙11L 3s↓12L 3s 13L 3s↘
Brightest mode LLLLLLsLLLLLLs
Period 1\2
Range for bright generator 1\14 (85.7¢) to 1\12 (100¢)
Range for dark generator 5\12 (500¢) to 6\14 (514.3¢)
Parent MOS 2L 10s
Sister MOS 2L 12s
Daughter MOSes 14L 12s, 12L 14s
Equal tunings
Supersoft (L:s = 4:3) 4\54 (88.9¢)
Soft (L:s = 3:2) 3\40 (90¢)
Semisoft (L:s = 5:3) 5\66 (90.9¢)
Basic (L:s = 2:1) 2\26 (92.3¢)
Semihard (L:s = 5:2) 5\64 (93.8¢)
Hard (L:s = 3:1) 3\38 (94.7¢)
Superhard (L:s = 4:1) 4\50 (96¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

12L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 2 small steps, with a period of 6 large steps and 1 small step that repeats every 600.0¢, or twice every octave. 12L 2s is a grandchild scale of 2L 8s, expanding it by 4 tones. Generators that produce this scale range from 85.7¢ to 100¢, or from 500¢ to 514.3¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

It appears as the mega chromatic scale of injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4 (simple) or +10 generators equals 5/3 (complex).

Scale tree

Scale tree and tuning spectrum of 12L 2s
Generator (in steps of edo) Cents Step ratio Comments
(Every true-MOS tuning produces a proper scale)
Bright Dark L:s Hardness
1\14 85.714 514.286 1:1 1.000 Equalized 12L 2s
6\82 87.805 512.195 6:5 1.200
5\68 88.235 511.765 5:4 1.250
9\122 88.525 511.475 9:7 1.286
4\54 88.889 511.111 4:3 1.333 Supersoft 12L 2s
11\148 89.189 510.811 11:8 1.375
7\94 89.362 510.638 7:5 1.400
10\134 89.552 510.448 10:7 1.429
3\40 90.000 510.000 3:2 1.500 Soft 12L 2s
11\146 90.411 509.589 11:7 1.571
8\106 90.566 509.434 8:5 1.600
13\172 90.698 509.302 13:8 1.625
5\66 90.909 509.091 5:3 1.667 Semisoft 12L 2s
12\158 91.139 508.861 12:7 1.714
7\92 91.304 508.696 7:4 1.750
9\118 91.525 508.475 9:5 1.800
2\26 92.308 507.692 2:1 2.000 Basic 12L 2s
9\116 93.103 506.897 9:4 2.250
7\90 93.333 506.667 7:3 2.333
12\154 93.506 506.494 12:5 2.400
5\64 93.750 506.250 5:2 2.500 Semihard 12L 2s
13\166 93.976 506.024 13:5 2.600
8\102 94.118 505.882 8:3 2.667
11\140 94.286 505.714 11:4 2.750
3\38 94.737 505.263 3:1 3.000 Hard 12L 2s
Injera
10\126 95.238 504.762 10:3 3.333
7\88 95.455 504.545 7:2 3.500
11\138 95.652 504.348 11:3 3.667
4\50 96.000 504.000 4:1 4.000 Superhard 12L 2s
9\112 96.429 503.571 9:2 4.500
5\62 96.774 503.226 5:1 5.000
6\74 97.297 502.703 6:1 6.000
1\12 100.000 500.000 1:0 → ∞ Collapsed 12L 2s