12L 3s

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↖11L 2s↑12L 2s 13L 2s↗
←11L 3s12L 3s13L 3s→
↙11L 4s↓12L 4s 13L 4s↘
Brightest mode LLLLsLLLLsLLLLs
Period 1\3
Range for bright generator 1\15 (80¢) to 1\12 (100¢)
Range for dark generator 3\12 (300¢) to 4\15 (320¢)
Parent MOS 3L 9s
Sister MOS 3L 12s
Daughter MOSes 15L 12s, 12L 15s
Equal tunings
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¢)
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¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

12L 3s is an 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 this form are proper if every period is the same, 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

1/15 80
7\102 82.353
6\87 82.759
5/72 83.333
4/57 84.2105
7/99 84.8485
3/42 85.714
86.27
8/111 86.4865
86.617
5/69 86.9565
7/96 87.5
2/27 88.889
11/147 89.796
9/120 90
7/93 90.323
5/66 90.909
91.283
8/105 91.429
91.578
3/39 92.308
92.629
7/90 93.333
4/51 94.118
5/63 95.238
6/75 96
7/87 96.552
1/12 100