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12L 3s (21/10-equivalent)

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↖ 11L 2s⟨21/10⟩ ↑ 12L 2s⟨21/10⟩ 13L 2s⟨21/10⟩ ↗
← 11L 3s⟨21/10⟩ 12L 3s (21/10-equivalent) 13L 3s⟨21/10⟩ →
↙ 11L 4s⟨21/10⟩ ↓ 12L 4s⟨21/10⟩ 13L 4s⟨21/10⟩ ↘ 
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Scale structure
Step pattern LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave 21/10 (1284.5 ¢)
Period 1\3 (428.2 ¢)
Generator size(ed21/10)
Bright 1\15 to 1\12 (85.6 ¢ to 107.0 ¢)
Dark 3\12 to 4\15 (321.1 ¢ to 342.5 ¢)
Related MOS scales
Parent 3L 9s⟨21/10⟩
Sister 3L 12s⟨21/10⟩
Daughters 15L 12s⟨21/10⟩, 12L 15s⟨21/10⟩
Neutralized 9L 6s⟨21/10⟩
2-Flought 27L 3s⟨21/10⟩, 12L 18s⟨21/10⟩
Equal tunings(ed21/10)
Equalized (L:s = 1:1) 1\15 (85.6 ¢)
Supersoft (L:s = 4:3) 4\57 (90.1 ¢)
Soft (L:s = 3:2) 3\42 (91.7 ¢)
Semisoft (L:s = 5:3) 5\69 (93.1 ¢)
Basic (L:s = 2:1) 2\27 (95.1 ¢)
Semihard (L:s = 5:2) 5\66 (97.3 ¢)
Hard (L:s = 3:1) 3\39 (98.8 ¢)
Superhard (L:s = 4:1) 4\51 (100.7 ¢)
Collapsed (L:s = 1:0) 1\12 (107.0 ¢)

12L 3s⟨21/10⟩ is a 21/10-equivalent (non-octave) 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 428.2 ¢, or 3 times every interval of 21/10 (1284.5 ¢). Generators that produce this scale range from 85.6 ¢ to 107 ¢, or from 321.1 ¢ to 342.5 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
  MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 12L 3s⟨21/10⟩
Generator(ed21/10) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 85.631 342.525 1:1 1.000 Equalized 12L 3s⟨21/10⟩
6\87 88.584 339.572 6:5 1.200
5\72 89.199 338.957 5:4 1.250
9\129 89.614 338.542 9:7 1.286
4\57 90.138 338.018 4:3 1.333 Supersoft 12L 3s⟨21/10⟩
11\156 90.571 337.584 11:8 1.375
7\99 90.821 337.335 7:5 1.400
10\141 91.097 337.059 10:7 1.429
3\42 91.748 336.408 3:2 1.500 Soft 12L 3s⟨21/10⟩
11\153 92.347 335.808 11:7 1.571
8\111 92.574 335.582 8:5 1.600
13\180 92.767 335.389 13:8 1.625
5\69 93.077 335.078 5:3 1.667 Semisoft 12L 3s⟨21/10⟩
12\165 93.416 334.740 12:7 1.714
7\96 93.659 334.497 7:4 1.750
9\123 93.985 334.170 9:5 1.800
2\27 95.146 333.010 2:1 2.000 Basic 12L 3s⟨21/10⟩
9\120 96.335 331.821 9:4 2.250
7\93 96.680 331.475 7:3 2.333
12\159 96.941 331.215 12:5 2.400
5\66 97.308 330.848 5:2 2.500 Semihard 12L 3s⟨21/10⟩
13\171 97.650 330.506 13:5 2.600
8\105 97.864 330.292 8:3 2.667
11\144 98.119 330.037 11:4 2.750
3\39 98.805 329.351 3:1 3.000 Hard 12L 3s⟨21/10⟩
10\129 99.571 328.585 10:3 3.333
7\90 99.903 328.253 7:2 3.500
11\141 100.207 327.949 11:3 3.667
4\51 100.743 327.413 4:1 4.000 Superhard 12L 3s⟨21/10⟩
9\114 101.405 326.750 9:2 4.500
5\63 101.942 326.214 5:1 5.000
6\75 102.757 325.398 6:1 6.000
1\12 107.039 321.117 1:0 → ∞ Collapsed 12L 3s⟨21/10⟩
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