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⟩ ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐
│║║║║│║║║║│║║║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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.

Modes

Modes of 12L 3s⟨21/10⟩
UDP Cyclic
order		 Step
pattern
12|0(3) 1 LLLLsLLLLsLLLLs
9|3(3) 2 LLLsLLLLsLLLLsL
6|6(3) 3 LLsLLLLsLLLLsLL
3|9(3) 4 LsLLLLsLLLLsLLL
0|12(3) 5 sLLLLsLLLLsLLLL

Intervals

Intervals of 12L 3s⟨21/10⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 85.6 ¢
Perfect 1-mosstep P1ms L 85.6 ¢ to 107.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 107.0 ¢ to 171.3 ¢
Major 2-mosstep M2ms 2L 171.3 ¢ to 214.1 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 214.1 ¢ to 256.9 ¢
Major 3-mosstep M3ms 3L 256.9 ¢ to 321.1 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 321.1 ¢ to 342.5 ¢
Augmented 4-mosstep A4ms 4L 342.5 ¢ to 428.2 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 428.2 ¢
6-mosstep Diminished 6-mosstep d6ms 4L + 2s 428.2 ¢ to 513.8 ¢
Perfect 6-mosstep P6ms 5L + s 513.8 ¢ to 535.2 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 535.2 ¢ to 599.4 ¢
Major 7-mosstep M7ms 6L + s 599.4 ¢ to 642.2 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 642.2 ¢ to 685.0 ¢
Major 8-mosstep M8ms 7L + s 685.0 ¢ to 749.3 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 749.3 ¢ to 770.7 ¢
Augmented 9-mosstep A9ms 8L + s 770.7 ¢ to 856.3 ¢
10-mosstep Perfect 10-mosstep P10ms 8L + 2s 856.3 ¢
11-mosstep Diminished 11-mosstep d11ms 8L + 3s 856.3 ¢ to 941.9 ¢
Perfect 11-mosstep P11ms 9L + 2s 941.9 ¢ to 963.4 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 963.4 ¢ to 1027.6 ¢
Major 12-mosstep M12ms 10L + 2s 1027.6 ¢ to 1070.4 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 1070.4 ¢ to 1113.2 ¢
Major 13-mosstep M13ms 11L + 2s 1113.2 ¢ to 1177.4 ¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 1177.4 ¢ to 1198.8 ¢
Augmented 14-mosstep A14ms 12L + 2s 1198.8 ¢ to 1284.5 ¢
15-mosstep Perfect 15-mosstep P15ms 12L + 3s 1284.5 ¢

Scale tree

Template:Scale tree


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