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.

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 diatonic interval categories.

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 ¢

Generator chain

Generator chain of 12L 3s⟨21/10⟩
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
8 Augmented 3-mosdegree A3md Augmented 8-mosdegree A8md Augmented 13-mosdegree A13md
7 Augmented 2-mosdegree A2md Augmented 7-mosdegree A7md Augmented 12-mosdegree A12md
6 Augmented 1-mosdegree A1md Augmented 6-mosdegree A6md Augmented 11-mosdegree A11md
5 Augmented 0-mosdegree A0md Augmented 5-mosdegree A5md Augmented 10-mosdegree A10md
4 Augmented 4-mosdegree A4md Augmented 9-mosdegree A9md Augmented 14-mosdegree A14md
3 Major 3-mosdegree M3md Major 8-mosdegree M8md Major 13-mosdegree M13md
2 Major 2-mosdegree M2md Major 7-mosdegree M7md Major 12-mosdegree M12md
1 Perfect 1-mosdegree P1md Perfect 6-mosdegree P6md Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md		 Perfect 5-mosdegree
Perfect 10-mosdegree		 P5md
P10md		 Perfect 10-mosdegree
Perfect 15-mosdegree		 P10md
P15md
−1 Perfect 4-mosdegree P4md Perfect 9-mosdegree P9md Perfect 14-mosdegree P14md
−2 Minor 3-mosdegree m3md Minor 8-mosdegree m8md Minor 13-mosdegree m13md
−3 Minor 2-mosdegree m2md Minor 7-mosdegree m7md Minor 12-mosdegree m12md
−4 Diminished 1-mosdegree d1md Diminished 6-mosdegree d6md Diminished 11-mosdegree d11md
−5 Diminished 5-mosdegree d5md Diminished 10-mosdegree d10md Diminished 15-mosdegree d15md
−6 Diminished 4-mosdegree d4md Diminished 9-mosdegree d9md Diminished 14-mosdegree d14md
−7 Diminished 3-mosdegree d3md Diminished 8-mosdegree d8md Diminished 13-mosdegree d13md
−8 Diminished 2-mosdegree d2md Diminished 7-mosdegree d7md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 12L 3s⟨21/10⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12|0(3) 1 LLLLsLLLLsLLLLs Perf. Perf. Maj. Maj. Aug. Perf. Perf. Maj. Maj. Aug. Perf. Perf. Maj. Maj. Aug. Perf.
9|3(3) 2 LLLsLLLLsLLLLsL Perf. Perf. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Perf. Perf.
6|6(3) 3 LLsLLLLsLLLLsLL Perf. Perf. Maj. Min. Perf. Perf. Perf. Maj. Min. Perf. Perf. Perf. Maj. Min. Perf. Perf.
3|9(3) 4 LsLLLLsLLLLsLLL Perf. Perf. Min. Min. Perf. Perf. Perf. Min. Min. Perf. Perf. Perf. Min. Min. Perf. Perf.
0|12(3) 5 sLLLLsLLLLsLLLL Perf. Dim. Min. Min. Perf. Perf. Dim. Min. Min. Perf. Perf. Dim. Min. Min. Perf. Perf.

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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