12L 3s (21/10-equivalent)
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Step pattern
LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave
21/10 (1284.5 ¢)
Period
1\3 (428.2 ¢)
Bright
1\15 to 1\12 (85.6 ¢ to 107.0 ¢)
Dark
3\12 to 4\15 (321.1 ¢ to 342.5 ¢)
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⟩
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 ¢)
↖ 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
sLLLLsLLLLsLLLL
Generator size(ed21/10)
Related MOS scales
Equal tunings(ed21/10)
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 | 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
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
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
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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