12L 3s (21/10-equivalent)
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Scale structure
Step pattern
LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave
21/10 (1284.5¢)
Period
1\3ed21/10 (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¢)
| ↖ 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⟩ ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║│║║║║│║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLsLLLL
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
| 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 | 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
| 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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