12L 3s
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Scale structure
Step pattern
LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
1\15 to 1\12 (80.0¢ to 100.0¢)
Dark
3\12 to 4\15 (300.0¢ to 320.0¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
3L 9s
Sister
3L 12s
Daughters
15L 12s, 12L 15s
Neutralized
9L 6s
2-Flought
27L 3s, 12L 18s
Equal tunings
Equalized (L:s = 1:1)
1\15 (80.0¢)
Supersoft (L:s = 4:3)
4\57 (84.2¢)
Soft (L:s = 3:2)
3\42 (85.7¢)
Semisoft (L:s = 5:3)
5\69 (87.0¢)
Basic (L:s = 2:1)
2\27 (88.9¢)
Semihard (L:s = 5:2)
5\66 (90.9¢)
Hard (L:s = 3:1)
3\39 (92.3¢)
Superhard (L:s = 4:1)
4\51 (94.1¢)
Collapsed (L:s = 1:0)
1\12 (100.0¢)
| ↖ 11L 2s | ↑ 12L 2s | 13L 2s ↗ |
| ← 11L 3s | 12L 3s | 13L 3s → |
| ↙ 11L 4s | ↓ 12L 4s | 13L 4s ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║│║║║║│║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLsLLLL
12L 3s is a 2/1-equivalent (octave-equivalent) 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 400.0¢, or 3 times every octave. 12L 3s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 80¢ to 100¢, or from 300¢ to 320¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].
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 80.0¢ |
| Perfect 1-mosstep | P1ms | L | 80.0¢ to 100.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 100.0¢ to 160.0¢ |
| Major 2-mosstep | M2ms | 2L | 160.0¢ to 200.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 200.0¢ to 240.0¢ |
| Major 3-mosstep | M3ms | 3L | 240.0¢ to 300.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | 3L + s | 300.0¢ to 320.0¢ |
| Augmented 4-mosstep | A4ms | 4L | 320.0¢ to 400.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 4L + s | 400.0¢ |
| 6-mosstep | Diminished 6-mosstep | d6ms | 4L + 2s | 400.0¢ to 480.0¢ |
| Perfect 6-mosstep | P6ms | 5L + s | 480.0¢ to 500.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 5L + 2s | 500.0¢ to 560.0¢ |
| Major 7-mosstep | M7ms | 6L + s | 560.0¢ to 600.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 6L + 2s | 600.0¢ to 640.0¢ |
| Major 8-mosstep | M8ms | 7L + s | 640.0¢ to 700.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | 7L + 2s | 700.0¢ to 720.0¢ |
| Augmented 9-mosstep | A9ms | 8L + s | 720.0¢ to 800.0¢ | |
| 10-mosstep | Perfect 10-mosstep | P10ms | 8L + 2s | 800.0¢ |
| 11-mosstep | Diminished 11-mosstep | d11ms | 8L + 3s | 800.0¢ to 880.0¢ |
| Perfect 11-mosstep | P11ms | 9L + 2s | 880.0¢ to 900.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 9L + 3s | 900.0¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 10L + 2s | 960.0¢ to 1000.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 10L + 3s | 1000.0¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 11L + 2s | 1040.0¢ to 1100.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 11L + 3s | 1100.0¢ to 1120.0¢ |
| Augmented 14-mosstep | A14ms | 12L + 2s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 12L + 3s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\15 | 80.000 | 320.000 | 1:1 | 1.000 | Equalized 12L 3s | |||||
| 6\87 | 82.759 | 317.241 | 6:5 | 1.200 | ||||||
| 5\72 | 83.333 | 316.667 | 5:4 | 1.250 | ||||||
| 9\129 | 83.721 | 316.279 | 9:7 | 1.286 | ||||||
| 4\57 | 84.211 | 315.789 | 4:3 | 1.333 | Supersoft 12L 3s | |||||
| 11\156 | 84.615 | 315.385 | 11:8 | 1.375 | ||||||
| 7\99 | 84.848 | 315.152 | 7:5 | 1.400 | ||||||
| 10\141 | 85.106 | 314.894 | 10:7 | 1.429 | ||||||
| 3\42 | 85.714 | 314.286 | 3:2 | 1.500 | Soft 12L 3s | |||||
| 11\153 | 86.275 | 313.725 | 11:7 | 1.571 | ||||||
| 8\111 | 86.486 | 313.514 | 8:5 | 1.600 | ||||||
| 13\180 | 86.667 | 313.333 | 13:8 | 1.625 | ||||||
| 5\69 | 86.957 | 313.043 | 5:3 | 1.667 | Semisoft 12L 3s | |||||
| 12\165 | 87.273 | 312.727 | 12:7 | 1.714 | ||||||
| 7\96 | 87.500 | 312.500 | 7:4 | 1.750 | ||||||
| 9\123 | 87.805 | 312.195 | 9:5 | 1.800 | ||||||
| 2\27 | 88.889 | 311.111 | 2:1 | 2.000 | Basic 12L 3s | |||||
| 9\120 | 90.000 | 310.000 | 9:4 | 2.250 | ||||||
| 7\93 | 90.323 | 309.677 | 7:3 | 2.333 | ||||||
| 12\159 | 90.566 | 309.434 | 12:5 | 2.400 | ||||||
| 5\66 | 90.909 | 309.091 | 5:2 | 2.500 | Semihard 12L 3s | |||||
| 13\171 | 91.228 | 308.772 | 13:5 | 2.600 | ||||||
| 8\105 | 91.429 | 308.571 | 8:3 | 2.667 | ||||||
| 11\144 | 91.667 | 308.333 | 11:4 | 2.750 | ||||||
| 3\39 | 92.308 | 307.692 | 3:1 | 3.000 | Hard 12L 3s | |||||
| 10\129 | 93.023 | 306.977 | 10:3 | 3.333 | ||||||
| 7\90 | 93.333 | 306.667 | 7:2 | 3.500 | ||||||
| 11\141 | 93.617 | 306.383 | 11:3 | 3.667 | ||||||
| 4\51 | 94.118 | 305.882 | 4:1 | 4.000 | Superhard 12L 3s | |||||
| 9\114 | 94.737 | 305.263 | 9:2 | 4.500 | ||||||
| 5\63 | 95.238 | 304.762 | 5:1 | 5.000 | ||||||
| 6\75 | 96.000 | 304.000 | 6:1 | 6.000 | ||||||
| 1\12 | 100.000 | 300.000 | 1:0 | → ∞ | Collapsed 12L 3s | |||||