3L 12s
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Scale structure
Step pattern
LssssLssssLssss
ssssLssssLssssL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
4\15 to 1\3 (320.0¢ to 400.0¢)
Dark
0\3 to 1\15 (0.0¢ to 80.0¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
3L 9s
Sister
12L 3s
Daughters
15L 3s, 3L 15s
Neutralized
6L 9s
2-Flought
18L 12s, 3L 27s
Equal tunings
Equalized (L:s = 1:1)
4\15 (320.0¢)
Supersoft (L:s = 4:3)
13\48 (325.0¢)
Soft (L:s = 3:2)
9\33 (327.3¢)
Semisoft (L:s = 5:3)
14\51 (329.4¢)
Basic (L:s = 2:1)
5\18 (333.3¢)
Semihard (L:s = 5:2)
11\39 (338.5¢)
Hard (L:s = 3:1)
6\21 (342.9¢)
Superhard (L:s = 4:1)
7\24 (350.0¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 11s | ↑ 3L 11s | 4L 11s ↗ |
| ← 2L 12s | 3L 12s | 4L 12s → |
| ↙ 2L 13s | ↓ 3L 13s | 4L 13s ↘ |
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║││││║││││║│││││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLssssLssssL
3L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 12 small steps, with a period of 1 large step and 4 small steps that repeats every 400.0¢, or 3 times every octave. 3L 12s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 320¢ to 400¢, or from 0¢ to 80¢.
It is the MOS of Inflated[15].
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0(3) | 1 | LssssLssssLssss |
| 9|3(3) | 5 | sLssssLssssLsss |
| 6|6(3) | 4 | ssLssssLssssLss |
| 3|9(3) | 3 | sssLssssLssssLs |
| 0|12(3) | 2 | ssssLssssLssssL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0¢ to 80.0¢ |
| Augmented 1-mosstep | A1ms | L | 80.0¢ to 400.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 160.0¢ |
| Major 2-mosstep | M2ms | L + s | 160.0¢ to 400.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 240.0¢ |
| Major 3-mosstep | M3ms | L + 2s | 240.0¢ to 400.0¢ | |
| 4-mosstep | Diminished 4-mosstep | d4ms | 4s | 0.0¢ to 320.0¢ |
| Perfect 4-mosstep | P4ms | L + 3s | 320.0¢ to 400.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 400.0¢ |
| 6-mosstep | Perfect 6-mosstep | P6ms | L + 5s | 400.0¢ to 480.0¢ |
| Augmented 6-mosstep | A6ms | 2L + 4s | 480.0¢ to 800.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 400.0¢ to 560.0¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 560.0¢ to 800.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 400.0¢ to 640.0¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 640.0¢ to 800.0¢ | |
| 9-mosstep | Diminished 9-mosstep | d9ms | L + 8s | 400.0¢ to 720.0¢ |
| Perfect 9-mosstep | P9ms | 2L + 7s | 720.0¢ to 800.0¢ | |
| 10-mosstep | Perfect 10-mosstep | P10ms | 2L + 8s | 800.0¢ |
| 11-mosstep | Perfect 11-mosstep | P11ms | 2L + 9s | 800.0¢ to 880.0¢ |
| Augmented 11-mosstep | A11ms | 3L + 8s | 880.0¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 800.0¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 3L + 9s | 960.0¢ to 1200.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 2L + 11s | 800.0¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 3L + 10s | 1040.0¢ to 1200.0¢ | |
| 14-mosstep | Diminished 14-mosstep | d14ms | 2L + 12s | 800.0¢ to 1120.0¢ |
| Perfect 14-mosstep | P14ms | 3L + 11s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 3L + 12s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\15 | 320.000 | 80.000 | 1:1 | 1.000 | Equalized 3L 12s | |||||
| 21\78 | 323.077 | 76.923 | 6:5 | 1.200 | ||||||
| 17\63 | 323.810 | 76.190 | 5:4 | 1.250 | ||||||
| 30\111 | 324.324 | 75.676 | 9:7 | 1.286 | ||||||
| 13\48 | 325.000 | 75.000 | 4:3 | 1.333 | Supersoft 3L 12s | |||||
| 35\129 | 325.581 | 74.419 | 11:8 | 1.375 | ||||||
| 22\81 | 325.926 | 74.074 | 7:5 | 1.400 | ||||||
| 31\114 | 326.316 | 73.684 | 10:7 | 1.429 | ||||||
| 9\33 | 327.273 | 72.727 | 3:2 | 1.500 | Soft 3L 12s | |||||
| 32\117 | 328.205 | 71.795 | 11:7 | 1.571 | ||||||
| 23\84 | 328.571 | 71.429 | 8:5 | 1.600 | ||||||
| 37\135 | 328.889 | 71.111 | 13:8 | 1.625 | ||||||
| 14\51 | 329.412 | 70.588 | 5:3 | 1.667 | Semisoft 3L 12s | |||||
| 33\120 | 330.000 | 70.000 | 12:7 | 1.714 | ||||||
| 19\69 | 330.435 | 69.565 | 7:4 | 1.750 | ||||||
| 24\87 | 331.034 | 68.966 | 9:5 | 1.800 | ||||||
| 5\18 | 333.333 | 66.667 | 2:1 | 2.000 | Basic 3L 12s Scales with tunings softer than this are proper | |||||
| 21\75 | 336.000 | 64.000 | 9:4 | 2.250 | ||||||
| 16\57 | 336.842 | 63.158 | 7:3 | 2.333 | ||||||
| 27\96 | 337.500 | 62.500 | 12:5 | 2.400 | ||||||
| 11\39 | 338.462 | 61.538 | 5:2 | 2.500 | Semihard 3L 12s | |||||
| 28\99 | 339.394 | 60.606 | 13:5 | 2.600 | ||||||
| 17\60 | 340.000 | 60.000 | 8:3 | 2.667 | ||||||
| 23\81 | 340.741 | 59.259 | 11:4 | 2.750 | ||||||
| 6\21 | 342.857 | 57.143 | 3:1 | 3.000 | Hard 3L 12s | |||||
| 19\66 | 345.455 | 54.545 | 10:3 | 3.333 | ||||||
| 13\45 | 346.667 | 53.333 | 7:2 | 3.500 | ||||||
| 20\69 | 347.826 | 52.174 | 11:3 | 3.667 | ||||||
| 7\24 | 350.000 | 50.000 | 4:1 | 4.000 | Superhard 3L 12s | |||||
| 15\51 | 352.941 | 47.059 | 9:2 | 4.500 | ||||||
| 8\27 | 355.556 | 44.444 | 5:1 | 5.000 | ||||||
| 9\30 | 360.000 | 40.000 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 0.000 | 1:0 | → ∞ | Collapsed 3L 12s | |||||
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