12L 4s
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Scale structure
Step pattern
LLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLL
Equave
2/1 (1200.0¢)
Period
1\4 (300.0¢)
Generator size
Bright
1\16 to 1\12 (75.0¢ to 100.0¢)
Dark
2\12 to 3\16 (200.0¢ to 225.0¢)
TAMNAMS information
Descends from
4L 4s (tetrawood)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
4L 8s
Sister
4L 12s
Daughters
16L 12s, 12L 16s
Neutralized
8L 8s
2-Flought
28L 4s, 12L 20s
Equal tunings
Equalized (L:s = 1:1)
1\16 (75.0¢)
Supersoft (L:s = 4:3)
4\60 (80.0¢)
Soft (L:s = 3:2)
3\44 (81.8¢)
Semisoft (L:s = 5:3)
5\72 (83.3¢)
Basic (L:s = 2:1)
2\28 (85.7¢)
Semihard (L:s = 5:2)
5\68 (88.2¢)
Hard (L:s = 3:1)
3\40 (90.0¢)
Superhard (L:s = 4:1)
4\52 (92.3¢)
Collapsed (L:s = 1:0)
1\12 (100.0¢)
| ↖ 11L 3s | ↑ 12L 3s | 13L 3s ↗ |
| ← 11L 4s | 12L 4s | 13L 4s → |
| ↙ 11L 5s | ↓ 12L 5s | 13L 5s ↘ |
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║│║║║││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLsLLL
12L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 4 small steps, with a period of 3 large steps and 1 small step that repeats every 300.0¢, or 4 times every octave. 12L 4s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 75¢ to 100¢, or from 200¢ to 225¢. 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(4) | 1 | LLLsLLLsLLLsLLLs |
| 8|4(4) | 2 | LLsLLLsLLLsLLLsL |
| 4|8(4) | 3 | LsLLLsLLLsLLLsLL |
| 0|12(4) | 4 | sLLLsLLLsLLLsLLL |
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 75.0¢ |
| Perfect 1-mosstep | P1ms | L | 75.0¢ to 100.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 100.0¢ to 150.0¢ |
| Major 2-mosstep | M2ms | 2L | 150.0¢ to 200.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 200.0¢ to 225.0¢ |
| Augmented 3-mosstep | A3ms | 3L | 225.0¢ to 300.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | 3L + s | 300.0¢ |
| 5-mosstep | Diminished 5-mosstep | d5ms | 3L + 2s | 300.0¢ to 375.0¢ |
| Perfect 5-mosstep | P5ms | 4L + s | 375.0¢ to 400.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 400.0¢ to 450.0¢ |
| Major 6-mosstep | M6ms | 5L + s | 450.0¢ to 500.0¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 5L + 2s | 500.0¢ to 525.0¢ |
| Augmented 7-mosstep | A7ms | 6L + s | 525.0¢ to 600.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 6L + 2s | 600.0¢ |
| 9-mosstep | Diminished 9-mosstep | d9ms | 6L + 3s | 600.0¢ to 675.0¢ |
| Perfect 9-mosstep | P9ms | 7L + 2s | 675.0¢ to 700.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 7L + 3s | 700.0¢ to 750.0¢ |
| Major 10-mosstep | M10ms | 8L + 2s | 750.0¢ to 800.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 8L + 3s | 800.0¢ to 825.0¢ |
| Augmented 11-mosstep | A11ms | 9L + 2s | 825.0¢ to 900.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 9L + 3s | 900.0¢ |
| 13-mosstep | Diminished 13-mosstep | d13ms | 9L + 4s | 900.0¢ to 975.0¢ |
| Perfect 13-mosstep | P13ms | 10L + 3s | 975.0¢ to 1000.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 10L + 4s | 1000.0¢ to 1050.0¢ |
| Major 14-mosstep | M14ms | 11L + 3s | 1050.0¢ to 1100.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 11L + 4s | 1100.0¢ to 1125.0¢ |
| Augmented 15-mosstep | A15ms | 12L + 3s | 1125.0¢ to 1200.0¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 12L + 4s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\16 | 75.000 | 225.000 | 1:1 | 1.000 | Equalized 12L 4s | |||||
| 6\92 | 78.261 | 221.739 | 6:5 | 1.200 | ||||||
| 5\76 | 78.947 | 221.053 | 5:4 | 1.250 | ||||||
| 9\136 | 79.412 | 220.588 | 9:7 | 1.286 | ||||||
| 4\60 | 80.000 | 220.000 | 4:3 | 1.333 | Supersoft 12L 4s | |||||
| 11\164 | 80.488 | 219.512 | 11:8 | 1.375 | ||||||
| 7\104 | 80.769 | 219.231 | 7:5 | 1.400 | ||||||
| 10\148 | 81.081 | 218.919 | 10:7 | 1.429 | ||||||
| 3\44 | 81.818 | 218.182 | 3:2 | 1.500 | Soft 12L 4s | |||||
| 11\160 | 82.500 | 217.500 | 11:7 | 1.571 | ||||||
| 8\116 | 82.759 | 217.241 | 8:5 | 1.600 | ||||||
| 13\188 | 82.979 | 217.021 | 13:8 | 1.625 | ||||||
| 5\72 | 83.333 | 216.667 | 5:3 | 1.667 | Semisoft 12L 4s | |||||
| 12\172 | 83.721 | 216.279 | 12:7 | 1.714 | ||||||
| 7\100 | 84.000 | 216.000 | 7:4 | 1.750 | ||||||
| 9\128 | 84.375 | 215.625 | 9:5 | 1.800 | ||||||
| 2\28 | 85.714 | 214.286 | 2:1 | 2.000 | Basic 12L 4s | |||||
| 9\124 | 87.097 | 212.903 | 9:4 | 2.250 | ||||||
| 7\96 | 87.500 | 212.500 | 7:3 | 2.333 | ||||||
| 12\164 | 87.805 | 212.195 | 12:5 | 2.400 | ||||||
| 5\68 | 88.235 | 211.765 | 5:2 | 2.500 | Semihard 12L 4s | |||||
| 13\176 | 88.636 | 211.364 | 13:5 | 2.600 | ||||||
| 8\108 | 88.889 | 211.111 | 8:3 | 2.667 | ||||||
| 11\148 | 89.189 | 210.811 | 11:4 | 2.750 | ||||||
| 3\40 | 90.000 | 210.000 | 3:1 | 3.000 | Hard 12L 4s | |||||
| 10\132 | 90.909 | 209.091 | 10:3 | 3.333 | ||||||
| 7\92 | 91.304 | 208.696 | 7:2 | 3.500 | ||||||
| 11\144 | 91.667 | 208.333 | 11:3 | 3.667 | ||||||
| 4\52 | 92.308 | 207.692 | 4:1 | 4.000 | Superhard 12L 4s | |||||
| 9\116 | 93.103 | 206.897 | 9:2 | 4.500 | ||||||
| 5\64 | 93.750 | 206.250 | 5:1 | 5.000 | ||||||
| 6\76 | 94.737 | 205.263 | 6:1 | 6.000 | ||||||
| 1\12 | 100.000 | 200.000 | 1:0 | → ∞ | Collapsed 12L 4s | |||||
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