4L 12s
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Scale structure
Step pattern
LsssLsssLsssLsss
sssLsssLsssLsssL
Equave
2/1 (1200.0¢)
Period
1\4 (300.0¢)
Generator size
Bright
3\16 to 1\4 (225.0¢ to 300.0¢)
Dark
0\4 to 1\16 (0.0¢ to 75.0¢)
TAMNAMS information
Descends from
4L 4s (tetrawood)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
4L 8s
Sister
12L 4s
Daughters
16L 4s, 4L 16s
Neutralized
8L 8s
2-Flought
20L 12s, 4L 28s
Equal tunings
Equalized (L:s = 1:1)
3\16 (225.0¢)
Supersoft (L:s = 4:3)
10\52 (230.8¢)
Soft (L:s = 3:2)
7\36 (233.3¢)
Semisoft (L:s = 5:3)
11\56 (235.7¢)
Basic (L:s = 2:1)
4\20 (240.0¢)
Semihard (L:s = 5:2)
9\44 (245.5¢)
Hard (L:s = 3:1)
5\24 (250.0¢)
Superhard (L:s = 4:1)
6\28 (257.1¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 11s | ↑ 4L 11s | 5L 11s ↗ |
| ← 3L 12s | 4L 12s | 5L 12s → |
| ↙ 3L 13s | ↓ 4L 13s | 5L 13s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┐ │║│││║│││║│││║││││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLsssLsssL
4L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 12 small steps, with a period of 1 large step and 3 small steps that repeats every 300.0¢, or 4 times every octave. 4L 12s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 225¢ to 300¢, or from 0¢ to 75¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0(4) | 1 | LsssLsssLsssLsss |
| 8|4(4) | 4 | sLsssLsssLsssLss |
| 4|8(4) | 3 | ssLsssLsssLsssLs |
| 0|12(4) | 2 | sssLsssLsssLsssL |
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 75.0¢ |
| Augmented 1-mosstep | A1ms | L | 75.0¢ to 300.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 150.0¢ |
| Major 2-mosstep | M2ms | L + s | 150.0¢ to 300.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0¢ to 225.0¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 225.0¢ to 300.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 300.0¢ |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 300.0¢ to 375.0¢ |
| Augmented 5-mosstep | A5ms | 2L + 3s | 375.0¢ to 600.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 300.0¢ to 450.0¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 450.0¢ to 600.0¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | L + 6s | 300.0¢ to 525.0¢ |
| Perfect 7-mosstep | P7ms | 2L + 5s | 525.0¢ to 600.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 2L + 6s | 600.0¢ |
| 9-mosstep | Perfect 9-mosstep | P9ms | 2L + 7s | 600.0¢ to 675.0¢ |
| Augmented 9-mosstep | A9ms | 3L + 6s | 675.0¢ to 900.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 600.0¢ to 750.0¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 750.0¢ to 900.0¢ | |
| 11-mosstep | Diminished 11-mosstep | d11ms | 2L + 9s | 600.0¢ to 825.0¢ |
| Perfect 11-mosstep | P11ms | 3L + 8s | 825.0¢ to 900.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 3L + 9s | 900.0¢ |
| 13-mosstep | Perfect 13-mosstep | P13ms | 3L + 10s | 900.0¢ to 975.0¢ |
| Augmented 13-mosstep | A13ms | 4L + 9s | 975.0¢ to 1200.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 3L + 11s | 900.0¢ to 1050.0¢ |
| Major 14-mosstep | M14ms | 4L + 10s | 1050.0¢ to 1200.0¢ | |
| 15-mosstep | Diminished 15-mosstep | d15ms | 3L + 12s | 900.0¢ to 1125.0¢ |
| Perfect 15-mosstep | P15ms | 4L + 11s | 1125.0¢ to 1200.0¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 4L + 12s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\16 | 225.000 | 75.000 | 1:1 | 1.000 | Equalized 4L 12s | |||||
| 16\84 | 228.571 | 71.429 | 6:5 | 1.200 | ||||||
| 13\68 | 229.412 | 70.588 | 5:4 | 1.250 | ||||||
| 23\120 | 230.000 | 70.000 | 9:7 | 1.286 | ||||||
| 10\52 | 230.769 | 69.231 | 4:3 | 1.333 | Supersoft 4L 12s | |||||
| 27\140 | 231.429 | 68.571 | 11:8 | 1.375 | ||||||
| 17\88 | 231.818 | 68.182 | 7:5 | 1.400 | ||||||
| 24\124 | 232.258 | 67.742 | 10:7 | 1.429 | ||||||
| 7\36 | 233.333 | 66.667 | 3:2 | 1.500 | Soft 4L 12s | |||||
| 25\128 | 234.375 | 65.625 | 11:7 | 1.571 | ||||||
| 18\92 | 234.783 | 65.217 | 8:5 | 1.600 | ||||||
| 29\148 | 235.135 | 64.865 | 13:8 | 1.625 | ||||||
| 11\56 | 235.714 | 64.286 | 5:3 | 1.667 | Semisoft 4L 12s | |||||
| 26\132 | 236.364 | 63.636 | 12:7 | 1.714 | ||||||
| 15\76 | 236.842 | 63.158 | 7:4 | 1.750 | ||||||
| 19\96 | 237.500 | 62.500 | 9:5 | 1.800 | ||||||
| 4\20 | 240.000 | 60.000 | 2:1 | 2.000 | Basic 4L 12s Scales with tunings softer than this are proper | |||||
| 17\84 | 242.857 | 57.143 | 9:4 | 2.250 | ||||||
| 13\64 | 243.750 | 56.250 | 7:3 | 2.333 | ||||||
| 22\108 | 244.444 | 55.556 | 12:5 | 2.400 | ||||||
| 9\44 | 245.455 | 54.545 | 5:2 | 2.500 | Semihard 4L 12s | |||||
| 23\112 | 246.429 | 53.571 | 13:5 | 2.600 | ||||||
| 14\68 | 247.059 | 52.941 | 8:3 | 2.667 | ||||||
| 19\92 | 247.826 | 52.174 | 11:4 | 2.750 | ||||||
| 5\24 | 250.000 | 50.000 | 3:1 | 3.000 | Hard 4L 12s | |||||
| 16\76 | 252.632 | 47.368 | 10:3 | 3.333 | ||||||
| 11\52 | 253.846 | 46.154 | 7:2 | 3.500 | ||||||
| 17\80 | 255.000 | 45.000 | 11:3 | 3.667 | ||||||
| 6\28 | 257.143 | 42.857 | 4:1 | 4.000 | Superhard 4L 12s | |||||
| 13\60 | 260.000 | 40.000 | 9:2 | 4.500 | ||||||
| 7\32 | 262.500 | 37.500 | 5:1 | 5.000 | ||||||
| 8\36 | 266.667 | 33.333 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 0.000 | 1:0 | → ∞ | Collapsed 4L 12s | |||||
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