3L 3s
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Brightest mode
LsLsLs
Period
1\3
Range for bright generator
1\6 (200¢) to 1\3 (400¢)
Range for dark generator
0\3 (0¢) to 1\6 (200¢)
TAMNAMS name
triwood
TAMNAMS prefix
triwd- (abbr. trw)
Parent MOS
none
Sister MOS
3L 3s
Daughter MOSes
6L 3s, 3L 6s
Equal tunings
Supersoft (L:s = 4:3)
4\21 (228.6¢)
Soft (L:s = 3:2)
3\15 (240¢)
Semisoft (L:s = 5:3)
5\24 (250¢)
Basic (L:s = 2:1)
2\9 (266.7¢)
Semihard (L:s = 5:2)
5\21 (285.7¢)
Hard (L:s = 3:1)
3\12 (300¢)
Superhard (L:s = 4:1)
4\15 (320¢)
| ↖2L 2s | ↑3L 2s | 4L 2s↗ |
| ←2L 3s | 3L 3s | 4L 3s→ |
| ↙2L 4s | ↓3L 4s | 4L 4s↘ |
3L 3s, named triwood, is an octave-equivalent moment of symmetry scale containing 3 large steps and 3 small steps, with a period of 1 large step and 1 small step that repeats every 400¢, or 3 times every octave. Modes of this scale are rotations of the step pattern LsLsLs. Generators that produce this scale range from 200¢ to 400¢, or from 0¢ to 200¢.
The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).
Out of all proper six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.
Scale tree
| Generator | Cents | L | s | L/s | Comments | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Chroma-positive | Chroma-negative | ||||||||||
| 1\6 | 200.000 | 200.000 | 1 | 1 | 1.000 | ||||||
| 6\33 | 218.182 | 181.818 | 6 | 5 | 1.200 | ||||||
| 5\27 | 222.222 | 177.778 | 5 | 4 | 1.250 | ||||||
| 9\48 | 225.000 | 175.000 | 9 | 7 | 1.286 | Oodako | |||||
| 4\21 | 228.571 | 171.429 | 4 | 3 | 1.333 | ||||||
| 11\57 | 231.579 | 168.421 | 11 | 8 | 1.375 | ||||||
| 7\36 | 233.333 | 166.667 | 7 | 5 | 1.400 | ||||||
| 10\51 | 235.294 | 164.706 | 10 | 7 | 1.428 | ||||||
| 3\15 | 240.000 | 160.000 | 3 | 2 | 1.500 | ||||||
| 11\54 | 244.444 | 155.556 | 11 | 7 | 1.571 | ||||||
| 8\39 | 246.154 | 153.846 | 8 | 5 | 1.600 | Triforce | |||||
| 13\63 | 247.619 | 152.381 | 13 | 8 | 1.625 | Unnamed golden tuning | |||||
| 5\24 | 250.000 | 150.000 | 5 | 3 | 1.667 | ||||||
| 12\57 | 252.632 | 147.368 | 12 | 7 | 1.714 | ||||||
| 7\33 | 254.545 | 145.455 | 7 | 4 | 1.750 | ||||||
| 9\42 | 257.143 | 142.857 | 9 | 5 | 1.800 | ||||||
| 2\9 | 266.667 | 133.333 | 2 | 1 | 2.000 | Basic triwood | |||||
| 9\39 | 276.923 | 123.077 | 9 | 4 | 2.250 | ||||||
| 7\30 | 280.000 | 120.000 | 7 | 3 | 2.333 | Deflated (optimal around here) | |||||
| 12\51 | 282.353 | 117.647 | 12 | 5 | 2.400 | ||||||
| 5\21 | 285.714 | 114.286 | 5 | 2 | 2.500 | ||||||
| 13\54 | 288.889 | 111.111 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 8\33 | 290.909 | 109.091 | 8 | 3 | 2.667 | ||||||
| 11\45 | 293.333 | 106.667 | 11 | 4 | 2.750 | August | |||||
| 3\12 | 300.000 | 100.000 | 3 | 1 | 3.000 | Trug (optimal around here) | |||||
| 10\39 | 307.692 | 92.308 | 10 | 3 | 3.333 | Augene | |||||
| 7\27 | 311.111 | 88.889 | 7 | 2 | 3.500 | ||||||
| 11\42 | 314.286 | 85.714 | 11 | 3 | 3.667 | ||||||
| 4\15 | 320.000 | 80.000 | 4 | 1 | 4.000 | Inflated | |||||
| 9\33 | 327.273 | 72.727 | 9 | 2 | 4.500 | ||||||
| 5\18 | 333.333 | 66.667 | 5 | 1 | 5.000 | ||||||
| 6\21 | 342.857 | 57.143 | 6 | 1 | 6.000 | Hemiug↓, hemiaug↓ | |||||
| 1\3 | 400.000 | 0.000 | 1 | 0 | → inf | ||||||