3L 3s
| ↖ 2L 2s | ↑ 3L 2s | 4L 2s ↗ |
| ← 2L 3s | 3L 3s | 4L 3s → |
| ↙ 2L 4s | ↓ 3L 4s | 4L 4s ↘ |
┌╥┬╥┬╥┬┐ │║│║│║││ ││││││││ └┴┴┴┴┴┴┘
sLsLsL
3L 3s, named triwood in TAMNAMS, is a 2/1-equivalent (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 400.0 ¢, or 3 times every octave. Generators that produce this scale range from 200 ¢ to 400 ¢, or from 0 ¢ to 200 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. 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.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 3|0(3) | 1 | LsLsLs |
| 0|3(3) | 2 | sLsLsL |
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 | ||||||