3L 3s
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Scale structure
Step pattern
LsLsLs
sLsLsL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
1\6 to 1\3 (200.0¢ to 400.0¢)
Dark
0\3 to 1\6 (0.0¢ to 200.0¢)
TAMNAMS information
Name
triwood
Prefix
triwd-
Abbrev.
trw
Related MOS scales
Parent
none
Sister
3L 3s (self)
Daughters
6L 3s
3L 6s
Equal tunings
Equalized (L:s = 1:1)
1\6 (200.0¢)
Supersoft (L:s = 4:3)
4\21 (228.6¢)
Soft (L:s = 3:2)
3\15 (240.0¢)
Semisoft (L:s = 5:3)
5\24 (250.0¢)
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 (300.0¢)
Superhard (L:s = 4:1)
4\15 (320.0¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖2L 2s | ↑3L 2s | 4L 2s↗ |
| ←2L 3s | 3L 3s | 4L 3s→ |
| ↙2L 4s | ↓3L 4s | 4L 4s↘ |
┌╥┬╥┬╥┬┐ │║│║│║││ ││││││││ └┴┴┴┴┴┴┘
sLsLsL
3L 6s
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.
In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than 1\9.
Out of all proper six-note MOS scales, this augmented scale probably has the lowest harmonic entropy[clarification needed].
Modes
| UDP | Rotational 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 | ||||||