3L 3s
| ↖ 2L 2s | ↑ 3L 2s | 4L 2s ↗ |
| ← 2L 3s | 3L 3s | 4L 3s → |
| ↙ 2L 4s | ↓ 3L 4s | 4L 4s ↘ |
┌╥┬╥┬╥┬┐ │║│║│║││ ││││││││ └┴┴┴┴┴┴┘
Scale structure
sLsLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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].
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-triwdstep | Perfect 0-triwdstep | P0tws | 0 | 0.0 ¢ |
| 1-triwdstep | Minor 1-triwdstep | m1tws | s | 0.0 ¢ to 200.0 ¢ |
| Major 1-triwdstep | M1tws | L | 200.0 ¢ to 400.0 ¢ | |
| 2-triwdstep | Perfect 2-triwdstep | P2tws | L + s | 400.0 ¢ |
| 3-triwdstep | Minor 3-triwdstep | m3tws | L + 2s | 400.0 ¢ to 600.0 ¢ |
| Major 3-triwdstep | M3tws | 2L + s | 600.0 ¢ to 800.0 ¢ | |
| 4-triwdstep | Perfect 4-triwdstep | P4tws | 2L + 2s | 800.0 ¢ |
| 5-triwdstep | Minor 5-triwdstep | m5tws | 2L + 3s | 800.0 ¢ to 1000.0 ¢ |
| Major 5-triwdstep | M5tws | 3L + 2s | 1000.0 ¢ to 1200.0 ¢ | |
| 6-triwdstep | Perfect 6-triwdstep | P6tws | 3L + 3s | 1200.0 ¢ |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (triwddegree) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
| 3|0(3) | 1 | LsLsLs | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. |
| 0|3(3) | 2 | sLsLsL | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\6 | 200.000 | 200.000 | 1:1 | 1.000 | Equalized 3L 3s | |||||
| 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 | ||||||
| 4\21 | 228.571 | 171.429 | 4:3 | 1.333 | Supersoft 3L 3s | |||||
| 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 | 1.429 | ||||||
| 3\15 | 240.000 | 160.000 | 3:2 | 1.500 | Soft 3L 3s | |||||
| 11\54 | 244.444 | 155.556 | 11:7 | 1.571 | ||||||
| 8\39 | 246.154 | 153.846 | 8:5 | 1.600 | ||||||
| 13\63 | 247.619 | 152.381 | 13:8 | 1.625 | ||||||
| 5\24 | 250.000 | 150.000 | 5:3 | 1.667 | Semisoft 3L 3s | |||||
| 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 3L 3s | |||||
| 9\39 | 276.923 | 123.077 | 9:4 | 2.250 | ||||||
| 7\30 | 280.000 | 120.000 | 7:3 | 2.333 | ||||||
| 12\51 | 282.353 | 117.647 | 12:5 | 2.400 | ||||||
| 5\21 | 285.714 | 114.286 | 5:2 | 2.500 | Semihard 3L 3s | |||||
| 13\54 | 288.889 | 111.111 | 13:5 | 2.600 | ||||||
| 8\33 | 290.909 | 109.091 | 8:3 | 2.667 | ||||||
| 11\45 | 293.333 | 106.667 | 11:4 | 2.750 | ||||||
| 3\12 | 300.000 | 100.000 | 3:1 | 3.000 | Hard 3L 3s | |||||
| 10\39 | 307.692 | 92.308 | 10:3 | 3.333 | ||||||
| 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 | Superhard 3L 3s | |||||
| 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 | ||||||
| 1\3 | 400.000 | 0.000 | 1:0 | → ∞ | Collapsed 3L 3s | |||||