3L 3s
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Step pattern
LsLsLs
sLsLsL
Equave
2/1 (1200.0 ¢)
Period
1\3 (400.0 ¢)
Bright
1\6 to 1\3 (200.0 ¢ to 400.0 ¢)
Dark
0\3 to 1\6 (0.0 ¢ to 200.0 ¢)
Name
triwood
Prefix
triwd-
Abbrev.
tw
Parent
none
Sister
3L 3s (self)
Daughters
6L 3s, 3L 6s
Neutralized
6edo
2-Flought
9L 3s, 3L 9s
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 ↘ |
┌╥┬╥┬╥┬┐ │║│║│║││ ││││││││ └┴┴┴┴┴┴┘
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 | 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 |