3L 3s

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↖2L 2s ↑3L 2s 4L 2s↗
←2L 3s3L 3s 4L 3s→
↙2L 4s ↓3L 4s 4L 4s↘
┌╥┬╥┬╥┬┐
│║│║│║││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLs
sLsLsL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Step size ranges
Large 1\6 to 1\3 (200.0¢ to 400.0¢)
Small 0\3 to 1\6 (0.0¢ to 200.0¢)
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¢)

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

Modes of 3L 3s
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