3L 3s

↖ 2L 2s	↑ 3L 2s	4L 2s ↗
← 2L 3s	3L 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 ¢)
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.	tw
Related MOS scales
Parent	none
Sister	3L 3s (self)
Daughters	6L 3s, 3L 6s
Neutralized	6edo
2-Flought	9L 3s, 3L 9s
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 ¢)

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.

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