3L 3s

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).

↖ 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 ¢)
View • Talk • Edit

Generator					Cents	Comments
0\3					0
			1\15		80	L/s = 4
				2\27	88.88	Optimal augmented is around here
					400/(1+pi)
		1\12			100	L/s = 3
					400/(1+e)
				3\33	109.09
					400/(2+phi)
			2\21		114.29
	1\9				133.33	Boundary of propriety for near-MOS Optimum rank range (L/s=2/1) for MOS
					400/(1+sqrt(3))
			3\24		150
					400/(1+phi)
				5\39	153.85
					400/(1+pi/2)
		2\15			160
1\6					200

Out of all proper six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.