4L 4s

The minimum harmonic entropy scale with this MOS pattern is diminished[8], basically the familiar octatonic scale of 12edo.

↖ 3L 3s	↑ 4L 3s	5L 3s ↗
← 3L 4s	4L 4s	5L 4s →
↙ 3L 5s	↓ 4L 5s	5L 5s ↘

Scale structure
Step pattern	LsLsLsLs sLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	1\8 to 1\4 (150.0 ¢ to 300.0 ¢)
Dark	0\4 to 1\8 (0.0 ¢ to 150.0 ¢)
TAMNAMS information
Name	tetrawood
Prefix	tetrawd-
Abbrev.	ttw
Related MOS scales
Parent	none
Sister	4L 4s (self)
Daughters	8L 4s, 4L 8s
Neutralized	8edo
2-Flought	12L 4s, 4L 12s
Equal tunings
Equalized (L:s = 1:1)	1\8 (150.0 ¢)
Supersoft (L:s = 4:3)	4\28 (171.4 ¢)
Soft (L:s = 3:2)	3\20 (180.0 ¢)
Semisoft (L:s = 5:3)	5\32 (187.5 ¢)
Basic (L:s = 2:1)	2\12 (200.0 ¢)
Semihard (L:s = 5:2)	5\28 (214.3 ¢)
Hard (L:s = 3:1)	3\16 (225.0 ¢)
Superhard (L:s = 4:1)	4\20 (240.0 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)

Generator					Cents	Comments
0\4					0
				1\24	50
			1\20		60	L/s = 4
					300/(1+pi)
		1\16			75	L/s = 3
					300/(1+e)
				3\44	81.82
			2\28		85.71
	1\12				100	Diminished is around here Optimum rank range (L/s=2/1) for MOS
					300/(1+sqrt(3))
			3\32		112.5
				5\52	115.38	Golden diminished
					300/(1+pi/2)
		2\20			120
			3\28		128.57
				4\36	133.33
1\8					150