4L 4s

↖ 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 ¢)

4L 4s, named tetrawood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 4 small steps, with a period of 1 large step and 1 small step that repeats every 300.0 ¢, or 4 times every octave. Generators that produce this scale range from 150 ¢ to 300 ¢, or from 0 ¢ to 150 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. The minimum harmonic entropy scale with this MOS pattern is diminished[8], basically the familiar octatonic scale of 12edo.

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.)

Modes

Modes of 4L 4s

UDP	Cyclic order	Step pattern
4|0(4)	1	LsLsLsLs
0|4(4)	2	sLsLsLsL

Scale tree

Generator						Cents		L	s	L/s	Comments
						Chroma-positive	Chroma-negative
1\8						150.000	150.000	1	1	1.000
					6\44	163.636	136.364	6	5	1.200	Fourfives↑
				5\36		166.667	133.333	5	4	1.250
					9\64	168.750	105.000	9	7	1.286
			4\28			171.429	128.571	4	3	1.333
					11\76	173.684	126.316	11	8	1.375
				7\48		175.000	125.000	7	5	1.400
					10\68	176.471	123.529	10	7	1.428
		3\20				180.000	60.000	3	2	1.500	L/s = 3/2
					11\72	183.333	116.667	11	7	1.571
				8\52		184.615	115.385	8	5	1.600
					13\84	185.714	114.286	13	8	1.625	Golden diminished
			5\32			187.500	112.500	5	3	1.667
					12\76	189.474	110.526	12	7	1.714
				7\44		190.909	109.091	7	4	1.750
					9\56	192.857	107.143	9	5	1.800
	2\12					200.000	100.000	2	1	2.000	Basic tetrawood Diminished is optimal around here
					9\52	207.692	92.308	9	4	2.250
				7\40		210.000	90.000	7	3	2.333
					12\68	211.765	88.235	12	5	2.400
			5\28			214.286	85.714	5	2	2.500
					13\72	216.667	83.333	13	5	2.600	Unnamed golden tuning
				8\44		218.182	81.818	8	3	2.667
					11\60	220.000	80.000	11	4	2.750
		3\16				225.000	75.000	3	1	3.000	L/s = 3/1
					10\52	230.769	69.231	10	3	3.333
				7\36		233.333	66.667	7	2	3.500
					11\56	235.714	64.286	11	3	3.667
			4\20			240.000	60.000	4	1	4.000
					9\44	245.455	54.545	9	2	4.500
				5\24		250.000	50.000	5	1	5.000
					6\28	257.143	42.857	6	1	6.000	Quadritikleismic↓
1\4						300.000	0.000	1	0	→ inf