4L 4s

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.

↖ 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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The minimum harmonic entropy scale with this mos pattern is Diminished[8], the familiar octatonic scale of 12edo.

In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-mos forms are only proper if the dark generator is larger than 1\12 (100 ¢).

Intervals

Intervals of 4L 4s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-tetrawdstep	Perfect 0-tetrawdstep	P0ttws	0	0.0 ¢
1-tetrawdstep	Minor 1-tetrawdstep	m1ttws	s	0.0 ¢ to 150.0 ¢
	Major 1-tetrawdstep	M1ttws	L	150.0 ¢ to 300.0 ¢
2-tetrawdstep	Perfect 2-tetrawdstep	P2ttws	L + s	300.0 ¢
3-tetrawdstep	Minor 3-tetrawdstep	m3ttws	L + 2s	300.0 ¢ to 450.0 ¢
	Major 3-tetrawdstep	M3ttws	2L + s	450.0 ¢ to 600.0 ¢
4-tetrawdstep	Perfect 4-tetrawdstep	P4ttws	2L + 2s	600.0 ¢
5-tetrawdstep	Minor 5-tetrawdstep	m5ttws	2L + 3s	600.0 ¢ to 750.0 ¢
	Major 5-tetrawdstep	M5ttws	3L + 2s	750.0 ¢ to 900.0 ¢
6-tetrawdstep	Perfect 6-tetrawdstep	P6ttws	3L + 3s	900.0 ¢
7-tetrawdstep	Minor 7-tetrawdstep	m7ttws	3L + 4s	900.0 ¢ to 1050.0 ¢
	Major 7-tetrawdstep	M7ttws	4L + 3s	1050.0 ¢ to 1200.0 ¢
8-tetrawdstep	Perfect 8-tetrawdstep	P8ttws	4L + 4s	1200.0 ¢

Modes

Scale degrees of the modes of 4L 4s

UDP	Cyclic order	Step pattern	Scale degree (tetrawddegree)
			0	1	2	3	4	5	6	7	8
4|0(4)	1	LsLsLsLs	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.
0|4(4)	2	sLsLsLsL	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 4L 4s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\8						150.000	150.000	1:1	1.000	Equalized 4L 4s
					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	131.250	9:7	1.286
			4\28			171.429	128.571	4:3	1.333	Supersoft 4L 4s
					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	1.429
		3\20				180.000	120.000	3:2	1.500	Soft 4L 4s
					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	Unnamed golden tuning
			5\32			187.500	112.500	5:3	1.667	Semisoft 4L 4s
					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 4L 4s Diminished
					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	Semihard 4L 4s
					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	Hard 4L 4s
					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	Superhard 4L 4s
					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	→ ∞	Collapsed 4L 4s