4L 8s

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Scale structure
Step pattern	LssLssLssLss ssLssLssLssL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	2\12 to 1\4 (200.0 ¢ to 300.0 ¢)
Dark	0\4 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 4s
Sister	8L 4s
Daughters	12L 4s, 4L 12s
Neutralized	8L 4s
2-Flought	16L 8s, 4L 20s
Equal tunings
Equalized (L:s = 1:1)	2\12 (200.0 ¢)
Supersoft (L:s = 4:3)	7\40 (210.0 ¢)
Soft (L:s = 3:2)	5\28 (214.3 ¢)
Semisoft (L:s = 5:3)	8\44 (218.2 ¢)
Basic (L:s = 2:1)	3\16 (225.0 ¢)
Semihard (L:s = 5:2)	7\36 (233.3 ¢)
Hard (L:s = 3:1)	4\20 (240.0 ¢)
Superhard (L:s = 4:1)	5\24 (250.0 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)

4L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 8 small steps, with a period of 1 large step and 2 small steps that repeats every 300.0 ¢, or 4 times every octave. 4L 8s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 200 ¢ to 300 ¢, or from 0 ¢ to 100 ¢.

This is the minor chromatic scale of Diminished temperament. Its period of 300 ¢ (~6:5) is divided into L s s, making a universally proper scale, but the harmonic entropy minimum for it is not particularly low. The name for this MOS scale is p-chro tetrawood.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 4L 8s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 100.0 ¢
	Augmented 1-mosstep	A1ms	L	100.0 ¢ to 300.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 200.0 ¢
	Perfect 2-mosstep	P2ms	L + s	200.0 ¢ to 300.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	300.0 ¢ to 400.0 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	400.0 ¢ to 600.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	300.0 ¢ to 500.0 ¢
	Perfect 5-mosstep	P5ms	2L + 3s	500.0 ¢ to 600.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	2L + 4s	600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	600.0 ¢ to 700.0 ¢
	Augmented 7-mosstep	A7ms	3L + 4s	700.0 ¢ to 900.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	600.0 ¢ to 800.0 ¢
	Perfect 8-mosstep	P8ms	3L + 5s	800.0 ¢ to 900.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	3L + 6s	900.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	3L + 7s	900.0 ¢ to 1000.0 ¢
	Augmented 10-mosstep	A10ms	4L + 6s	1000.0 ¢ to 1200.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	3L + 8s	900.0 ¢ to 1100.0 ¢
	Perfect 11-mosstep	P11ms	4L + 7s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	4L + 8s	1200.0 ¢

Generator chain

Generator chain of 4L 8s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
3	Augmented 0-mosdegree	A0md	Augmented 3-mosdegree	A3md	Augmented 6-mosdegree	A6md	Augmented 9-mosdegree	A9md
2	Augmented 1-mosdegree	A1md	Augmented 4-mosdegree	A4md	Augmented 7-mosdegree	A7md	Augmented 10-mosdegree	A10md
1	Perfect 2-mosdegree	P2md	Perfect 5-mosdegree	P5md	Perfect 8-mosdegree	P8md	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md	Perfect 3-mosdegree Perfect 6-mosdegree	P3md P6md	Perfect 6-mosdegree Perfect 9-mosdegree	P6md P9md	Perfect 9-mosdegree Perfect 12-mosdegree	P9md P12md
−1	Perfect 1-mosdegree	P1md	Perfect 4-mosdegree	P4md	Perfect 7-mosdegree	P7md	Perfect 10-mosdegree	P10md
−2	Diminished 2-mosdegree	d2md	Diminished 5-mosdegree	d5md	Diminished 8-mosdegree	d8md	Diminished 11-mosdegree	d11md
−3	Diminished 3-mosdegree	d3md	Diminished 6-mosdegree	d6md	Diminished 9-mosdegree	d9md	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 4L 8s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12
8|0(4)	1	LssLssLssLss	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.
4|4(4)	3	sLssLssLssLs	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.
0|8(4)	2	ssLssLssLssL	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.

Scale tree

Scale tree and tuning spectrum of 4L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\12						200.000	100.000	1:1	1.000	Equalized 4L 8s
					11\64	206.250	93.750	6:5	1.200
				9\52		207.692	92.308	5:4	1.250
					16\92	208.696	91.304	9:7	1.286
			7\40			210.000	90.000	4:3	1.333	Supersoft 4L 8s
					19\108	211.111	88.889	11:8	1.375
				12\68		211.765	88.235	7:5	1.400
					17\96	212.500	87.500	10:7	1.429
		5\28				214.286	85.714	3:2	1.500	Soft 4L 8s
					18\100	216.000	84.000	11:7	1.571
				13\72		216.667	83.333	8:5	1.600
					21\116	217.241	82.759	13:8	1.625
			8\44			218.182	81.818	5:3	1.667	Semisoft 4L 8s
					19\104	219.231	80.769	12:7	1.714
				11\60		220.000	80.000	7:4	1.750
					14\76	221.053	78.947	9:5	1.800
	3\16					225.000	75.000	2:1	2.000	Basic 4L 8s Scales with tunings softer than this are proper
					13\68	229.412	70.588	9:4	2.250
				10\52		230.769	69.231	7:3	2.333
					17\88	231.818	68.182	12:5	2.400
			7\36			233.333	66.667	5:2	2.500	Semihard 4L 8s
					18\92	234.783	65.217	13:5	2.600
				11\56		235.714	64.286	8:3	2.667
					15\76	236.842	63.158	11:4	2.750
		4\20				240.000	60.000	3:1	3.000	Hard 4L 8s
					13\64	243.750	56.250	10:3	3.333
				9\44		245.455	54.545	7:2	3.500
					14\68	247.059	52.941	11:3	3.667
			5\24			250.000	50.000	4:1	4.000	Superhard 4L 8s
					11\52	253.846	46.154	9:2	4.500
				6\28		257.143	42.857	5:1	5.000
					7\32	262.500	37.500	6:1	6.000
1\4						300.000	0.000	1:0	→ ∞	Collapsed 4L 8s