8L 4s

8L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 4 small steps, with a period of 2 large steps and 1 small step that repeats every 300.0 ¢, or 4 times every octave. 8L 4s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 100 ¢ to 150 ¢, or from 150 ¢ to 200 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 7L 3s	↑ 8L 3s	9L 3s ↗
← 7L 4s	8L 4s	9L 4s →
↙ 7L 5s	↓ 8L 5s	9L 5s ↘

Scale structure
Step pattern	LLsLLsLLsLLs sLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	1\12 to 1\8 (100.0 ¢ to 150.0 ¢)
Dark	1\8 to 2\12 (150.0 ¢ to 200.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	4L 4s
Sister	4L 8s
Daughters	12L 8s, 8L 12s
Neutralized	4L 8s
2-Flought	20L 4s, 8L 16s
Equal tunings
Equalized (L:s = 1:1)	1\12 (100.0 ¢)
Supersoft (L:s = 4:3)	4\44 (109.1 ¢)
Soft (L:s = 3:2)	3\32 (112.5 ¢)
Semisoft (L:s = 5:3)	5\52 (115.4 ¢)
Basic (L:s = 2:1)	2\20 (120.0 ¢)
Semihard (L:s = 5:2)	5\48 (125.0 ¢)
Hard (L:s = 3:1)	3\28 (128.6 ¢)
Superhard (L:s = 4:1)	4\36 (133.3 ¢)
Collapsed (L:s = 1:0)	1\8 (150.0 ¢)
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This is the chromatic scale of Golden diminished temperament.

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 8L 4s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 100.0 ¢
	Perfect 1-mosstep	P1ms	L	100.0 ¢ to 150.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	150.0 ¢ to 200.0 ¢
	Augmented 2-mosstep	A2ms	2L	200.0 ¢ to 300.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	300.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	300.0 ¢ to 400.0 ¢
	Perfect 4-mosstep	P4ms	3L + s	400.0 ¢ to 450.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	450.0 ¢ to 500.0 ¢
	Augmented 5-mosstep	A5ms	4L + s	500.0 ¢ to 600.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	4L + 2s	600.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	600.0 ¢ to 700.0 ¢
	Perfect 7-mosstep	P7ms	5L + 2s	700.0 ¢ to 750.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	750.0 ¢ to 800.0 ¢
	Augmented 8-mosstep	A8ms	6L + 2s	800.0 ¢ to 900.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	6L + 3s	900.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	6L + 4s	900.0 ¢ to 1000.0 ¢
	Perfect 10-mosstep	P10ms	7L + 3s	1000.0 ¢ to 1050.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	1050.0 ¢ to 1100.0 ¢
	Augmented 11-mosstep	A11ms	8L + 3s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	8L + 4s	1200.0 ¢

Generator chain

Generator chain of 8L 4s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
4	Augmented 1-mosdegree	A1md	Augmented 4-mosdegree	A4md	Augmented 7-mosdegree	A7md	Augmented 10-mosdegree	A10md
3	Augmented 0-mosdegree	A0md	Augmented 3-mosdegree	A3md	Augmented 6-mosdegree	A6md	Augmented 9-mosdegree	A9md
2	Augmented 2-mosdegree	A2md	Augmented 5-mosdegree	A5md	Augmented 8-mosdegree	A8md	Augmented 11-mosdegree	A11md
1	Perfect 1-mosdegree	P1md	Perfect 4-mosdegree	P4md	Perfect 7-mosdegree	P7md	Perfect 10-mosdegree	P10md
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 2-mosdegree	P2md	Perfect 5-mosdegree	P5md	Perfect 8-mosdegree	P8md	Perfect 11-mosdegree	P11md
−2	Diminished 1-mosdegree	d1md	Diminished 4-mosdegree	d4md	Diminished 7-mosdegree	d7md	Diminished 10-mosdegree	d10md
−3	Diminished 3-mosdegree	d3md	Diminished 6-mosdegree	d6md	Diminished 9-mosdegree	d9md	Diminished 12-mosdegree	d12md
−4	Diminished 2-mosdegree	d2md	Diminished 5-mosdegree	d5md	Diminished 8-mosdegree	d8md	Diminished 11-mosdegree	d11md

Modes

Scale degrees of the modes of 8L 4s

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	LLsLLsLLsLLs	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.
4|4(4)	2	LsLLsLLsLLsL	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.
0|8(4)	3	sLLsLLsLLsLL	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 8L 4s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\12						100.000	200.000	1:1	1.000	Equalized 8L 4s
					6\68	105.882	194.118	6:5	1.200
				5\56		107.143	192.857	5:4	1.250
					9\100	108.000	192.000	9:7	1.286
			4\44			109.091	190.909	4:3	1.333	Supersoft 8L 4s
					11\120	110.000	190.000	11:8	1.375
				7\76		110.526	189.474	7:5	1.400
					10\108	111.111	188.889	10:7	1.429
		3\32				112.500	187.500	3:2	1.500	Soft 8L 4s
					11\116	113.793	186.207	11:7	1.571
				8\84		114.286	185.714	8:5	1.600
					13\136	114.706	185.294	13:8	1.625
			5\52			115.385	184.615	5:3	1.667	Semisoft 8L 4s
					12\124	116.129	183.871	12:7	1.714
				7\72		116.667	183.333	7:4	1.750
					9\92	117.391	182.609	9:5	1.800
	2\20					120.000	180.000	2:1	2.000	Basic 8L 4s
					9\88	122.727	177.273	9:4	2.250
				7\68		123.529	176.471	7:3	2.333
					12\116	124.138	175.862	12:5	2.400
			5\48			125.000	175.000	5:2	2.500	Semihard 8L 4s
					13\124	125.806	174.194	13:5	2.600
				8\76		126.316	173.684	8:3	2.667
					11\104	126.923	173.077	11:4	2.750
		3\28				128.571	171.429	3:1	3.000	Hard 8L 4s
					10\92	130.435	169.565	10:3	3.333
				7\64		131.250	168.750	7:2	3.500
					11\100	132.000	168.000	11:3	3.667
			4\36			133.333	166.667	4:1	4.000	Superhard 8L 4s
					9\80	135.000	165.000	9:2	4.500
				5\44		136.364	163.636	5:1	5.000
					6\52	138.462	161.538	6:1	6.000
1\8						150.000	150.000	1:0	→ ∞	Collapsed 8L 4s

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