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.

Modes

Modes of 8L 4s

UDP	Cyclic order	Step pattern
8|0(4)	1	LLsLLsLLsLLs
4|4(4)	2	LsLLsLLsLLsL
0|8(4)	3	sLLsLLsLLsLL

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 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

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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