8L 4s

↖ 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 ¢)

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.

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

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