8L 1s (3/1-equivalent)

← 7L 1s⟨3/1⟩	8L 1s (3/1-equivalent)	9L 1s⟨3/1⟩ →
↙ 7L 2s⟨3/1⟩	↓ 8L 2s⟨3/1⟩	9L 2s⟨3/1⟩ ↘

┌╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLs sLLLLLLLL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	1\9 to 1\8 (211.3 ¢ to 237.7 ¢)
Dark	7\8 to 8\9 (1664.2 ¢ to 1690.6 ¢)
Related MOS scales
Parent	1L 7s⟨3/1⟩
Sister	1L 8s⟨3/1⟩
Daughters	9L 8s⟨3/1⟩, 8L 9s⟨3/1⟩
Neutralized	7L 2s⟨3/1⟩
2-Flought	17L 1s⟨3/1⟩, 8L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	1\9 (211.3 ¢)
Supersoft (L:s = 4:3)	4\35 (217.4 ¢)
Soft (L:s = 3:2)	3\26 (219.5 ¢)
Semisoft (L:s = 5:3)	5\43 (221.2 ¢)
Basic (L:s = 2:1)	2\17 (223.8 ¢)
Semihard (L:s = 5:2)	5\42 (226.4 ¢)
Hard (L:s = 3:1)	3\25 (228.2 ¢)
Superhard (L:s = 4:1)	4\33 (230.5 ¢)
Collapsed (L:s = 1:0)	1\8 (237.7 ¢)

8L 1s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 8 large steps and 1 small step, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 211.3 ¢ to 237.7 ¢, or from 1664.2 ¢ to 1690.6 ¢. Scales of this form are always proper because there is only one small step.

Theory

Temperament interpretations

Todo: expand

Modes

Modes of 8L 1s⟨3/1⟩

UDP	Cyclic order	Step pattern
8|0	1	LLLLLLLLs
7|1	2	LLLLLLLsL
6|2	3	LLLLLLsLL
5|3	4	LLLLLsLLL
4|4	5	LLLLsLLLL
3|5	6	LLLsLLLLL
2|6	7	LLsLLLLLL
1|7	8	LsLLLLLLL
0|8	9	sLLLLLLLL

Intervals

Intervals of 8L 1s⟨3/1⟩

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 211.3 ¢
	Perfect 1-mosstep	P1ms	L	211.3 ¢ to 237.7 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	237.7 ¢ to 422.7 ¢
	Major 2-mosstep	M2ms	2L	422.7 ¢ to 475.5 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	475.5 ¢ to 634.0 ¢
	Major 3-mosstep	M3ms	3L	634.0 ¢ to 713.2 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	713.2 ¢ to 845.3 ¢
	Major 4-mosstep	M4ms	4L	845.3 ¢ to 951.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	951.0 ¢ to 1056.6 ¢
	Major 5-mosstep	M5ms	5L	1056.6 ¢ to 1188.7 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	1188.7 ¢ to 1268.0 ¢
	Major 6-mosstep	M6ms	6L	1268.0 ¢ to 1426.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	1426.5 ¢ to 1479.3 ¢
	Major 7-mosstep	M7ms	7L	1479.3 ¢ to 1664.2 ¢
8-mosstep	Perfect 8-mosstep	P8ms	7L + s	1664.2 ¢ to 1690.6 ¢
	Augmented 8-mosstep	A8ms	8L	1690.6 ¢ to 1902.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	8L + s	1902.0 ¢

Scale degrees

Scale degrees of the modes of 8L 1s⟨3/1⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9
8|0	1	LLLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
7|1	2	LLLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
6|2	3	LLLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
5|3	4	LLLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
4|4	5	LLLLsLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
3|5	6	LLLsLLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
2|6	7	LLsLLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
1|7	8	LsLLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0|8	9	sLLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

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