2L 5s (3/1-equivalent)

↖ 1L 4s⟨3/1⟩	↑ 2L 4s⟨3/1⟩	3L 4s⟨3/1⟩ ↗
← 1L 5s⟨3/1⟩	2L 5s (3/1-equivalent)	3L 5s⟨3/1⟩ →
↙ 1L 6s⟨3/1⟩	↓ 2L 6s⟨3/1⟩	3L 6s⟨3/1⟩ ↘

┌╥┬┬╥┬┬┬┐ │║││║││││ │││││││││ └┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLsss sssLssL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	3\7 to 1\2 (815.1 ¢ to 951.0 ¢)
Dark	1\2 to 4\7 (951.0 ¢ to 1086.8 ¢)
Related MOS scales
Parent	2L 3s⟨3/1⟩
Sister	5L 2s⟨3/1⟩
Daughters	7L 2s⟨3/1⟩, 2L 7s⟨3/1⟩
Neutralized	4L 3s⟨3/1⟩
2-Flought	9L 5s⟨3/1⟩, 2L 12s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	3\7 (815.1 ¢)
Supersoft (L:s = 4:3)	10\23 (826.9 ¢)
Soft (L:s = 3:2)	7\16 (832.1 ¢)
Semisoft (L:s = 5:3)	11\25 (836.9 ¢)
Basic (L:s = 2:1)	4\9 (845.3 ¢)
Semihard (L:s = 5:2)	9\20 (855.9 ¢)
Hard (L:s = 3:1)	5\11 (864.5 ¢)
Superhard (L:s = 4:1)	6\13 (877.8 ¢)
Collapsed (L:s = 1:0)	1\2 (951.0 ¢)

2L 5s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 815.1 ¢ to 951 ¢, or from 951 ¢ to 1086.8 ¢.

Theory

Modes

Modes of 2L 5s⟨3/1⟩

UDP	Cyclic order	Step pattern
6|0	1	LssLsss
5|1	4	LsssLss
4|2	7	sLssLss
3|3	3	sLsssLs
2|4	6	ssLssLs
1|5	2	ssLsssL
0|6	5	sssLssL

Temperament interpretations

Todo: expand

Intervals

Intervals of 2L 5s⟨3/1⟩

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 271.7 ¢
	Major 1-mosstep	M1ms	L	271.7 ¢ to 951.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 543.4 ¢
	Major 2-mosstep	M2ms	L + s	543.4 ¢ to 951.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 815.1 ¢
	Perfect 3-mosstep	P3ms	L + 2s	815.1 ¢ to 951.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	951.0 ¢ to 1086.8 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	1086.8 ¢ to 1902.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	951.0 ¢ to 1358.5 ¢
	Major 5-mosstep	M5ms	2L + 3s	1358.5 ¢ to 1902.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	951.0 ¢ to 1630.2 ¢
	Major 6-mosstep	M6ms	2L + 4s	1630.2 ¢ to 1902.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	1902.0 ¢

Scale degrees

Scale degrees of the modes of 2L 5s⟨3/1⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7
6|0	1	LssLsss	Perf.	Maj.	Maj.	Perf.	Aug.	Maj.	Maj.	Perf.
5|1	4	LsssLss	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
4|2	7	sLssLss	Perf.	Min.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
3|3	3	sLsssLs	Perf.	Min.	Maj.	Perf.	Perf.	Min.	Maj.	Perf.
2|4	6	ssLssLs	Perf.	Min.	Min.	Perf.	Perf.	Min.	Maj.	Perf.
1|5	2	ssLsssL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0|6	5	sssLssL	Perf.	Min.	Min.	Dim.	Perf.	Min.	Min.	Perf.

Scale tree

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