3L 4s (3/1-equivalent)

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

┌╥┬╥┬╥┬┬┐ │║│║│║│││ │││││││││ └┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLss ssLsLsL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	2\7 to 1\3 (543.4 ¢ to 634.0 ¢)
Dark	2\3 to 5\7 (1268.0 ¢ to 1358.5 ¢)
Related MOS scales
Parent	3L 1s⟨3/1⟩
Sister	4L 3s⟨3/1⟩
Daughters	7L 3s⟨3/1⟩, 3L 7s⟨3/1⟩
Neutralized	6L 1s⟨3/1⟩
2-Flought	10L 4s⟨3/1⟩, 3L 11s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	2\7 (543.4 ¢)
Supersoft (L:s = 4:3)	7\24 (554.7 ¢)
Soft (L:s = 3:2)	5\17 (559.4 ¢)
Semisoft (L:s = 5:3)	8\27 (563.5 ¢)
Basic (L:s = 2:1)	3\10 (570.6 ¢)
Semihard (L:s = 5:2)	7\23 (578.9 ¢)
Hard (L:s = 3:1)	4\13 (585.2 ¢)
Superhard (L:s = 4:1)	5\16 (594.4 ¢)
Collapsed (L:s = 1:0)	1\3 (634.0 ¢)

3L 4s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 4 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 543.4 ¢ to 634 ¢, or from 1268 ¢ to 1358.5 ¢.

Theory

Modes

Modes of 3L 4s⟨3/1⟩

UDP	Cyclic order	Step pattern
6|0	1	LsLsLss
5|1	3	LsLssLs
4|2	5	LssLsLs
3|3	7	sLsLsLs
2|4	2	sLsLssL
1|5	4	sLssLsL
0|6	6	ssLsLsL

Temperament interpretations

Todo: expand

Intervals

Intervals of 3L 4s⟨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 634.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 543.4 ¢
	Perfect 2-mosstep	P2ms	L + s	543.4 ¢ to 634.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	634.0 ¢ to 815.1 ¢
	Major 3-mosstep	M3ms	2L + s	815.1 ¢ to 1268.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	634.0 ¢ to 1086.8 ¢
	Major 4-mosstep	M4ms	2L + 2s	1086.8 ¢ to 1268.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	1268.0 ¢ to 1358.5 ¢
	Augmented 5-mosstep	A5ms	3L + 2s	1358.5 ¢ to 1902.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	1268.0 ¢ to 1630.2 ¢
	Major 6-mosstep	M6ms	3L + 3s	1630.2 ¢ to 1902.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	3L + 4s	1902.0 ¢

Scale degrees

Scale degrees of the modes of 3L 4s⟨3/1⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7
6|0	1	LsLsLss	Perf.	Maj.	Perf.	Maj.	Maj.	Aug.	Maj.	Perf.
5|1	3	LsLssLs	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.
4|2	5	LssLsLs	Perf.	Maj.	Perf.	Min.	Maj.	Perf.	Maj.	Perf.
3|3	7	sLsLsLs	Perf.	Min.	Perf.	Min.	Maj.	Perf.	Maj.	Perf.
2|4	2	sLsLssL	Perf.	Min.	Perf.	Min.	Maj.	Perf.	Min.	Perf.
1|5	4	sLssLsL	Perf.	Min.	Perf.	Min.	Min.	Perf.	Min.	Perf.
0|6	6	ssLsLsL	Perf.	Min.	Dim.	Min.	Min.	Perf.	Min.	Perf.

Scale tree

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