7L 4s (3/1-equivalent)

Todo: expand This page is a WIP (work-in-progress).

↖ 6L 3s⟨3/1⟩	↑ 7L 3s⟨3/1⟩	8L 3s⟨3/1⟩ ↗
← 6L 4s⟨3/1⟩	7L 4s (3/1-equivalent)	8L 4s⟨3/1⟩ →
↙ 6L 5s⟨3/1⟩	↓ 7L 5s⟨3/1⟩	8L 5s⟨3/1⟩ ↘

┌╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLLsLs sLsLLsLLsLL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	3\11 to 2\7 (518.7 ¢ to 543.4 ¢)
Dark	5\7 to 8\11 (1358.5 ¢ to 1383.2 ¢)
Related MOS scales
Parent	4L 3s⟨3/1⟩
Sister	4L 7s⟨3/1⟩
Daughters	11L 7s⟨3/1⟩, 7L 11s⟨3/1⟩
Neutralized	3L 8s⟨3/1⟩
2-Flought	18L 4s⟨3/1⟩, 7L 15s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	3\11 (518.7 ¢)
Supersoft (L:s = 4:3)	11\40 (523.0 ¢)
Soft (L:s = 3:2)	8\29 (524.7 ¢)
Semisoft (L:s = 5:3)	13\47 (526.1 ¢)
Basic (L:s = 2:1)	5\18 (528.3 ¢)
Semihard (L:s = 5:2)	12\43 (530.8 ¢)
Hard (L:s = 3:1)	7\25 (532.5 ¢)
Superhard (L:s = 4:1)	9\32 (534.9 ¢)
Collapsed (L:s = 1:0)	2\7 (543.4 ¢)

7L 4s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 7 large steps and 4 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 518.7 ¢ to 543.4 ¢, or from 1358.5 ¢ to 1383.2 ¢.

Temperaments

7L 4s⟨3/1⟩ MOS scales can be used for the Electra temperament, in which three generators down is approximately 13/11 and one generator up is approximately 15/11. If 11:13:15 is treated as the fundamental sonority of no-2's music, then Electra can be viewed as the analogue to meantone and 7L 4s⟨3/1⟩ can be viewed as the analogue to the diatonic scale. If twos are admitted, the hard end of the Electra heptatonic spectrum can be viewed as the subharmonic version of Pythagorean/Classical tuning.

Modes

Modes of 7L 4s⟨3/1⟩

UDP	Cyclic order	Step pattern
10|0	1	LLsLLsLLsLs
9|1	4	LLsLLsLsLLs
8|2	7	LLsLsLLsLLs
7|3	10	LsLLsLLsLLs
6|4	2	LsLLsLLsLsL
5|5	5	LsLLsLsLLsL
4|6	8	LsLsLLsLLsL
3|7	11	sLLsLLsLLsL
2|8	3	sLLsLLsLsLL
1|9	6	sLLsLsLLsLL
0|10	9	sLsLLsLLsLL

Intervals

Intervals of 7L 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 172.9 ¢
	Major 1-mosstep	M1ms	L	172.9 ¢ to 271.7 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	271.7 ¢ to 345.8 ¢
	Major 2-mosstep	M2ms	2L	345.8 ¢ to 543.4 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	271.7 ¢ to 518.7 ¢
	Perfect 3-mosstep	P3ms	2L + s	518.7 ¢ to 543.4 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	543.4 ¢ to 691.6 ¢
	Major 4-mosstep	M4ms	3L + s	691.6 ¢ to 815.1 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	815.1 ¢ to 864.5 ¢
	Major 5-mosstep	M5ms	4L + s	864.5 ¢ to 1086.8 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	815.1 ¢ to 1037.4 ¢
	Major 6-mosstep	M6ms	4L + 2s	1037.4 ¢ to 1086.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	1086.8 ¢ to 1210.3 ¢
	Major 7-mosstep	M7ms	5L + 2s	1210.3 ¢ to 1358.5 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	1358.5 ¢ to 1383.2 ¢
	Augmented 8-mosstep	A8ms	6L + 2s	1383.2 ¢ to 1630.2 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	1358.5 ¢ to 1556.1 ¢
	Major 9-mosstep	M9ms	6L + 3s	1556.1 ¢ to 1630.2 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	1630.2 ¢ to 1729.1 ¢
	Major 10-mosstep	M10ms	7L + 3s	1729.1 ¢ to 1902.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	1902.0 ¢