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> (or superelectric) refers to a tritave-repeating MOS scale with seven large steps and four small steps. It is generated by any interval between 3\11edt and 2\7edt.

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 meantone chromatic scale.

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 ¢