4L 3s (3/1-equivalent)

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

┌╥╥┬╥┬╥┬┐ │║║│║│║││ │││││││││ └┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLs sLsLsLL
Equave	3/1 (1902.0¢)
Period	3/1 (1902.0¢)
Generator size(edt)
Bright	5\7 to 3\4 (1358.5¢ to 1426.5¢)
Dark	1\4 to 2\7 (475.5¢ to 543.4¢)
Related MOS scales
Parent	3L 1s⟨3/1⟩
Sister	3L 4s⟨3/1⟩
Daughters	7L 4s⟨3/1⟩, 4L 7s⟨3/1⟩
Neutralized	1L 6s⟨3/1⟩
2-Flought	11L 3s⟨3/1⟩, 4L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	5\7 (1358.5¢)
Supersoft (L:s = 4:3)	18\25 (1369.4¢)
Soft (L:s = 3:2)	13\18 (1373.6¢)
Semisoft (L:s = 5:3)	21\29 (1377.3¢)
Basic (L:s = 2:1)	8\11 (1383.2¢)
Semihard (L:s = 5:2)	19\26 (1389.9¢)
Hard (L:s = 3:1)	11\15 (1394.8¢)
Superhard (L:s = 4:1)	14\19 (1401.4¢)
Collapsed (L:s = 1:0)	3\4 (1426.5¢)

4L 3s⟨3/1⟩, also called electric, is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 4 large steps and 3 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1358.5¢ to 1426.5¢, or from 475.5¢ to 543.4¢.

Temperaments

4L 3s<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 4L 3s<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

Mode	UDP	Name
LLsLsLs	6|0
LsLLsLs	5|1
LsLsLLs	4|2
LsLsLsL	3|3
sLLsLsL	2|4
sLsLLsL	1|5
sLsLsLL	0|6

Todo: complete table

Intervals

Intervals of 4L 3s⟨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 475.5¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	475.5¢ to 543.4¢
	Augmented 2-mosstep	A2ms	2L	543.4¢ to 951.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	475.5¢ to 815.1¢
	Major 3-mosstep	M3ms	2L + s	815.1¢ to 951.0¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	951.0¢ to 1086.8¢
	Major 4-mosstep	M4ms	3L + s	1086.8¢ to 1426.5¢
5-mosstep	Diminished 5-mosstep	d5ms	2L + 3s	951.0¢ to 1358.5¢
	Perfect 5-mosstep	P5ms	3L + 2s	1358.5¢ to 1426.5¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	1426.5¢ to 1630.2¢
	Major 6-mosstep	M6ms	4L + 2s	1630.2¢ to 1902.0¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	1902.0¢

Scales

Generator (chroma-positive)	Cents (chroma-positive)	Cents (chroma-negative)	L	s	L/s	Comments
5\7edt	1358.539	543.416	1	1	1.0000
23\32edt	1367.03	534.925	5	4	1.2500
18\25edt	1369.41	532.55	4	3	1.3333	Electra is in this region
13\18edt	1373.634	528.321	3	2	1.5000
21\29edt	1377.2778	524.6772	5	3	1.6667
8\11edt	1383.2	518.7	2	1	2.0000	Basic electric (generators smaller than this are proper)
19\26edt	1389.9	512.1	5	2	2.5000
11\15edt	1394.767	507.188	3	1	3.0000
14\19edt	1401.441	500.514	4	1	4.0000
17\23edt	1405.7928	496.1622	5	1	5.0000
3\4edt	1426.4663	475.4888	1	0	-> inf