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 ¢)
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4L 3s⟨3/1⟩ 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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 4L 3s⟨3/1⟩

Bright gens	Scale degree	Abbrev.
10	Augmented 1-mosdegree	A1md
9	Augmented 3-mosdegree	A3md
8	Augmented 5-mosdegree	A5md
7	Augmented 0-mosdegree	A0md
6	Augmented 2-mosdegree	A2md
5	Major 4-mosdegree	M4md
4	Major 6-mosdegree	M6md
3	Major 1-mosdegree	M1md
2	Major 3-mosdegree	M3md
1	Perfect 5-mosdegree	P5md
0	Perfect 0-mosdegree Perfect 7-mosdegree	P0md P7md
−1	Perfect 2-mosdegree	P2md
−2	Minor 4-mosdegree	m4md
−3	Minor 6-mosdegree	m6md
−4	Minor 1-mosdegree	m1md
−5	Minor 3-mosdegree	m3md
−6	Diminished 5-mosdegree	d5md
−7	Diminished 7-mosdegree	d7md
−8	Diminished 2-mosdegree	d2md
−9	Diminished 4-mosdegree	d4md
−10	Diminished 6-mosdegree	d6md

Modes

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

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7
6|0	1	LLsLsLs	Perf.	Maj.	Aug.	Maj.	Maj.	Perf.	Maj.	Perf.
5|1	6	LsLLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.
4|2	4	LsLsLLs	Perf.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Perf.
3|3	2	LsLsLsL	Perf.	Maj.	Perf.	Maj.	Min.	Perf.	Min.	Perf.
2|4	7	sLLsLsL	Perf.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Perf.
1|5	5	sLsLLsL	Perf.	Min.	Perf.	Min.	Min.	Perf.	Min.	Perf.
0|6	3	sLsLsLL	Perf.	Min.	Perf.	Min.	Min.	Dim.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 4L 3s⟨3/1⟩

Generator(edt)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\7						1358.539	543.416	1:1	1.000	Equalized 4L 3s⟨3/1⟩
					28\39	1365.506	536.449	6:5	1.200
				23\32		1367.030	534.925	5:4	1.250
					41\57	1368.073	533.882	9:7	1.286
			18\25			1369.408	532.547	4:3	1.333	Supersoft 4L 3s⟨3/1⟩
					49\68	1370.526	531.429	11:8	1.375
				31\43		1371.177	530.778	7:5	1.400
					44\61	1371.902	530.053	10:7	1.429
		13\18				1373.634	528.321	3:2	1.500	Soft 4L 3s⟨3/1⟩
					47\65	1375.260	526.695	11:7	1.571
				34\47		1375.882	526.073	8:5	1.600
					55\76	1376.415	525.540	13:8	1.625
			21\29			1377.278	524.677	5:3	1.667	Semisoft 4L 3s⟨3/1⟩
					50\69	1378.228	523.727	12:7	1.714
				29\40		1378.917	523.038	7:4	1.750
					37\51	1379.850	522.105	9:5	1.800
	8\11					1383.240	518.715	2:1	2.000	Basic 4L 3s⟨3/1⟩ Scales with tunings softer than this are proper
					35\48	1386.842	515.113	9:4	2.250
				27\37		1387.913	514.042	7:3	2.333
					46\63	1388.729	513.226	12:5	2.400
			19\26			1389.890	512.065	5:2	2.500	Semihard 4L 3s⟨3/1⟩
					49\67	1390.982	510.973	13:5	2.600
				30\41		1391.674	510.281	8:3	2.667
					41\56	1392.503	509.452	11:4	2.750
		11\15				1394.767	507.188	3:1	3.000	Hard 4L 3s⟨3/1⟩
					36\49	1397.355	504.600	10:3	3.333
				25\34		1398.496	503.459	7:2	3.500
					39\53	1399.552	502.403	11:3	3.667
			14\19			1401.441	500.514	4:1	4.000	Superhard 4L 3s⟨3/1⟩
					31\42	1403.824	498.131	9:2	4.500
				17\23		1405.793	496.162	5:1	5.000
					20\27	1408.856	493.099	6:1	6.000
3\4						1426.466	475.489	1:0	→ ∞	Collapsed 4L 3s⟨3/1⟩