4L 3s (3/1-equivalent)

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↖ 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.

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⟩
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