7L 4s (3/1-equivalent)

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↖ 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¢

Scale tree

Scale Tree and Tuning Spectrum of 7L 4s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
3\11 518.715 1383.240 1:1 1.000 Equalized 7L 4s⟨3/1⟩
17\62 521.504 1380.451 6:5 1.200
14\51 522.105 1379.850 5:4 1.250
25\91 522.515 1379.440 9:7 1.286
11\40 523.038 1378.917 4:3 1.333 Supersoft 7L 4s⟨3/1⟩
30\109 523.474 1378.481 11:8 1.375
19\69 523.727 1378.228 7:5 1.400
27\98 524.008 1377.947 10:7 1.429
8\29 524.677 1377.278 3:2 1.500 Soft 7L 4s⟨3/1⟩
29\105 525.302 1376.653 11:7 1.571
21\76 525.540 1376.415 8:5 1.600
34\123 525.744 1376.211 13:8 1.625
13\47 526.073 1375.882 5:3 1.667 Semisoft 7L 4s⟨3/1⟩
31\112 526.434 1375.521 12:7 1.714
18\65 526.695 1375.260 7:4 1.750
23\83 527.048 1374.907 9:5 1.800
5\18 528.321 1373.634 2:1 2.000 Basic 7L 4s⟨3/1⟩
Scales with tunings softer than this are proper
22\79 529.658 1372.297 9:4 2.250
17\61 530.053 1371.902 7:3 2.333
29\104 530.353 1371.602 12:5 2.400
12\43 530.778 1371.177 5:2 2.500 Semihard 7L 4s⟨3/1⟩
31\111 531.177 1370.778 13:5 2.600
19\68 531.429 1370.526 8:3 2.667
26\93 531.729 1370.226 11:4 2.750
7\25 532.547 1369.408 3:1 3.000 Hard 7L 4s⟨3/1⟩
23\82 533.475 1368.480 10:3 3.333
16\57 533.882 1368.073 7:2 3.500
25\89 534.257 1367.698 11:3 3.667
9\32 534.925 1367.030 4:1 4.000 Superhard 7L 4s⟨3/1⟩
20\71 535.762 1366.193 9:2 4.500
11\39 536.449 1365.506 5:1 5.000
13\46 537.509 1364.446 6:1 6.000
2\7 543.416 1358.539 1:0 → ∞ Collapsed 7L 4s⟨3/1⟩
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