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⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 7 large steps and 4 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 518.7¢ to 543.4¢, or from 1358.5¢ to 1383.2¢.

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 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

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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