4L 7s (3/1-equivalent)

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↖ 3L 6s⟨3/1⟩ ↑ 4L 6s⟨3/1⟩ 5L 6s⟨3/1⟩ ↗
← 3L 7s⟨3/1⟩ 4L 7s (3/1-equivalent) 5L 7s⟨3/1⟩ →
↙ 3L 8s⟨3/1⟩ ↓ 4L 8s⟨3/1⟩ 5L 8s⟨3/1⟩ ↘
Scale structure
Step pattern LsLssLssLss
ssLssLssLsL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 8\11 to 3\4 (1383.2 ¢ to 1426.5 ¢)
Dark 1\4 to 3\11 (475.5 ¢ to 518.7 ¢)
Related MOS scales
Parent 4L 3s⟨3/1⟩
Sister 7L 4s⟨3/1⟩
Daughters 11L 4s⟨3/1⟩, 4L 11s⟨3/1⟩
Neutralized 8L 3s⟨3/1⟩
2-Flought 15L 7s⟨3/1⟩, 4L 18s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 8\11 (1383.2 ¢)
Supersoft (L:s = 4:3) 27\37 (1387.9 ¢)
Soft (L:s = 3:2) 19\26 (1389.9 ¢)
Semisoft (L:s = 5:3) 30\41 (1391.7 ¢)
Basic (L:s = 2:1) 11\15 (1394.8 ¢)
Semihard (L:s = 5:2) 25\34 (1398.5 ¢)
Hard (L:s = 3:1) 14\19 (1401.4 ¢)
Superhard (L:s = 4:1) 17\23 (1405.8 ¢)
Collapsed (L:s = 1:0) 3\4 (1426.5 ¢)
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4L 7s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 4 large steps and 7 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1383.2 ¢ to 1426.5 ¢, or from 475.5 ¢ to 518.7 ¢.

Theory

Modes

Modes of 4L 7s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
10|0 1 LsLssLssLss
9|1 9 LssLsLssLss
8|2 6 LssLssLsLss
7|3 3 LssLssLssLs
6|4 11 sLsLssLssLs
5|5 8 sLssLsLssLs
4|6 5 sLssLssLsLs
3|7 2 sLssLssLssL
2|8 10 ssLsLssLssL
1|9 7 ssLssLsLssL
0|10 4 ssLssLssLsL

Temperament interpretations

The temperament that joins 15edt and 26edt produces this MOS. Both 15edt and 26edt are no-twos zeta peaks. 56edt, another no-twos zeta peak, also supports this temperament.

Other EDTs supporting it include: 41, 67, 71…

In 15edt it is generated by 4\15 (~507.2¢) and has a hardness of exactly 2.0.

In 56edt it is generated by 15\56 (~509.5¢) and has a hardness of exactly 1.75.

In 26edt (’double Bohlen-Pierce’) it is generated by 7\26 (~512.1) and has a hardness of exactly 1.5.

In 56edt this MOS has the intervals (in cents):

  • 136.045
  • 373.455
  • 509.500
  • 645.545
  • 882.955
  • 1019.000
  • 1256.410
  • 1392.455
  • 1528.500
  • 1765.910
  • 1901.955

(And rotations thereof.)

That roughly approximates this 13-limit JI scale:

  • 13/12
  • 5/4
  • 4/3
  • 13/9
  • 5/3
  • 9/5
  • 25/12
  • 20/9
  • 12/5
  • 25/9
  • 3/1

(The intervals with multiple-of-3 denominators gain consonance in higher tritaves.)

Intervals

Intervals of 4L 7s⟨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 475.5 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 345.8 ¢
Major 2-mosstep M2ms L + s 345.8 ¢ to 475.5 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 475.5 ¢ to 518.7 ¢
Augmented 3-mosstep A3ms 2L + s 518.7 ¢ to 951.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 475.5 ¢ to 691.6 ¢
Major 4-mosstep M4ms 2L + 2s 691.6 ¢ to 951.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 475.5 ¢ to 864.5 ¢
Major 5-mosstep M5ms 2L + 3s 864.5 ¢ to 951.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 951.0 ¢ to 1037.4 ¢
Major 6-mosstep M6ms 3L + 3s 1037.4 ¢ to 1426.5 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 951.0 ¢ to 1210.3 ¢
Major 7-mosstep M7ms 3L + 4s 1210.3 ¢ to 1426.5 ¢
8-mosstep Diminished 8-mosstep d8ms 2L + 6s 951.0 ¢ to 1383.2 ¢
Perfect 8-mosstep P8ms 3L + 5s 1383.2 ¢ to 1426.5 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 1426.5 ¢ to 1556.1 ¢
Major 9-mosstep M9ms 4L + 5s 1556.1 ¢ to 1902.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 1426.5 ¢ to 1729.1 ¢
Major 10-mosstep M10ms 4L + 6s 1729.1 ¢ to 1902.0 ¢
11-mosstep Perfect 11-mosstep P11ms 4L + 7s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 4L 7s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 LsLssLssLss Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
9|1 9 LssLsLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
8|2 6 LssLssLsLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf.
7|3 3 LssLssLssLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
6|4 11 sLsLssLssLs Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
5|5 8 sLssLsLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Perf.
4|6 5 sLssLssLsLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Perf.
3|7 2 sLssLssLssL Perf. Min. Maj. Perf. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|8 10 ssLsLssLssL Perf. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|9 7 ssLssLsLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|10 4 ssLssLssLsL Perf. Min. Min. Perf. Min. Min. Min. Min. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 7s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
8\11 1383.240 518.715 1:1 1.000 Equalized 4L 7s⟨3/1⟩
43\59 1386.171 515.784 6:5 1.200
35\48 1386.842 515.113 5:4 1.250
62\85 1387.308 514.647 9:7 1.286
27\37 1387.913 514.042 4:3 1.333 Supersoft 4L 7s⟨3/1⟩
73\100 1388.427 513.528 11:8 1.375
46\63 1388.729 513.226 7:5 1.400
65\89 1389.068 512.887 10:7 1.429
19\26 1389.890 512.065 3:2 1.500 Soft 4L 7s⟨3/1⟩
68\93 1390.677 511.278 11:7 1.571
49\67 1390.982 510.973 8:5 1.600
79\108 1391.245 510.710 13:8 1.625
30\41 1391.674 510.281 5:3 1.667 Semisoft 4L 7s⟨3/1⟩
71\97 1392.153 509.802 12:7 1.714
41\56 1392.503 509.452 7:4 1.750
52\71 1392.981 508.974 9:5 1.800
11\15 1394.767 507.188 2:1 2.000 Basic 4L 7s⟨3/1⟩
Scales with tunings softer than this are proper
47\64 1396.748 505.207 9:4 2.250
36\49 1397.355 504.600 7:3 2.333
61\83 1397.822 504.133 12:5 2.400
25\34 1398.496 503.459 5:2 2.500 Semihard 4L 7s⟨3/1⟩
64\87 1399.139 502.816 13:5 2.600
39\53 1399.552 502.403 8:3 2.667
53\72 1400.050 501.905 11:4 2.750
14\19 1401.441 500.514 3:1 3.000 Hard 4L 7s⟨3/1⟩
45\61 1403.082 498.873 10:3 3.333
31\42 1403.824 498.131 7:2 3.500
48\65 1404.521 497.434 11:3 3.667
17\23 1405.793 496.162 4:1 4.000 Superhard 4L 7s⟨3/1⟩
37\50 1407.447 494.508 9:2 4.500
20\27 1408.856 493.099 5:1 5.000
23\31 1411.128 490.827 6:1 6.000
3\4 1426.466 475.489 1:0 → ∞ Collapsed 4L 7s⟨3/1⟩
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