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4L 1s (3/1-equivalent)

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4L 1s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 4 large steps and 1 small step, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 380.4 ¢ to 475.5 ¢, or from 1426.5 ¢ to 1521.6 ¢. Scales of this form are always proper because there is only one small step.

← 3L 1s⟨3/1⟩ 4L 1s (3/1-equivalent) 5L 1s⟨3/1⟩ →
↙ 3L 2s⟨3/1⟩ ↓ 4L 2s⟨3/1⟩ 5L 2s⟨3/1⟩ ↘
Scale structure
Step pattern LLLLs
sLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 1\5 to 1\4 (380.4 ¢ to 475.5 ¢)
Dark 3\4 to 4\5 (1426.5 ¢ to 1521.6 ¢)
Related MOS scales
Parent 1L 3s⟨3/1⟩
Sister 1L 4s⟨3/1⟩
Daughters 5L 4s⟨3/1⟩, 4L 5s⟨3/1⟩
Neutralized 3L 2s⟨3/1⟩
2-Flought 9L 1s⟨3/1⟩, 4L 6s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 1\5 (380.4 ¢)
Supersoft (L:s = 4:3) 4\19 (400.4 ¢)
Soft (L:s = 3:2) 3\14 (407.6 ¢)
Semisoft (L:s = 5:3) 5\23 (413.5 ¢)
Basic (L:s = 2:1) 2\9 (422.7 ¢)
Semihard (L:s = 5:2) 5\22 (432.3 ¢)
Hard (L:s = 3:1) 3\13 (438.9 ¢)
Superhard (L:s = 4:1) 4\17 (447.5 ¢)
Collapsed (L:s = 1:0) 1\4 (475.5 ¢)
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Theory

Modes

Modes of 4L 1s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
4|0 1 LLLLs
3|1 2 LLLsL
2|2 3 LLsLL
1|3 4 LsLLL
0|4 5 sLLLL

Temperament interpretations

  Todo: expand

Intervals

Intervals of 4L 1s⟨3/1⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 380.4 ¢
Perfect 1-mosstep P1ms L 380.4 ¢ to 475.5 ¢
2-mosstep Minor 2-mosstep m2ms L + s 475.5 ¢ to 760.8 ¢
Major 2-mosstep M2ms 2L 760.8 ¢ to 951.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 951.0 ¢ to 1141.2 ¢
Major 3-mosstep M3ms 3L 1141.2 ¢ to 1426.5 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 1426.5 ¢ to 1521.6 ¢
Augmented 4-mosstep A4ms 4L 1521.6 ¢ to 1902.0 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 4L 1s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 LLLLs Perf. Perf. Maj. Maj. Aug. Perf.
3|1 2 LLLsL Perf. Perf. Maj. Maj. Perf. Perf.
2|2 3 LLsLL Perf. Perf. Maj. Min. Perf. Perf.
1|3 4 LsLLL Perf. Perf. Min. Min. Perf. Perf.
0|4 5 sLLLL Perf. Dim. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 1s⟨3/1⟩
Generator(edt) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\5 380.391 1521.564 1:1 1.000 Equalized 4L 1s⟨3/1⟩
6\29 393.508 1508.447 6:5 1.200
5\24 396.241 1505.714 5:4 1.250
9\43 398.084 1503.871 9:7 1.286
4\19 400.412 1501.543 4:3 1.333 Supersoft 4L 1s⟨3/1⟩
11\52 402.337 1499.618 11:8 1.375
7\33 403.445 1498.510 7:5 1.400
10\47 404.671 1497.284 10:7 1.429
3\14 407.562 1494.393 3:2 1.500 Soft 4L 1s⟨3/1⟩
11\51 410.226 1491.729 11:7 1.571
8\37 411.234 1490.721 8:5 1.600
13\60 412.090 1489.865 13:8 1.625
5\23 413.468 1488.487 5:3 1.667 Semisoft 4L 1s⟨3/1⟩
12\55 414.972 1486.983 12:7 1.714
7\32 416.053 1485.902 7:4 1.750
9\41 417.502 1484.453 9:5 1.800
2\9 422.657 1479.298 2:1 2.000 Basic 4L 1s⟨3/1⟩
9\40 427.940 1474.015 9:4 2.250
7\31 429.474 1472.481 7:3 2.333
12\53 430.631 1471.324 12:5 2.400
5\22 432.263 1469.693 5:2 2.500 Semihard 4L 1s⟨3/1⟩
13\57 433.779 1468.176 13:5 2.600
8\35 434.733 1467.222 8:3 2.667
11\48 435.865 1466.090 11:4 2.750
3\13 438.913 1463.042 3:1 3.000 Hard 4L 1s⟨3/1⟩
10\43 442.315 1459.640 10:3 3.333
7\30 443.790 1458.166 7:2 3.500
11\47 445.138 1456.817 11:3 3.667
4\17 447.519 1454.436 4:1 4.000 Superhard 4L 1s⟨3/1⟩
9\38 450.463 1451.492 9:2 4.500
5\21 452.846 1449.109 5:1 5.000
6\25 456.469 1445.486 6:1 6.000
1\4 475.489 1426.466 1:0 → ∞ Collapsed 4L 1s⟨3/1⟩
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