5L 4s (3/1-equivalent)

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↖ 4L 3s⟨3/1⟩ ↑ 5L 3s⟨3/1⟩ 6L 3s⟨3/1⟩ ↗
← 4L 4s⟨3/1⟩ 5L 4s (3/1-equivalent) 6L 4s⟨3/1⟩ →
↙ 4L 5s⟨3/1⟩ ↓ 5L 5s⟨3/1⟩ 6L 5s⟨3/1⟩ ↘ 
┌╥╥┬╥┬╥┬╥┬┐
│║║│║│║│║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLs
sLsLsLsLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 7\9 to 4\5 (1479.3 ¢ to 1521.6 ¢)
Dark 1\5 to 2\9 (380.4 ¢ to 422.7 ¢)
Related MOS scales
Parent 4L 1s⟨3/1⟩
Sister 4L 5s⟨3/1⟩
Daughters 9L 5s⟨3/1⟩, 5L 9s⟨3/1⟩
Neutralized 1L 8s⟨3/1⟩
2-Flought 14L 4s⟨3/1⟩, 5L 13s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 7\9 (1479.3 ¢)
Supersoft (L:s = 4:3) 25\32 (1485.9 ¢)
Soft (L:s = 3:2) 18\23 (1488.5 ¢)
Semisoft (L:s = 5:3) 29\37 (1490.7 ¢)
Basic (L:s = 2:1) 11\14 (1494.4 ¢)
Semihard (L:s = 5:2) 26\33 (1498.5 ¢)
Hard (L:s = 3:1) 15\19 (1501.5 ¢)
Superhard (L:s = 4:1) 19\24 (1505.7 ¢)
Collapsed (L:s = 1:0) 4\5 (1521.6 ¢)

5L 4s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 4 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1479.3 ¢ to 1521.6 ¢, or from 380.4 ¢ to 422.7 ¢.

Theory

Modes

Modes of 5L 4s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
8|0 1 LLsLsLsLs
7|1 8 LsLLsLsLs
6|2 6 LsLsLLsLs
5|3 4 LsLsLsLLs
4|4 2 LsLsLsLsL
3|5 9 sLLsLsLsL
2|6 7 sLsLLsLsL
1|7 5 sLsLsLLsL
0|8 3 sLsLsLsLL

Temperament interpretations

Todo: expand

Intervals

Intervals of 5L 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 211.3 ¢
Major 1-mosstep M1ms L 211.3 ¢ to 380.4 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 380.4 ¢ to 422.7 ¢
Augmented 2-mosstep A2ms 2L 422.7 ¢ to 760.8 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 380.4 ¢ to 634.0 ¢
Major 3-mosstep M3ms 2L + s 634.0 ¢ to 760.8 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 760.8 ¢ to 845.3 ¢
Major 4-mosstep M4ms 3L + s 845.3 ¢ to 1141.2 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 760.8 ¢ to 1056.6 ¢
Major 5-mosstep M5ms 3L + 2s 1056.6 ¢ to 1141.2 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 1141.2 ¢ to 1268.0 ¢
Major 6-mosstep M6ms 4L + 2s 1268.0 ¢ to 1521.6 ¢
7-mosstep Diminished 7-mosstep d7ms 3L + 4s 1141.2 ¢ to 1479.3 ¢
Perfect 7-mosstep P7ms 4L + 3s 1479.3 ¢ to 1521.6 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 1521.6 ¢ to 1690.6 ¢
Major 8-mosstep M8ms 5L + 3s 1690.6 ¢ to 1902.0 ¢
9-mosstep Perfect 9-mosstep P9ms 5L + 4s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 5L 4s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
7|1 8 LsLLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
6|2 6 LsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Perf. Maj. Perf.
5|3 4 LsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Perf. Maj. Perf.
4|4 2 LsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Perf. Min. Perf.
3|5 9 sLLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Perf. Min. Perf.
2|6 7 sLsLLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Perf. Min. Perf.
1|7 5 sLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Perf. Min. Perf.
0|8 3 sLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Dim. Min. Perf.

Scale tree

Template:Scale tree

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