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4L 1s (3/1-equivalent)

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← 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 ¢)

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.

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

Template:Scale tree

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