5L 1s (3/2-equivalent)

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← 4L 1s⟨3/2⟩ 5L 1s (3/2-equivalent) 6L 1s⟨3/2⟩ →
↙ 4L 2s⟨3/2⟩ ↓ 5L 2s⟨3/2⟩ 6L 2s⟨3/2⟩ ↘ 
┌╥╥╥╥╥┬┐
│║║║║║││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLs
sLLLLL
Equave 3/2 (702.0 ¢)
Period 3/2 (702.0 ¢)
Generator size(edf)
Bright 1\6 to 1\5 (117.0 ¢ to 140.4 ¢)
Dark 4\5 to 5\6 (561.6 ¢ to 585.0 ¢)
Related MOS scales
Parent 1L 4s⟨3/2⟩
Sister 1L 5s⟨3/2⟩
Daughters 6L 5s⟨3/2⟩, 5L 6s⟨3/2⟩
Neutralized 4L 2s⟨3/2⟩
2-Flought 11L 1s⟨3/2⟩, 5L 7s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 1\6 (117.0 ¢)
Supersoft (L:s = 4:3) 4\23 (122.1 ¢)
Soft (L:s = 3:2) 3\17 (123.9 ¢)
Semisoft (L:s = 5:3) 5\28 (125.3 ¢)
Basic (L:s = 2:1) 2\11 (127.6 ¢)
Semihard (L:s = 5:2) 5\27 (130.0 ¢)
Hard (L:s = 3:1) 3\16 (131.6 ¢)
Superhard (L:s = 4:1) 4\21 (133.7 ¢)
Collapsed (L:s = 1:0) 1\5 (140.4 ¢)

5L 1s⟨3/2⟩ is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 5 large steps and 1 small step, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 117 ¢ to 140.4 ¢, or from 561.6 ¢ to 585 ¢. Scales of this form are always proper because there is only one small step.

It is most notable as the hexatonic scale of halftone temperament, with the bright generator being a sharp 15/14 and the dark generator being a flat 7/5.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 5L 1s⟨3/2⟩
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 117.0 ¢
Perfect 1-mosstep P1ms L 117.0 ¢ to 140.4 ¢
2-mosstep Minor 2-mosstep m2ms L + s 140.4 ¢ to 234.0 ¢
Major 2-mosstep M2ms 2L 234.0 ¢ to 280.8 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 280.8 ¢ to 351.0 ¢
Major 3-mosstep M3ms 3L 351.0 ¢ to 421.2 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 421.2 ¢ to 468.0 ¢
Major 4-mosstep M4ms 4L 468.0 ¢ to 561.6 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 561.6 ¢ to 585.0 ¢
Augmented 5-mosstep A5ms 5L 585.0 ¢ to 702.0 ¢
6-mosstep Perfect 6-mosstep P6ms 5L + s 702.0 ¢

Generator chain

Generator chain of 5L 1s⟨3/2⟩
Bright gens Scale degree Abbrev.
10 Augmented 4-mosdegree A4md
9 Augmented 3-mosdegree A3md
8 Augmented 2-mosdegree A2md
7 Augmented 1-mosdegree A1md
6 Augmented 0-mosdegree A0md
5 Augmented 5-mosdegree A5md
4 Major 4-mosdegree M4md
3 Major 3-mosdegree M3md
2 Major 2-mosdegree M2md
1 Perfect 1-mosdegree P1md
0 Perfect 0-mosdegree
Perfect 6-mosdegree		 P0md
P6md
−1 Perfect 5-mosdegree P5md
−2 Minor 4-mosdegree m4md
−3 Minor 3-mosdegree m3md
−4 Minor 2-mosdegree m2md
−5 Diminished 1-mosdegree d1md
−6 Diminished 6-mosdegree d6md
−7 Diminished 5-mosdegree d5md
−8 Diminished 4-mosdegree d4md
−9 Diminished 3-mosdegree d3md
−10 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 5L 1s⟨3/2⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6
5|0 1 LLLLLs Perf. Perf. Maj. Maj. Maj. Aug. Perf.
4|1 2 LLLLsL Perf. Perf. Maj. Maj. Maj. Perf. Perf.
3|2 3 LLLsLL Perf. Perf. Maj. Maj. Min. Perf. Perf.
2|3 4 LLsLLL Perf. Perf. Maj. Min. Min. Perf. Perf.
1|4 5 LsLLLL Perf. Perf. Min. Min. Min. Perf. Perf.
0|5 6 sLLLLL Perf. Dim. Min. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 1s⟨3/2⟩
Generator(edf) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\6 116.993 584.963 1:1 1.000 Equalized 5L 1s⟨3/2⟩
6\35 120.335 581.620 6:5 1.200
5\29 121.027 580.928 5:4 1.250
9\52 121.492 580.463 9:7 1.286
4\23 122.079 579.876 4:3 1.333 Supersoft 5L 1s⟨3/2⟩
11\63 122.564 579.391 11:8 1.375
7\40 122.842 579.113 7:5 1.400
10\57 123.150 578.805 10:7 1.429
3\17 123.874 578.081 3:2 1.500 Soft 5L 1s⟨3/2⟩
11\62 124.540 577.415 11:7 1.571
8\45 124.792 577.163 8:5 1.600
13\73 125.006 576.949 13:8 1.625
5\28 125.349 576.606 5:3 1.667 Semisoft 5L 1s⟨3/2⟩
12\67 125.723 576.232 12:7 1.714
7\39 125.992 575.963 7:4 1.750
9\50 126.352 575.603 9:5 1.800
2\11 127.628 574.327 2:1 2.000 Basic 5L 1s⟨3/2⟩
9\49 128.931 573.024 9:4 2.250
7\38 129.308 572.648 7:3 2.333
12\65 129.592 572.363 12:5 2.400
5\27 129.992 571.963 5:2 2.500 Semihard 5L 1s⟨3/2⟩
Halftone is in this region
13\70 130.363 571.592 13:5 2.600
8\43 130.596 571.359 8:3 2.667
11\59 130.873 571.082 11:4 2.750
3\16 131.617 570.338 3:1 3.000 Hard 5L 1s⟨3/2⟩
10\53 132.444 569.511 10:3 3.333
7\37 132.802 569.153 7:2 3.500
11\58 133.129 568.826 11:3 3.667
4\21 133.706 568.249 4:1 4.000 Superhard 5L 1s⟨3/2⟩
9\47 134.417 567.538 9:2 4.500
5\26 134.991 566.964 5:1 5.000
6\31 135.862 566.093 6:1 6.000
1\5 140.391 561.564 1:0 → ∞ Collapsed 5L 1s⟨3/2⟩
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