1L 3s (3/2-equivalent)

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↑1L 2s⟨3/2⟩ 2L 2s⟨3/2⟩↗
1L 3s⟨3/2⟩2L 3s⟨3/2⟩→
↓1L 4s⟨3/2⟩ 2L 4s⟨3/2⟩↘
Brightest mode Lsss
Period 3/2
Range for bright generator 3\4edf (526.5¢) to 1\1edf (702¢)
Range for dark generator 0\1edf (0¢) to 1\4edf (175.5¢)
Parent MOS 1L 2s⟨3/2⟩
Sister MOS 3L 1s⟨3/2⟩
Daughter MOSes 4L 1s⟨3/2⟩, 1L 4s⟨3/2⟩
Equal tunings
Supersoft (L:s = 4:3) 10\13edf (540¢)
Soft (L:s = 3:2) 7\9edf (546¢)
Semisoft (L:s = 5:3) 11\14edf (551.5¢)
Basic (L:s = 2:1) 4\5edf (561.6¢)
Semihard (L:s = 5:2) 9\11edf (574.3¢)
Hard (L:s = 3:1) 5\6edf (585¢)
Superhard (L:s = 4:1) 6\7edf (601.7¢)

1L 3s<3/2> (or neptunian), is a fifth-repeating MOS scale with 1 large step and 3 small steps. The name "neptunian" was given by CompactStar in analogy to "uranian" name for 3L 2s<3/2>.

Notation

Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for L/s < 2/1) so similar note names can be used. Although, one difference is that the "perfect fourth" can go up to a subfifth in the most extreme case.

Modes

  • 3|0 Lsss "tritonian"
  • 2|1 sLss "protean"
  • 1|2 ssLs "nereidian"
  • 0|3 sssL "larissan"

Scale tree

Steps of ED Generator in cents Step ratio Comments
Bright Dark L:s Hardness
3\4edf 526.466 175.489 1:1 1 Equalized 1L 3s⟨3/2⟩
16\21edf 534.823 167.132 6:5 1.2
13\17edf 536.789 165.166 5:4 1.25
23\30edf 538.166 163.79 9:7 1.286
10\13edf 539.965 161.99 4:3 1.333 Supersoft 1L 3s⟨3/2⟩
27\35edf 541.508 160.447 11:8 1.375
17\22edf 542.42 159.535 7:5 1.4
24\31edf 543.449 158.506 10:7 1.429
7\9edf 545.965 155.99 3:2 1.5 Soft 1L 3s⟨3/2⟩
Poseidon and Auk are around here
25\32edf 548.402 153.553 11:7 1.571
18\23edf 549.356 152.599 8:5 1.6
29\37edf 550.181 151.774 13:8 1.625
11\14edf 551.536 150.419 5:3 1.667 Semisoft 1L 3s⟨3/2⟩
26\33edf 553.055 148.9 12:7 1.714
15\19edf 554.175 147.78 7:4 1.75
19\24edf 555.714 146.241 9:5 1.8
4\5edf 561.564 140.391 2:1 2 Basic 1L 3s⟨3/2⟩
(Generators smaller than this are proper)
17\21edf 568.249 133.706 9:4 2.25
13\16edf 570.338 131.617 7:3 2.333
22\27edf 571.963 129.992 12:5 2.4
9\11edf 574.327 127.628 5:2 2.5 Semihard 1L 3s⟨3/2⟩
Halftone (incomplete)
23\28edf 576.606 125.349 13:5 2.6
14\17edf 578.081 123.874 8:3 2.667
19\23edf 579.876 122.079 11:4 2.75
5\6edf 584.963 116.993 3:1 3 Hard 1L 3s⟨3/2⟩
16\19edf 591.12 110.835 10:3 3.333
11\13edf 593.962 107.993 7:2 3.5
17\20edf 596.662 105.293 11:3 3.667
6\7edf 601.676 100.279 4:1 4 Superhard 1L 3s⟨3/2⟩
13\15edf 608.361 93.594 9:2 4.5
7\8edf 614.211 87.744 5:1 5
8\9edf 623.96 77.995 6:1 6
1\1edf 701.955 0 1:0 → ∞ Collapsed 1L 3s⟨3/2⟩

Temperaments

Poseidon

This temperament equates 2 11/8 with 5/4. It contains an 8:10:11 triad, which sounds quite similar to a major triad although with increased tension. 9edf (and thus Carlos Alpha) is a good tuning for this temperament with its accurate 5/4 and 11/8.

Subgroup: 3/2.5/4.11/8

Comma list: 121/120

Gencom: [3/2 12/11; 121/120]

POTE generator: ~12/11 = 158.29

Mapping: [1 1 1], 0 2 -1]]

Supporting EDFs: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49

Auk

Main article: Auk

Subgroup: 3/2.7.13

Comma list: 87808/85293

CTE generator: ~28/9 = 1950.859

Mapping: [1 2 -2], 0 1 3]]

Supporting ETs: 5, 9, 13, 14, 6[+13], 17[-7, -13], 7[-7, -13], 22[-7], 19[+13], 23[+13], 11[+13], 21[-7, -13], 31[-7], 25[-7, -13]

Halftone

Main article: Halftone

Subgroup: 3/2.5/2.7/2

Comma list: 9604/9375

Sval mapping[1 3 4], 0 -4 -5]]

sval mapping generators: ~3/2, ~15/14

Optimal tuning (subgroup CTE): ~3/2 = 1\1edf, ~15/14 = 128.783

Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49

* wart for 3/2