1L 3s (3/2-equivalent)

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↑1L 2s⟨3/2⟩ 2L 2s⟨3/2⟩ ↗
1L 3s (3/2-equivalent) 2L 3s⟨3/2⟩ →
↓1L 4s⟨3/2⟩ 2L 4s⟨3/2⟩ ↘
┌╥┬┬┬┐
│║││││
││││││
└┴┴┴┴┘
Scale structure
Step pattern Lsss
sssL
Equave 3/2 (702.0¢)
Period 3/2 (702.0¢)
Generator size(edf)
Bright 3\4 to 1\1 (526.5¢ to 702.0¢)
Dark 0\1 to 1\4 (0.0¢ to 175.5¢)
Related MOS scales
Parent 1L 2s⟨3/2⟩
Sister 3L 1s⟨3/2⟩
Daughters 4L 1s⟨3/2⟩, 1L 4s⟨3/2⟩
Neutralized 2L 2s⟨3/2⟩
2-Flought 5L 3s⟨3/2⟩, 1L 7s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 3\4 (526.5¢)
Supersoft (L:s = 4:3) 10\13 (540.0¢)
Soft (L:s = 3:2) 7\9 (546.0¢)
Semisoft (L:s = 5:3) 11\14 (551.5¢)
Basic (L:s = 2:1) 4\5 (561.6¢)
Semihard (L:s = 5:2) 9\11 (574.3¢)
Hard (L:s = 3:1) 5\6 (585.0¢)
Superhard (L:s = 4:1) 6\7 (601.7¢)
Collapsed (L:s = 1:0) 1\1 (702.0¢)

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

Scale Tree and Tuning Spectrum of 1L 3s⟨3/2⟩
Generator(edf) Cents Step Ratio Comments
Bright Dark L:s Hardness
3\4 526.466 175.489 1:1 1.000 Equalized 1L 3s⟨3/2⟩
16\21 534.823 167.132 6:5 1.200
13\17 536.789 165.166 5:4 1.250
23\30 538.166 163.790 9:7 1.286
10\13 539.965 161.990 4:3 1.333 Supersoft 1L 3s⟨3/2⟩
27\35 541.508 160.447 11:8 1.375
17\22 542.420 159.535 7:5 1.400
24\31 543.449 158.506 10:7 1.429
7\9 545.965 155.990 3:2 1.500 Soft 1L 3s⟨3/2⟩
Poseidon and Auk are around here
25\32 548.402 153.553 11:7 1.571
18\23 549.356 152.599 8:5 1.600
29\37 550.181 151.774 13:8 1.625
11\14 551.536 150.419 5:3 1.667 Semisoft 1L 3s⟨3/2⟩
26\33 553.055 148.900 12:7 1.714
15\19 554.175 147.780 7:4 1.750
19\24 555.714 146.241 9:5 1.800
4\5 561.564 140.391 2:1 2.000 Basic 1L 3s⟨3/2⟩
Scales with tunings softer than this are proper
17\21 568.249 133.706 9:4 2.250
13\16 570.338 131.617 7:3 2.333
22\27 571.963 129.992 12:5 2.400
9\11 574.327 127.628 5:2 2.500 Semihard 1L 3s⟨3/2⟩
Halftone (incomplete)
23\28 576.606 125.349 13:5 2.600
14\17 578.081 123.874 8:3 2.667
19\23 579.876 122.079 11:4 2.750
5\6 584.963 116.993 3:1 3.000 Hard 1L 3s⟨3/2⟩
16\19 591.120 110.835 10:3 3.333
11\13 593.962 107.993 7:2 3.500
17\20 596.662 105.293 11:3 3.667
6\7 601.676 100.279 4:1 4.000 Superhard 1L 3s⟨3/2⟩
13\15 608.361 93.594 9:2 4.500
7\8 614.211 87.744 5:1 5.000
8\9 623.960 77.995 6:1 6.000
1\1 701.955 0.000 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