1L 3s (3/2-equivalent): Difference between revisions

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[[Support]]ing [[ET]]s: 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]
[[Support]]ing [[ET]]s: 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
{{Mapping|legend=2| 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
<nowiki>*</nowiki> wart for 3/2

Revision as of 09:11, 11 June 2023

↑ 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

Template:Scale tree

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

Subgroup-val 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

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