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

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|13\[[17edf]]
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|Poseidon is around here
|Poseidon is around here
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|11\[[14edf]]
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|4\[[5edf]]
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|9\[[11edf]]
|9\[[11edf]]
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|5\[[6edf]]
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== Temperaments ==
== Temperaments ==

Revision as of 03:45, 4 April 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.

Modes

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

Scale tree

Generator (chroma-positive) Cents (chroma-positive) L s L/s Comments
3\4edf 526.5 1 1 1.0000
13\17edf 536.8 5 4 1.2500
10\13edf 540.0 4 3 1.3333
7\9edf 546.0 3 2 1.5000 Poseidon is around here
11\14edf 551.5 5 3 1.6667
15\19edf 554.2 7 4 1.7500
4\5edf 561.6 2 1 2.0000
9\11edf 574.3 5 2 2.5000
5\6edf 585.0 3 1 3.0000
6\7edf 601.7 4 1 4.0000
7\8edf 614.2 5 1 5.0000
1\1edf 702.0 1 0 -> inf

Temperaments

Poseidon

This temperament equates 2 11/8 with 5/4. It contains an 8:10:11 triad.

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]]

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

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