1L 3s (3/2-equivalent): Difference between revisions
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m == Intervals == {{MOS intervals}} |
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== Notation == | == Notation == | ||
Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for L/s <u><</u> 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. | Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for L/s <u><</u> 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 == | == Modes == | ||
* 3|0 Lsss "tritonian" | * 3|0 Lsss "tritonian" | ||
| Line 16: | Line 17: | ||
* 1|2 ssLs "nereidian" | * 1|2 ssLs "nereidian" | ||
* 0|3 sssL "larissan" | * 0|3 sssL "larissan" | ||
== Intervals == | |||
{{MOS intervals}} | |||
== Scale tree == | == Scale tree == | ||
{{Scale tree|Comments=3/2:Poseidon and Auk are around here;5/2:Halftone (incomplete)}} | {{Scale tree|Comments=3/2:Poseidon and Auk are around here;5/2:Halftone (incomplete)}} | ||
== Temperaments == | == Temperaments == | ||
=== Poseidon === | === Poseidon === | ||
Revision as of 08:23, 15 December 2024
| ↑ 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⟩ ↘ |
┌╥┬┬┬┐ │║││││ ││││││ └┴┴┴┴┘
sssL
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"
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0 ¢ to 175.5 ¢ |
| Augmented 1-mosstep | A1ms | L | 175.5 ¢ to 702.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 351.0 ¢ |
| Major 2-mosstep | M2ms | L + s | 351.0 ¢ to 702.0 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0 ¢ to 526.5 ¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 526.5 ¢ to 702.0 ¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 702.0 ¢ |
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