1L 3s (3/2-equivalent)
| ↑1L 2s⟨3/2⟩ | 2L 2s⟨3/2⟩↗ | |
| 1L 3s⟨3/2⟩ | 2L 3s⟨3/2⟩→ | |
| ↓1L 4s⟨3/2⟩ | 2L 4s⟨3/2⟩↘ |
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