Oneirotonic
Zheanist theory
A-Team oneirotonic may be a particularly good place to bring to bear Zheanism's high harmonic chords, as A-Team temperament doesn't yield many low-complexity chords.
18edo may be a better basis for a style of oneirotonic Zheanism using comma sharp and comma flat fifths than 13edo (in particular diesis sharp and diesis flat fifths; diesis is a category with a central region of 32 to 40c). In 18edo both the major fifth (+31.4c) and the minor fifth (-35.3) are about a diesis off from a just perfect fifth. In 13edo only the major fifth is a diesis sharp, and it is +36.5c off from just; so there's less wiggle room for a neji if you want every major fifth to be at most a diesis sharp).
31nejis and 34nejis also provide opportunities to use dieses directly, since 1\31 (38.71c) and 1\34 (35.29c) are both dieses.
Primodal chords
These are just oneirotonic-inspired chords, they aren't guaranteed to fit in your neji.
/13
- 13:16:19 Tridecimal Squashed Major Triad
- 13:17:19 Tridecimal Naiadic Maj2
- 13:17:20 Tridecimal Squashed 2nd Inversion Minor Triad
- 13:17:21 Tridecimal Squashed 2nd Inversion Major Triad
- 13:16:19:22 Tridecimal Oneiro Major Tetrad
/17
- 17:20:25 Septen Squashed Minor Triad
- 17:20:26 Septen Squashed 1st Inversion Major Triad
- 17:20:25:29 Septen Minor Oneiro Tetrad
- 17:21:25:29 Septen Major Oneiro Tetrad
- 17:20:26:29 Septen Squashed 1st Inversion Major Triad addM6
- 34:40:47:55 Septen Orwell Tetrad
- 34:40:52:58:76:89:102:129 (Celephaïsian + P5; R-min3-sup5-M6-M9-sub11-P12(fc)-M14)
- 34:40:52:58:76:89:102:110:129 (Celephaïsian + P5; R-min3-sup5-M6-M9-sub11-P12(fc)-supmin13-M14)
- 34:40:50:58:89:102:129 (R-min3-sub5-M6-M9-sub11-P12(rc)-M14)
- 34:40:50:58:89:102:110:129 (R-min3-sub5-M6-M9-sub11-P12(rc)-supmin13-M14)
- 34:40:50:58:76:89:110:129 (R-m3-sub5-M6-M9-sub11-supm13-M7)
- 34:40:50:58:76:89:102:110:129:208 (R-m3-sub5-M6-M9-sub11-P12(rc)-supm13-M14-sup19(rc^2))
/23
- 23:27:30 Vice Squashed Min4
- 23:27:30:35:44 Vice Squashed Min4 addM5,M7
- 23:27:37 Vice Orwell Tetrad no5
- 46:54:63:76 Vice Orwell Tetrad
- 46:54:67:78 Vice Minor Oneiro Tetrad
- 46:54:60:67:78 Vice Min4 Oneiro Pentad
/29
- 29:34:38 Vicenon Squashed Sus4
- 29:34:42 Vicenon Squashed Minor Triad
- 29:36:42 Vicenon Squashed Major Triad
- 29:34:40:47 Vicenon Orwell Tetrad
- 29:38:65:84:99 Vicenon Oneiro Core Pentad
- 29:38:65:84:99:110 Vicenon Oneiro Core Hexad
- 58:65:72:80:84:94:99:110:116 Vicenon Dylathian &4
- 58:65:72:76:84:94:99:110:116 Vicenon Dylathian
- 58:65:72:76:84:89:99:110:116 Vicenon Ilarnekian
- 58:65:72:76:84:89:99:104:116 Vicenon Ilarnekian @8
- 58:65:68:76:84:94:99:110:116 Vicenon Celephaïsian &6
- 58:65:68:76:84:89:99:110:116 Vicenon Celephaïsian
- 58:65:68:76:84:89:99:104:116 Vicenon Ultharian
- 58:65:68:76:80:89:99:104:116 Vicenon Mnarian
- 58:65:68:76:80:89:99:110:116 Vicenon Mnarian &8
- 58:65:68:76:80:89:94:104:116 Vicenon Hlanithian &2
- 58:61:68:76:80:89:99:104:116 Vicenon Kadathian
- 58:61:68:76:84:89:99:104:116 Vicenon Ultharian @2
- 58:61:68:76:80:89:94:104:116 Vicenon Hlanithian
- 58:61:68:72:80:89:99:104:116 Vicenon Sarnathian &6
- 58:61:68:72:80:89:94:104:116 Vicenon Sarnathian
- 58:61:68:72:80:84:94:104:116 Vicenon Sarnathian @6
Over small prime multiples
Some oneirotonic nejis
- 58:61:65:68:72:76:80:84:89:94:99:104:110:116 A very low-complexity 13neji; not optimized for transposability.
Rank-2 temperaments
A-Team (13&18, 4:5:9:21)
Sortable table of intervals in the Dylathian mode and their A-Team interpretations:
| Degree | Size in 13edo | Size in 18edo | Size in 31edo | Note name on L | Approximate ratios[1] | #Gens up |
|---|---|---|---|---|---|---|
| 1 | 0\13, 0.00 | 0\18, 0.00 | 0\31, 0.00 | L | 1/1 | 0 |
| 2 | 2\13, 184.62 | 3\18, 200.00 | 5\31, 193.55 | M | 9/8, 10/9 | +3 |
| 3 | 4\13, 369.23 | 6\18, 400.00 | 10\31, 387.10 | N | 5/4 | +6 |
| 4 | 5\13, 461.54 | 7\18, 466.67 | 12\31, 464.52 | O | 21/16, 13/10 | +1 |
| 5 | 7\13, 646.15 | 10\18, 666.66 | 17\31, 658.06 | P | 13/9, 16/11 | +4 |
| 6 | 9\13, 830.77 | 13\18, 866.66 | 22\31, 851.61 | Q | 13/8, 18/11 | +7 |
| 7 | 10\13, 923.08 | 14\18, 933.33 | 24\31, 929.03 | J | 12/7 | +2 |
| 8 | 12\13, 1107.69 | 17\18, 1133.33 | 29\31, 1122.58 | K | +5 |
- ↑ The harmonics over 1/1 are in bold. The ratio interpretations that are not valid for 18edo are italicized.
Petrtri (13&21, 4:5:9:11:13:17)
Intervals
Sortable table of intervals in the Dylathian mode and their Petrtri interpretations:
| Degree | Size in 13edo | Size in 21edo | Size in 34edo | Size in POTE tuning | Note name on L | Approximate ratios | #Gens up |
|---|---|---|---|---|---|---|---|
| 1 | 0\13, 0.00 | 0\21, 0.00 | 0\34, 0.00 | 0.00 | L | 1/1 | 0 |
| 2 | 2\13, 184.62 | 3\21, 171.43 | 5\34, 176.47 | 177.45 | M | 10/9, 11/10 | +3 |
| 3 | 4\13, 369.23 | 6\21, 342.86 | 10\34, 352.94 | 354.90 | N | 11/9, 16/13 | +6 |
| 4 | 5\13, 461.54 | 8\21, 457.14 | 13\34, 458.82 | 459.15 | O | 13/10, 17/13, 22/17 | +1 |
| 5 | 7\13, 646.15 | 11\21, 628.57 | 18\34, 635.294 | 636.60 | P | 13/9, 16/11 | +4 |
| 6 | 9\13, 830.77 | 14\21, 800.00 | 23\34, 811.77 | 814.05 | Q | 8/5 | +7 |
| 7 | 10\13, 923.08 | 16\21, 914.29 | 26\34, 917.65 | 918.30 | J | 17/10 | +2 |
| 8 | 12\13, 1107.69 | 19\21, 1085.71 | 31\34, 1094.12 | 1095.75 | K | 17/9, 32/17 | +5 |
Samples
(A rather classical-sounding 3-part harmonization of the ascending J Ilarnekian scale; tuning is 13edo)
(13edo, first 30 seconds is in J Celephaïsian)
(13edo, L Ilarnekian)
(by Igliashon Jones, 13edo, J Celephaïsian)