Oneirotonic: Difference between revisions

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== 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 ==
== Rank-2 temperaments ==
=== A-Team (13&18, 4:5:9:21) ===
=== A-Team (13&18, 4:5:9:21) ===

Revision as of 14:25, 1 February 2021

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
  1. ↑ 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)

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