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== "Oneirotonic maqam" ==
"Oneirotonic maqam" is based on the idea "If [[maqam]] is loosely an extension of diatonic that uses neutral intervals, what is the oneirotonic counterpart that uses oneirotonic neutral intervals?" or "What if we distorted maqam scales similarly to how oneirotonic distorts diatonic scales?" The following assumes an edo with A-Team oneirotonic scales and neutral mosseconds (i.e. half of an oneirotonic minor mosthird) such as [[18edo]] and [[26edo]]. In rank-2 [[temperament]] terms, this requires a loosely 18&26 structure.
* 26edo can be used if you want neutral mosseconds and minor mosthirds closer to their [[24edo]] counterparts. In 26edo these are 138c and 277c respectively, but in 18edo these are 133c and 267c.
* 18edo can be used if you want neutral mosthirds (neutral mos2nd + major mos2nd) closer to conventional neutral thirds. The neutral mos3rd is 333c in 18edo and 323c in 26edo.
== Zheanist theory ==
== 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.
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.

Revision as of 14:24, 1 February 2021

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
  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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