User:FloraC/Temperament proposal

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Ideas welcome!

Temperament names:

  • Semicanousmic (87 & 94 & 111 & 118f) – full 19-limit rank-4 nullity-4 temperament, my most important discovery
    • Deuteromere (94 & 111 & 118) – 2.3.5.11.17.19 retraction, part of a series of -mere names devised in cooperation with Aura
      • Syndeute (94 & 111 & 118f) – 19-limit extension thereof
  • Orthocanousmic (94 & 99 & 99ef & 118f) – full 19-limit rank-4 nullity-4 temperament
    • Canou (94 & 99 & 118) – 2.3.5.7.17.19 retraction, a counterpart of deuteromere
      • Synca (94 & 99ef & 118f) – 19-limit extension thereof
      • Canta (75e & 80 & 104c) – alternative 13-limit extension thereof
      • Humorous (198 & 311) – 13-limit temperament thereof, weak extension of amicable
      • Superlimmal (80 & 311) – 13-limit temperament thereof, with its own extensions in the higher limit
  • Paracanousmic (87 & 99ef & 111 & 113ghh) – full 19-limit rank-4 nullity-4 temperament
    • Reiwa (99 & 111 & 113ghh) – 2.3.5.7.17.19 retraction, another counterpart of deuteromere
      • Synre (99ef & 111 & 113ghh) – 19-limit extension thereof
  • Demisymbiotic (94 & 99ef & 111 & 118f) – full 19-limit rank-4 nullity-4 temperament. Symbiotic was found by Aura. This extends it through a split of the second generator.
    • Demiwill – 2.3.5.13.17.19 retraction thereof
  • Semicanou (94 & 118f & 198gh) – merge of semicanousmic and orthocanousmic
  • Hemireiwa (87 & 111 & 212gh) – merge of semicanousmic and paracanousmic
  • Floral (198 & 212) – merge of semicanou and hemireiwa, weak extension of amicable
  • Lux (41 & 46 & 270) named in cooperation with Godtone
    • Luminal (183 & 311) – as a result of tempering out lux and meter
  • Hera (46 & 53 & 130) – strong extension of porwell that seems really natural and spells much better than "hewuermity"
  • Akua (41 & 46 & 53 & 58) – the Hawaiian word for "god"

Comma names:

  • Canousma (4802000/4782969 = [4 -14 3 4)
  • Reiwa comma (1280000000/1275989841 = [14 -12 7 -4)
  • Semicanousma (14641/14580)
  • Semiporwellisma (16384/16335)
  • Wilschisma (532480/531441)
  • Aureusma (1445/1444)
  • Noellisma (1225/1224)
  • Olympia (131072/130977)
  • Lambeth comma (1573/1568)

Variations on existing roots:

  • Parakleismic extensions
    • Paralytic (99e & 118) – analogous to catalytic
    • Semiparamint (80 & 118)
    • Semiparawolf (80 & 118f)
  • Semiseptiquarter (94 & 198)
  • Luna extensions
    • Semiluna (118 & 292)
    • Hemiluna (87 & 323)
  • Misty extensions
    • Semimist (12f & 198)
  • Term extensions
    • Semiterm (12f & 342f) – originally proposed by Xenllium as hemiterm, normalized to semi- for split period
    • Hemiterm (159 & 183)
  • Gary (41 & 135, 2.3.7.11)
  • Countertertiaschis (159 & 224) – by community request
  • Alternative 13-limit extensions tempering out 2080/2079 instead of 4096/4095
    • Bischis (118f & 130)
    • Kleischis (94 & 118f)
    • Helenois (53 & 118f)
    • Guironis (41 & 118f)
    • Pontis (118f & 171)
    • Octowerckis (72 & 104c)
    • Slenderman (94 & 125f)
    • Countermanna (145 & 176)
    • Ennealimmalis (99ef & 171ef)
    • Hemienneadecalis (152f & 342f)
    • Hemipentalis (125f & 130)
  • Immediate extensions of amicable:
    • Amical (311 & 410)
    • Amorous (212 & 311)
    • Pseudoamical (113 & 212)
    • Pseudoamorous (14cf & 99ef)
  • Semiporwell (46 & 68 & 130) – one of many neat ways to exploit the semiporwellisma
  • Mistynex (24 & 87 & 111)
  • Squad (14cf & 17c) – an alternative 13-limit extension of squares that's good for detempering
  • Undim extensions:
    • Unlit (152f & 316)
    • Twilight (152f & 176)

Orthocanousmic

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4621925/4605822

Mapping: [1 0 0 -1 0 -6], 0 1 2 2 0 3], 0 0 -4 3 0 7], 0 0 0 0 1 1]]

Optimal tuning (CTE): ~3/2 = 702.3120, ~81/70 = 254.6177, ~11/8 = 551.2945

Optimal GPV sequence94, 113, 193e, 193f, 198, 311, 509, 721, 938, 1249

Badness: 26.5 × 10-6

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 1225/1224, 2080/2079, 256564/255879

Mapping: [1 0 0 -1 0 -6 -5], 0 1 2 2 0 3 6], 0 0 -4 3 0 7 -2], 0 0 0 0 1 1 0]]

Optimal tuning (CTE): ~3/2 = 702.3391, ~81/70 = 254.6143, ~11/8 = 551.2678

Optimal GPV sequence: 94, 118f, 193e, 193f, 198g, 212g, 217, 311, 509, 721, 938, 1447b, 1659b

Badness: 41.6 × 10-6

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1216/1215, 1225/1224, 1445/1444, 2080/2079

Mapping: [1 0 0 -1 0 -6 -5 -6], 0 1 2 2 0 3 6 7], 0 0 -4 3 0 7 -2 -4], 0 0 0 0 1 1 0 0]]

Optimal tuning (CTE): ~3/2 = 702.3182, ~81/70 = 254.6205, ~11/8 = 551.2767

Optimal GPV sequence: 94, 118f, 193e, 193f, 198gh, 212gh, 217, 311, 627h, 721, 938, 1032, 1249

Badness: 47.2 × 10-6

Paracanousmic

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 831875/830466

Mapping: [1 0 2 7 0 0], 0 1 0 -3 0 0], 0 0 4 7 0 3], 0 0 0 0 1 1]]

Optimal tuning (CTE): ~3/2 = 702.1596, ~55/52 = 96.5027, ~11/8 = 551.1788

Optimal GPV sequence87, 111, 186, 198, 224, 311, 422, 634, 733f, 858, 945, 1169, 1367, 1591f

Badness: 9.66 × 10-6

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 2080/2079, 2500/2499, 41140/41067

Mapping: [1 0 2 7 0 0 -4], 0 1 0 -3 0 0 5], 0 0 4 7 0 3 2], 0 0 0 0 1 1 0]]

Optimal tuning (CTE): ~3/2 = 702.3034, ~55/52 = 96.5472, ~11/8 = 551.1166

Optimal GPV sequence: 87, 99ef, 111, 198g, 212g, 299, 311, 422, 721, 733f, 931fg, 1143, 1565bf

Badness: 32.2 × 10-6

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1216/1215, 1445/1444, 2080/2079, 2500/2499

Mapping: [1 0 2 7 0 0 -4 -4], 0 1 0 -3 0 0 5 5], 0 0 4 7 0 3 2 4], 0 0 0 0 1 1 0 0]]

Optimal tuning (CTE): ~3/2 = 702.2902, ~55/52 = 96.5420, ~11/8 = 551.1238

Optimal GPV sequence: 87, 99ef, 111, 198gh, 210efgh, 212g, 299, 311, 422, 733f, 1056, 1143h, 1454fh

Badness: 37.2 × 10-6

87 & 94 & 111

An unnamed 13-limit rank-3 temperament. Gotta find a name from Hawaiian myth like other hemifamity temperaments.

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 14641/14580

Mapping: [1 0 2 12 1 6], 0 1 2 -4 2 -1], 0 0 4 4 1 1]]

Optimal GPV sequence87, 111, 181, 198, 379f, 490f

Badness: 1.650 × 10-3