User:FloraC/Temperament name proposal: Difference between revisions

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Ideas welcome!
For the record, edo pages I created: [[275edo]], [[316edo]], [[330edo]], [[354edo]], [[357edo]], [[431edo]], [[552edo]], [[566edo]], [[634edo]], [[639edo]], [[692edo]], [[718edo]], [[851edo]], [[894edo]], [[981edo]], [[1205edo]], [[5809edo]], [[6349edo]], [[8404edo]], [[10729edo]], [[28472edo]], [[148418edo]].


= 22 & 46 & 72 =
== Temperament names ==
An 11-limit rank-3 temperament. Announced in FB group. To be called "quasiquarter".
* Cathartic (94 & 99e & 118) – no-13 23-limit rank-3 temperament, one of my early discoveries
** Canta (75e & 80 & 104c) – alternative 11-limit extension thereof
** Semicathart (94 & 104c & 118) – weak 11-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
* Semicathartismic (87 & 94 & 111 & 118) – rank-4 detemperament of semicathart
** Deuteromere (94 & 111 & 118) – no-7 retraction, part of a series of -mere names devised in cooperation with Aura
** Floral (198 & 212) – 13-limit temperament thereof, weak extension of amicable
* 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
* 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"
* Lycoris (152 & 171 & 176)
* Orthoschismic (41 & 53 & 130)
* Cassaschismic (41 & 53 & 270)
* Androschismic (29 & 41 & 270)
* Sif (46 & 270 & 1236)
* Lif (41 & 130 & 270)
* Freyr (41 & 58h & 270)
* Counterpyth (7-limit add-19 41 & 53 & 58h) – NTT object analogous to parapyth, not related to countercomp


== 7-limit ==
* Artoneutral (87 & 94)
* Cutefourths (58 & 181)


Comma: 1500625/1492992
== Comma names ==
* Cathartic comma 4802000/4782969 ({{monzo| 4 -14 3 4 }}) (2020, modified in 2026)
* Semicathartisma 14641/14580 (2020, modified in 2026)
* Semiporwellisma 16384/16335 (2021)
* Wilschisma 532480/531441 (2021)
* Olympia 131072/130977 (2021)
* Aureusma 1445/1444 (2021)
* Noellisma 1225/1224 (2022)
* Lambeth comma 1573/1568 (2022)
* Semitonisma 289/288 (2023)
* Quadrantonisma 1156/1155 (2023)
* Sextantonisma 2601/2600 (2023)
* Countercomp comma, Pythagorean countercomma (2021)
* Gothic comma, Pythagorean gothma (2023)
* Nommisma {{monzo| -55 30 2 1 }} (2023)
* Counterwürschmidt comma (2023)
* Lifthrasirsma (2023)
* <s>Undecapyth comma (2024)</s>


Map: [<2 1 0 7|, <0 2 0 3|, <0 0 1 -1|]
== Variations on existing roots ==
 
* Parakleismic extensions:  
Mapping generators: ~1225/864, ~35/24, ~5
** Parakleismic extensions:  
 
*** Paralytic (11-limit 99e & 118) – analogous to catalytic
Wedgie: <<< 4 -4 -6 11 |||
*** Semiparamint (13-limit 80 & 118)
 
*** Semiparawolf (13-limit 80 & 118f)
POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326
** Counterpara (11-limit 118 & 137)
 
* Semiseptiquarter (94 & 198)
EDOs: {{EDOs| 22, 46, 68, 72, 118, 140, 212, 330, 470 }}
* Luna extensions
 
** Semiluna (118 & 292)
Badness: 0.7042 × 10<sup>-3</sup>
** Hemiluna (87 & 323)
 
* Misty extensions
== 11-limit ==
** Semimist (12f & 198)
 
* Term extensions
Commas: 385/384, 9801/9800
** Semiterm (12f & 342f) – originally proposed by Xenllium as ''hemiterm'', normalized to semi- for split period
 
** Hemiterm (159 & 183)
Map: [<2 1 0 7 8|, <0 2 0 3 -1|, <0 0 1 -1 0|]
* Gary (41 & 135, 2.3.7.11)
 
* Countertertiaschis (159 & 224) – by community request
Mapping generators: ~99/70, ~16/11, ~5
* Alternative 13-limit extensions tempering out 2080/2079 instead of 4096/4095
 
** Bischis (118f & 130)
POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315
** Kleischis (94 & 118f)
 
** <s>Helenois (53 & 118f)</s>
EDOs: {{EDOs| 22, 46, 68, 72, 118, 190, 212, 284, 330e }}
** Guillon (41 & 118f)
 
** <s>Pontis (118f & 171)</s>
Badness: 0.5292 × 10<sup>-3</sup>
** Octowerckis (72 & 104c)
 
** Slenderman (94 & 125f)
= 87 & 94 & 111 =
** Countermanna (145 & 176)
An unnamed 13-limit rank-3 temperament.
** Hemienneadecalis (152f & 342f)
 
** Hemipentalis (125f & 130)
Commas: 352/351, 847/845, 14641/14580
* Amity extensions:  
 
** Calamity (46 & 311)
Map: [<1 0 2 12 1 6|, <0 1 2 -4 2 -1|, <0 0 4 4 1 1|]
** Chromat extension:  
 
*** Hemichromat (159 & 198)
EDOs: 7, 17c, 24d, 87, 111, 181, 198
** Immediate extensions of amicable:  
 
*** Amical (311 & 410)
Badness: 0.0540 × 10<sup>-3</sup>
*** Amorous (212 & 311)
 
*** Pseudoamical (113 & 212)
= 41 & 46 & 53 & 58 =
*** Pseudoamorous (14cf & 99ef)
An unnamed 13-limit rank-4 temperament.
* Semiporwell (46 & 68 & 130) – one of many neat ways to exploit the semiporwellisma
 
* Squad (14cf & 17c) – an alternative 13-limit extension of squares that's good for detempering
Commas: 352/351, 847/845
* Undim extensions:
 
** Unlit (152f & 316)
Map: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]
** Twilight (152f & 176)
 
* Countritonic extensions:  
Wedgie: <<<<0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0||||
** Ragitritonic (53 & 369f)
 
** Garitritonic (53 & 581)
POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538
* Vishnu extensions:  
 
** Trivish (84 & 186)
EDOs: 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198
* Counterwürschmidt (5-limit 31 & 152)
 
* Quasiultra (27 & 32) – superpyth : quasisuper :: ultrapyth : quasiultra
Badness: 2.550 × 10<sup>-6</sup>
* Flattertone (26 & 33cd) – a flat-of-flattone meantone extension
* Leapmonth (63 & 80) – ''cf''. leapday (29 & 46) and leapweek (46 & 63)

Latest revision as of 13:34, 10 August 2026

For the record, edo pages I created: 275edo, 316edo, 330edo, 354edo, 357edo, 431edo, 552edo, 566edo, 634edo, 639edo, 692edo, 718edo, 851edo, 894edo, 981edo, 1205edo, 5809edo, 6349edo, 8404edo, 10729edo, 28472edo, 148418edo.

Temperament names

  • Cathartic (94 & 99e & 118) – no-13 23-limit rank-3 temperament, one of my early discoveries
    • Canta (75e & 80 & 104c) – alternative 11-limit extension thereof
    • Semicathart (94 & 104c & 118) – weak 11-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
  • Semicathartismic (87 & 94 & 111 & 118) – rank-4 detemperament of semicathart
    • Deuteromere (94 & 111 & 118) – no-7 retraction, part of a series of -mere names devised in cooperation with Aura
    • Floral (198 & 212) – 13-limit temperament thereof, weak extension of amicable
  • 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
  • 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"
  • Lycoris (152 & 171 & 176)
  • Orthoschismic (41 & 53 & 130)
  • Cassaschismic (41 & 53 & 270)
  • Androschismic (29 & 41 & 270)
  • Sif (46 & 270 & 1236)
  • Lif (41 & 130 & 270)
  • Freyr (41 & 58h & 270)
  • Counterpyth (7-limit add-19 41 & 53 & 58h) – NTT object analogous to parapyth, not related to countercomp
  • Artoneutral (87 & 94)
  • Cutefourths (58 & 181)

Comma names

  • Cathartic comma 4802000/4782969 ([4 -14 3 4⟩) (2020, modified in 2026)
  • Semicathartisma 14641/14580 (2020, modified in 2026)
  • Semiporwellisma 16384/16335 (2021)
  • Wilschisma 532480/531441 (2021)
  • Olympia 131072/130977 (2021)
  • Aureusma 1445/1444 (2021)
  • Noellisma 1225/1224 (2022)
  • Lambeth comma 1573/1568 (2022)
  • Semitonisma 289/288 (2023)
  • Quadrantonisma 1156/1155 (2023)
  • Sextantonisma 2601/2600 (2023)
  • Countercomp comma, Pythagorean countercomma (2021)
  • Gothic comma, Pythagorean gothma (2023)
  • Nommisma [-55 30 2 1⟩ (2023)
  • Counterwürschmidt comma (2023)
  • Lifthrasirsma (2023)
  • Undecapyth comma (2024)

Variations on existing roots

  • Parakleismic extensions:
    • Parakleismic extensions:
      • Paralytic (11-limit 99e & 118) – analogous to catalytic
      • Semiparamint (13-limit 80 & 118)
      • Semiparawolf (13-limit 80 & 118f)
    • Counterpara (11-limit 118 & 137)
  • 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)
    • Guillon (41 & 118f)
    • Pontis (118f & 171)
    • Octowerckis (72 & 104c)
    • Slenderman (94 & 125f)
    • Countermanna (145 & 176)
    • Hemienneadecalis (152f & 342f)
    • Hemipentalis (125f & 130)
  • Amity extensions:
    • Calamity (46 & 311)
    • Chromat extension:
      • Hemichromat (159 & 198)
    • 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
  • Squad (14cf & 17c) – an alternative 13-limit extension of squares that's good for detempering
  • Undim extensions:
    • Unlit (152f & 316)
    • Twilight (152f & 176)
  • Countritonic extensions:
    • Ragitritonic (53 & 369f)
    • Garitritonic (53 & 581)
  • Vishnu extensions:
    • Trivish (84 & 186)
  • Counterwürschmidt (5-limit 31 & 152)
  • Quasiultra (27 & 32) – superpyth : quasisuper :: ultrapyth : quasiultra
  • Flattertone (26 & 33cd) – a flat-of-flattone meantone extension
  • Leapmonth (63 & 80) – cf. leapday (29 & 46) and leapweek (46 & 63)
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