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User:FloraC/Temperament name proposal: Difference between revisions

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For the record, edo pages I created: [[275edo]], [[316edo]], [[330edo]], [[354edo]], [[357edo]], [[431edo]], [[566edo]], [[634edo]], [[639edo]], [[718edo]], [[981edo]], [[148418edo]].  
For the record, edo pages I created: [[275edo]], [[316edo]], [[330edo]], [[354edo]], [[357edo]], [[431edo]], [[552edo]], [[566edo]], [[634edo]], [[639edo]], [[718edo]], [[851edo]], [[981edo]], [[148418edo]].  


Temperament names:
== Temperament names ==
* Semicanousmic (87 & 94 & 111 & 118f) – full 19-limit rank-4 nullity-4 temperament, my most important discovery
* 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
** 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
*** 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 subgroup temperament
** Canou (94 & 99 & 118) – 2.3.5.7.17.19 retraction, a counterpart of deuteromere
** Synca (94 & 99ef & 118f) – 19-limit extension thereof
*** Synca (94 & 99ef & 118f) – 19-limit extension thereof
** Canta (75e & 80 & 104c) – alternative 13-limit extension thereof
*** Canta (75e & 80 & 104c) – alternative 13-limit extension thereof
** Semicanou (94 & 118f & 198gh)
*** Humorous (198 & 311) – 13-limit temperament thereof, weak extension of amicable
** 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
** 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 subgroup temperament, another counterpart of deuteromere
** Reiwa (99 & 111 & 113ghh) – 2.3.5.7.17.19 retraction, another counterpart of deuteromere
** Synre (99ef & 111 & 113ghh) – 19-limit extension thereof
*** Synre (99ef & 111 & 113ghh) – 19-limit extension thereof
** Hemireiwa (87 & 111 & 212gh)
* 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.  
* 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
** 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
* Floral (198 & 212) – merge of semicanou and hemireiwa, weak extension of amicable
* Artoneutral (87 & 94)
* Artoneutral (87 & 94)
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* Hera (46 & 53 & 130) – strong extension of porwell that seems really natural and spells much better than "hewuermity"
* 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"
* 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)
* Counterpyth (2.3.5.7.19 subgroup 41 & 53 & 58h) – NTT object analogous to parapyth, not related to countercomp


Comma names:
== Comma names ==
* Canousma 4802000/4782969 = {{monzo| 4 -14 3 4 }} (2020)
* Canousma 4802000/4782969 = {{monzo| 4 -14 3 4 }} (2020)
* Semicanousma 14641/14580 (2020)
* Semicanousma 14641/14580 (2020)
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* Quadrantonisma 1156/1155 (2023)
* Quadrantonisma 1156/1155 (2023)
* Sextantonisma 2601/2600 (2023)
* Sextantonisma 2601/2600 (2023)
* Countercomp comma, Pythagorean countercomma (2021)
* Gothic comma, Pythagorean gothma (2023)
* Nommisma {{monzo| -55 30 2 1 }} (2023)
* Nommisma {{monzo| -55 30 2 1 }} (2023)
* Counterwürschmidt comma (2023)
* Lifthrasirsma (2023)
* Undecapyth comma (2024)


Variations on existing roots:
== Variations on existing roots ==
* Parakleismic extensions
* Parakleismic extensions:  
** Paralytic (99e & 118) – analogous to catalytic
** Parakleismic extensions:
** Semiparamint (80 & 118)
*** Paralytic (11-limit 99e & 118) – analogous to catalytic
** Semiparawolf (80 & 118f)
*** Semiparamint (13-limit 80 & 118)
*** Semiparawolf (13-limit 80 & 118f)
** Counterpara (11-limit 118 & 137)
* Semiseptiquarter (94 & 198)
* Semiseptiquarter (94 & 198)
* Luna extensions
* Luna extensions
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** Bischis (118f & 130)
** Bischis (118f & 130)
** Kleischis (94 & 118f)
** Kleischis (94 & 118f)
** Helenois (53 & 118f)
** <s>Helenois (53 & 118f)</s>
** Guironis (41 & 118f)
** Guillon (41 & 118f)
** Pontis (118f & 171)
** <s>Pontis (118f & 171)</s>
** Octowerckis (72 & 104c)
** Octowerckis (72 & 104c)
** Slenderman (94 & 125f)
** Slenderman (94 & 125f)
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** Hemienneadecalis (152f & 342f)
** Hemienneadecalis (152f & 342f)
** Hemipentalis (125f & 130)
** Hemipentalis (125f & 130)
* Immediate extensions of amicable:  
* Amity extensions:
** Amical (311 & 410)
** Calamity (46 & 311)
** Amorous (212 & 311)
** Chromat extension:
** Pseudoamical (113 & 212)
*** Hemichromat (159 & 198)
** Pseudoamorous (14cf & 99ef)
** 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
* 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
* Squad (14cf & 17c) – an alternative 13-limit extension of squares that's good for detempering
* Undim extensions:  
* Undim extensions:  
** Unlit (152f & 316)
** Unlit (152f & 316)
** Twilight (152f & 176)
** Twilight (152f & 176)
 
* Countritonic extensions:  
== Orthocanousmic ==
** Countritonic (53 & 422)
[[Subgroup]]: 2.3.5.7.11.13
* Counterwürschmidt (5-limit 31 & 152)
 
* Quasiultra (27 & 32) – superpyth : quasisuper :: ultrapyth : quasiultra
[[Comma list]]: 2080/2079, 4621925/4605822
* Flattertone (26 & 33cd) – a flat-of-flattone meantone extension
 
[[Mapping]]: [{{val| 1 0 0 -1 0 -6 }}, {{val| 0 1 2 2 0 3 }}, {{val| 0 0 -4 3 0 7 }}, {{val| 0 0 0 0 1 1 }}]
 
[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.3120, ~81/70 = 254.6177, ~11/8 = 551.2945
 
{{Optimal ET sequence|legend=1| 94, 113, 193e, 193f, 198, 311, 509, 721, 938, 1249 }}
 
[[Badness]]: 26.5 × 10<sup>-6</sup>
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 1225/1224, 2080/2079, 256564/255879
 
Mapping: [{{val| 1 0 0 -1 0 -6 -5 }}, {{val| 0 1 2 2 0 3 6 }}, {{val| 0 0 -4 3 0 7 -2 }}, {{val| 0 0 0 0 1 1 0 }}]
 
Optimal tuning (CTE): ~3/2 = 702.3391, ~81/70 = 254.6143, ~11/8 = 551.2678
 
{{Optimal ET sequence|legend=1| 94, 118f, 193e, 193f, 198g, 212g, 217, 311, 509, 721, 938, 1447b, 1659b }}
 
Badness: 41.6 × 10<sup>-6</sup>
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 1216/1215, 1225/1224, 1445/1444, 2080/2079
 
Mapping: [{{val| 1 0 0 -1 0 -6 -5 -6 }}, {{val| 0 1 2 2 0 3 6 7 }}, {{val| 0 0 -4 3 0 7 -2 -4 }}, {{val| 0 0 0 0 1 1 0 0 }}]
 
Optimal tuning (CTE): ~3/2 = 702.3182, ~81/70 = 254.6205, ~11/8 = 551.2767
 
{{Optimal ET sequence|legend=1| 94, 118f, 193e, 193f, 198gh, 212gh, 217, 311, 627h, 721, 938, 1032, 1249 }}
 
Badness: 47.2 × 10<sup>-6</sup>
 
== Paracanousmic ==
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 2080/2079, 831875/830466
 
[[Mapping]]: [{{val| 1 0 2 7 0 0 }}, {{val| 0 1 0 -3 0 0 }}, {{val| 0 0 4 7 0 3 }}, {{val| 0 0 0 0 1 1 }}]
 
[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.1596, ~55/52 = 96.5027, ~11/8 = 551.1788
 
{{Optimal ET sequence|legend=1| 87, 111, 186, 198, 224, 311, 422, 634, 733f, 858, 945, 1169, 1367, 1591f }}
 
[[Badness]]: 9.66 × 10<sup>-6</sup>
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 2080/2079, 2500/2499, 41140/41067
 
Mapping: [{{val| 1 0 2 7 0 0 -4 }}, {{val| 0 1 0 -3 0 0 5 }}, {{val| 0 0 4 7 0 3 2 }}, {{val| 0 0 0 0 1 1 0 }}]
 
Optimal tuning (CTE): ~3/2 = 702.3034, ~55/52 = 96.5472, ~11/8 = 551.1166
 
{{Optimal ET sequence|legend=1| 87, 99ef, 111, 198g, 212g, 299, 311, 422, 721, 733f, 931fg, 1143, 1565bf }}
 
Badness: 32.2 × 10<sup>-6</sup>
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 1216/1215, 1445/1444, 2080/2079, 2500/2499
 
Mapping: [{{val| 1 0 2 7 0 0 -4 -4 }}, {{val| 0 1 0 -3 0 0 5 5 }}, {{val| 0 0 4 7 0 3 2 4 }}, {{val| 0 0 0 0 1 1 0 0 }}]
 
Optimal tuning (CTE): ~3/2 = 702.2902, ~55/52 = 96.5420, ~11/8 = 551.1238
 
{{Optimal ET sequence|legend=1| 87, 99ef, 111, 198gh, 210efgh, 212g, 299, 311, 422, 733f, 1056, 1143h, 1454fh }}
 
Badness: 37.2 × 10<sup>-6</sup>


== 87 & 94 & 111 ==
== 87 & 94 & 111 ==
An unnamed 13-limit rank-3 temperament. Gotta find a name from Hawaiian myth like other hemifamity temperaments.  
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
[[Subgroup]]: 2.3.5.7.11.13


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


[[Mapping]]: [{{val| 1 0 2 12 1 6 }}, {{val| 0 1 2 -4 2 -1 }}, {{val| 0 0 4 4 1 1 }}]
{{Mapping|legend=1| 1 0 2 12 1 6 | 0 1 2 -4 2 -1 | 0 0 4 4 1 1 }}


{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 379f, 490f }}
{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 379f, 490f }}


[[Badness]]: 1.650 × 10<sup>-3</sup>
[[Badness]]: 1.650 × 10<sup>-3</sup>
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