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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]], [[718edo]], [[851edo]], [[981edo]], [[148418edo]].


= 22 & 46 & 72 =
== Temperament names ==
An 11-limit rank-3 temperament. Announced in FB group. <s>To be called "quasiquarter"</s> I don't like this name.  
* 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
* Canou (94 & 99 & 118) – 2.3.5.7.17.19 subgroup temperament
** Synca (94 & 99ef & 118f) – 19-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
** Superlimmal (80 & 311) – 13-limit temperament thereof, with its own extensions in the higher limit
* Reiwa (99 & 111 & 113ghh) – 2.3.5.7.17.19 subgroup temperament, another counterpart of deuteromere
** 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.
** Demiwill – 2.3.5.13.17.19 retraction thereof
* Floral (198 & 212) – merge of semicanou and hemireiwa, weak extension of amicable
* Artoneutral (87 & 94)


It tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, [[385/384]], the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit.
* Lux (41 & 46 & 270) named in cooperation with Godtone
** Luminal (183 & 311) – as a result of tempering out lux and meter


It features splitting the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most valuable for those who would like to make extensive use of quartertones.
* 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)
* Counterpyth (2.3.5.7.19 subgroup 41 & 53 & 58h) – NTT object analogous to parapyth, not related to countercomp


It can be viewed as one which is joined by the three quartertone-sized edos: [[22edo]], [[24edo]], and [[26edo]]. It shares the [[optimal patent val]], [[284edo]] with [[Keenanismic family|keenanismic]].
== Comma names ==
* Canousma 4802000/4782969 = {{monzo| 4 -14 3 4 }} (2020)
* Semicanousma 14641/14580 (2020)
* 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)
* Reiwa comma 1280000000/1275989841 = {{monzo| 14 -12 7 -4 }} (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)
* Undecapyth comma (2024)


== 7-limit ==
== 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)
** <s>Helenois (53 & 118f)</s>
** Guillon (41 & 118f)
** <s>Pontis (118f & 171)</s>
** Octowerckis (72 & 104c)
** Slenderman (94 & 125f)
** Countermanna (145 & 176)
** Ennealimmalis (99ef & 171ef)
** 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:
** Countritonic (53 & 422)
* Counterwürschmidt (5-limit 31 & 152)
* Quasiultra (27 & 32) – superpyth : quasisuper :: ultrapyth : quasiultra
* Flattertone (26 & 33cd) – a flat-of-flattone meantone extension


[[Comma list]]: 1500625/1492992
== 87 & 94 & 111 ==
An unnamed 13-limit rank-3 temperament. Gotta find a name from Hawaiian myth like other hemifamity temperaments.


[[Mapping]]: [<2 1 0 7|, <0 2 0 3|, <0 0 1 -1|]
[[Subgroup]]: 2.3.5.7.11.13
 
Mapping generators: ~1225/864, ~35/24, ~5
 
{{Multival|legend=1|rank=3| 4 -4 -6 11 }}
 
[[POTE generator]]s: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326
 
{{Val list|legend=1| 22, 46, 68, 72, 118, 140, 212, 330, 470 }}
 
[[Badness]]: 0.7042 × 10<sup>-3</sup>
 
== 11-limit ==
 
Comma list: 385/384, 9801/9800
 
Mapping: [<2 1 0 7 8|, <0 2 0 3 -1|, <0 0 1 -1 0|]
 
Mapping generators: ~99/70, ~16/11, ~5
 
POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315
 
Vals: {{val list| 22, 46, 68, 72, 118, 190, 212, 284, 330e }}
 
Badness: 0.5292 × 10<sup>-3</sup>
 
= 87 & 94 & 111 =
An unnamed 13-limit rank-3 temperament.


[[Comma list]]: 352/351, 847/845, 14641/14580
[[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|]
{{Mapping|legend=1| 1 0 2 12 1 6 | 0 1 2 -4 2 -1 | 0 0 4 4 1 1 }}
 
{{Val list|legend=1| 7, 17c, 24d, 87, 111, 181, 198 }}
 
[[Badness]]: 0.0540 × 10<sup>-3</sup>
 
= 41 & 46 & 53 & 58 =
An unnamed 13-limit rank-4 temperament.
 
[[Comma list]]: 352/351, 847/845
 
[[Mapping]]: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]
 
{{Multival|legend=1|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 }}
 
POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538


{{Val list|legend=1| 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198 }}
{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 379f, 490f }}


[[Badness]]: 2.550 × 10<sup>-6</sup>
[[Badness]]: 1.650 × 10<sup>-3</sup>
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