Ragismic microtemperaments: Difference between revisions
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* ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]] | * ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]] | ||
Considered below, sorted by increasing [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, palladium, and | Considered below, sorted by increasing [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, palladium, quindro, and euphrosynean. | ||
== Supermajor == | == Supermajor == | ||
| Line 1,604: | Line 1,604: | ||
Badness (Sintel): 1.02 | Badness (Sintel): 1.02 | ||
== Euphrosynean == | |||
Euphrosynean may be described as the 217 & 1178 temperament, which combines two large supersets of [[31edo]] [[consistent]] in the [[21-odd-limit]]. It was named by [[Eliora]] in 2026 after the minor planet {{w|31 Euphrosyne}}. [[1395edo]], also consistent in 21-odd-limit, is another possible tuning. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 4375/4374, {{monzo| -153 42 7 25 }} | |||
{{Mapping|legend=1| 31 2 -38 197 | 0 3 7 -7 }} | |||
: mapping generators: ~562711519881/549755813888, ~67108864/47258883 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~562711519881/549755813888 = 38.7109{{c}}, ~67108864/47258883 = 608.1819{{c}} | |||
: [[error map]]: {{val| +0.037 +0.012 -0.053 -0.061 }} | |||
* [[CWE]]: ~562711519881/549755813888 = 38.7097{{c}}, ~67108864/47258883 = 608.1644{{c}} | |||
: error map: {{val| 0.000 -0.042 -0.131 -0.170 }} | |||
{{Optimal ET sequence|legend=1| 217, 744c, 961, 1178, 1395, 2573, 6541cd, 9114ccdd }} | |||
[[Badness]] (Sintel): 14.1 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 4375/4374, 820125/819896, {{monzo| -37 12 -1 6 1 }} | |||
{{Mapping|legend=0| 31 2 -38 197 -97 | 0 3 7 -7 13 }} | |||
Optimal tunings: | |||
* WE: ~45/44 = 38.7108{{c}}, ~14553/10240 = 608.1781{{c}} | |||
* CWE: ~45/44 = 38.7097{{c}}, ~14553/10240 = 608.1620{{c}} | |||
{{Optimal ET sequence|legend=0| 217, 961e, 1178, 2573, 8897ccdde }} | |||
Badness (Sintel): 3.70 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 4225/4224, 4375/4374, 225000/224939, 18753525/18743296 | |||
{{Mapping|legend=0| 31 2 -38 197 -97 99 | 0 3 7 -7 13 1 }} | |||
Optimal tunings: | |||
* WE: ~45/44 = 38.7108{{c}}, ~14553/10240 = 608.1778{{c}} | |||
* CWE: ~45/44 = 38.7097{{c}}, ~14553/10240 = 608.1620{{c}} | |||
{{Optimal ET sequence|legend=0| 217, 961e, 1178, 1395, 2573, 8897ccddef }} | |||
Badness (Sintel): 1.59 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 4225/4224, 4375/4374, 14400/14399, 14875/14872, 56595/56576 | |||
{{Mapping|legend=0| 31 2 -38 197 -97 99 111 | 0 3 7 -7 13 1 1 }} | |||
Optimal tunings: | |||
* WE: ~45/44 = 38.7106{{c}}, ~1989/1400 = 608.1761{{c}} | |||
* CWE: ~45/44 = 38.7097{{c}}, ~1989/1400 = 608.1625{{c}} | |||
{{Optimal ET sequence|legend=0| 217, 961e, 1178, 1395, 2573 }} | |||
Badness (Sintel): 1.10 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 4200/4199, 4225/4224, 4375/4374, 5929/5928, 5985/5984, 14875/14872 | |||
{{Mapping|legend=0| 31 2 -38 197 -97 99 111 6 | 0 3 7 -7 13 1 1 8 }} | |||
Optimal tunings: | |||
* WE: ~45/44 = 38.7105{{c}}, ~665/468 = 608.1732{{c}} | |||
* CWE: ~45/44 = 38.7097{{c}}, ~665/468 = 608.1613{{c}} | |||
{{Optimal ET sequence|legend=0| 217, 961e, 1178, 2573 }} | |||
Badness (Sintel): 0.944 | |||
; Music | |||
* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] by [[Eliora]] (2023) – in euphrosynean and enneadecal, 1178edo tuning | |||
== References == | == References == | ||