Varunismic temperaments: Difference between revisions
Improve intro, + units, misc. cleanup, - redundant category |
Sort links by ploidacot. Sort main entries by badness |
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Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | * ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | ||
* | * [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]] | ||
* ''[[ | * ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]] | ||
* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]] | |||
* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]] | * ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]] | ||
* [[ | * ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]] | ||
* [[ | * ''[[Decile]]'' (+235298/234375) → [[Quintile family #Decile|Quintile family]] | ||
* | * [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]] | ||
* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity family]] | |||
* ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]] | * ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]] | ||
* ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]] | * ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]] | ||
* ''[[Bosonic]]'' (+589824/588245) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]] | * ''[[Bosonic]]'' (+589824/588245) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]] | ||
Considered below are octowerck and essence, in the order of increasing [[badness]]. | Considered below are octowerck and essence, in the order of increasing [[badness]]. | ||
== Octowerck == | == Octowerck == | ||
| Line 112: | Line 70: | ||
Badness (Smith): 0.030192 | Badness (Smith): 0.030192 | ||
== Essence == | |||
Essence is of interest because of the abundant supply of [[essentially tempered chord]]s. Specifically, [[werckismic chords]], [[squbemic chords]], [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the [[13-odd-limit]], in addition to [[nicolic chords]] in the [[15-odd-limit]]. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 321489/320000, 823543/820125 | |||
{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }} | |||
: mapping generators: ~567/400, ~243/196 | |||
[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~243/196 = 372.597{{c}} (~343/300 = 227.403{{c}}) | |||
{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }} | |||
[[Badness]] (Smith): 0.173565 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 8019/8000, 456533/455625 | |||
Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }} | |||
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~150/121 = 372.599{{c}} (~154/135 = 227.401{{c}}) | |||
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }} | |||
Badness (Smith): 0.046447 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 441/440, 729/728, 847/845, 1001/1000 | |||
Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }} | |||
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~26/21 = 372.602{{c}} (~154/135 = 227.398{{c}}) | |||
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }} | |||
Badness (Smith): 0.026107 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Varunismic temperaments| ]] <!-- main article --> | [[Category:Varunismic temperaments| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||