Varunismic temperaments: Difference between revisions

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-This is a collection of temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.
+{{Technical data page}}
+This is a collection of rank-2 temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.
 Temperaments discussed elsewhere are:
-* [[Meantone family #Injera|Injera]] ({50/49, 81/80})
+* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
-* [[Diaschismic family #Diaschismic|Diaschismic]] ({126/125, 2048/2025})
+* ''[[Diaschismic]]'' (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
-* [[Pythagorean family #Compton|Compton]] ({225/224, 250047/250000})
+* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
-* [[Amity family #Bamity|Bamity]] ({245/243, 64827/64000})
+* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]]
-* [[Gamelismic clan #Unidec|Unidec]] ({1029/1024, 4375/4374})
+* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]
-* [[Breedsmic temperaments #Harry|Harry]] ({2401/2400, 19683/19600})
+* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
-* [[Schismatic family #Bischismic|Bischismic]] ({3136/3125, 32805/32768})
+* ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]]
-* [[Sensipent family #Bison|Bison]] ({6144/6125, 78732/78125})
+* ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]]
-* [[Hemimage temperaments #Commatic|Commatic]] ({10976/10935, 50421/50000})
+* ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]]
-* [[26th-octave temperaments #Bosonic|Bosonic]] ({321489/320000, 589824/588245})
+* ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]]
+* ''[[Decal]]'' (+235298/234375) → [[Pental family #Decal|Pental family]]
+* ''[[Bosonic]]'' (+589824/588245) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]
-= Essence =
+== Essence ==
-Essence is of interest because of the abundant supply of essentially tempered chords.
+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.
-Commas: 321489/320000, 823543/820125
+[[Subgroup]]: 2.3.5.7
-POTE generator: ~243/196 = 372.597
+[[Comma list]]: 321489/320000, 823543/820125
-Map: [&lt;2 10 27 23|, &lt;0 -11 -36 -28|]
+{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}
-Wedgie: &lt;&lt;22 72 56 63 27 -72||
+: mapping generators: ~567/400, ~243/196
-EDOs: 58, 190, 248, 438d, 686d
+[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~243/196 = 372.597 (~343/300 = 227.403)
-Badness: 0.1736
+{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}
-== 11-limit ==
+[[Badness]]: 0.173565
-Commas: 441/440, 8019/8000, 456533/455625
-POTE generator: ~243/196 = 372.599
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Map: [&lt;2 10 27 23 33|, &lt;0 -11 -36 -28 -42|]
+Comma list: 441/440, 8019/8000, 456533/455625
-EDOs: 58, 190, 248, 438d
+Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}
-Badness: 0.0464
+Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 (~154/135 = 227.401)
-== 13-limit ==
+{{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }}
-Commas: 441/440, 729/728, 847/845, 1001/1000
-POTE generator: ~243/196 = 372.602
+Badness: 0.046447
-Map: [&lt;2 10 27 23 33 31|, &lt;0 -11 -36 -28 -42 -38|]
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-EDOs: 58, 190, 248, 438d
+Comma list: 441/440, 729/728, 847/845, 1001/1000
-Badness: 0.0261
+Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}
-= Octowerck =
+Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 (~154/135 = 227.398)
-Commas: 321489/320000, 420175/419904
-POTE generator: ~350/243 = 633.738
+{{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }}
-Map: [&lt;8 0 -11 14|, &lt;0 3 7 2|]
+Badness: 0.026107
-EDOs: 72, 176, 248, 320
+== Octowerck ==
+[[Subgroup]]: 2.3.5.7
-Badness: 0.1023
+[[Comma list]]: 321489/320000, 420175/419904
-== 11-limit ==
+{{Mapping|legend=1| 8 0 -11 14 | 0 3 7 2 }}
-Commas: 441/440, 8019/8000, 41503/41472
-POTE generator: ~121/84 = 633.355
+: mapping generators: ~160/147, ~350/243
-Map: [&lt;8 0 -11 14 15|, &lt;0 3 7 2 3|]
+[[Optimal tuning]] ([[POTE]]): ~160/147 = 1\8, ~350/243 = 633.738 (~49/48 = 33.738)
-EDOs: 72, 176, 248, 320
+{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
-Badness: 0.0302
+[[Badness]]: 0.102295
-== 13-limit ==
+=== 11-limit ===
-Commas: 441/440, 729/728, 1001/1000, 6656/6655
+Subgroup: 2.3.5.7.11
-POTE generator: ~75/52 = 633.742
+Comma list: 441/440, 8019/8000, 41503/41472
-Map: [&lt;8 0 -11 14 15 -38|, &lt;0 3 7 2 3 16|]
+Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}
-EDOs: 72, 248, 320
+Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 (~49/48 = 33.755)
-Badness: 0.0276
+{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
-[[Category:Regular temperament theory]]
+Badness: 0.030159
-[[Category:Temperament collection]]
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 441/440, 729/728, 1001/1000, 6656/6655
+Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}
+Optimal tuning (POTE): ~12/11 = 1\8, ~75/52 = 633.742 (~49/48 = 33.742)
+{{Optimal ET sequence|legend=1| 72, 176f, 248, 320 }}
+Badness: 0.027632
+==== Octowerckis ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 364/363, 441/440, 2197/2187
+Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}
+Optimal tuning (POTE): ~12/11 = 1\8, ~13/9 = 633.8370 (~49/48 = 33.8370)
+{{Optimal ET sequence|legend=1| 32cf, 72, 176, 248f }}
+Badness: 0.030192
+[[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Varunismic temperaments| ]] <!-- main article -->
-[[Category:Varuna]]
+[[Category:Varuna| ]] <!-- key article -->
 [[Category:Rank 2]]
-{{todo| cleanup }}