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:  
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: [<2 10 27 23|, <0 -11 -36 -28|]
{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}


Wedgie: <<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: [<2 10 27 23 33|, <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: [<2 10 27 23 33 31|, <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: [<8 0 -11 14|, <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: [<8 0 -11 14 15|, <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: [<8 0 -11 14 15 -38|, <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:Varunismic temperaments| ]] <!-- main article -->
[[Category:Varuna]]
[[Category:Varuna| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
{{todo| cleanup }}

Latest revision as of 00:34, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the varunisma, 321489/320000 = [-9 8 -4 2⟩.

Temperaments discussed elsewhere are:

Essence

Essence is of interest because of the abundant supply of essentially tempered chords. 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: [⟨2 10 27 23], ⟨0 -11 -36 -28]]

mapping generators: ~567/400, ~243/196

Optimal tuning (POTE): ~567/400 = 1\2, ~243/196 = 372.597 (~343/300 = 227.403)

Optimal ET sequence: 58, 132d, 190, 248, 438d, 686d

Badness: 0.173565

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 8019/8000, 456533/455625

Mapping: [⟨2 10 27 23 33], ⟨0 -11 -36 -28 -42]]

Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 (~154/135 = 227.401)

Optimal ET sequence: 58, 132de, 190, 248, 438d

Badness: 0.046447

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 729/728, 847/845, 1001/1000

Mapping: [⟨2 10 27 23 33 31], ⟨0 -11 -36 -28 -42 -38]]

Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 (~154/135 = 227.398)

Optimal ET sequence: 58, 132de, 190, 248, 438d

Badness: 0.026107

Octowerck

Subgroup: 2.3.5.7

Comma list: 321489/320000, 420175/419904

Mapping: [⟨8 0 -11 14], ⟨0 3 7 2]]

mapping generators: ~160/147, ~350/243

Optimal tuning (POTE): ~160/147 = 1\8, ~350/243 = 633.738 (~49/48 = 33.738)

Optimal ET sequence: 32c, 72, 176, 248, 320

Badness: 0.102295

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 8019/8000, 41503/41472

Mapping: [⟨8 0 -11 14 15], ⟨0 3 7 2 3]]

Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 (~49/48 = 33.755)

Optimal ET sequence: 32c, 72, 176, 248, 320

Badness: 0.030159

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 729/728, 1001/1000, 6656/6655

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: 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: [⟨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: 32cf, 72, 176, 248f

Badness: 0.030192

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