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Varunismic temperaments: Difference between revisions

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* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]
* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]
* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]]
* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]]
* ''[[Fifives]]'' (+875/864) → [[Fifive family #Fifives|Fifive family]]
* ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]]
* ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]]
* ''[[Decile]]'' (+235298/234375) → [[Quintile family #Decile|Quintile family]]
* ''[[Decile]]'' (+235298/234375) → [[Quintile family #Decile|Quintile family]]
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* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity 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) → [[Vishnu family #Narayana|Vishnu family]]
* ''[[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, bosonic, and essence, in the order of increasing [[badness]].  


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


[[Optimal tuning]] ([[POTE]]): ~160/147 = 150.000{{c}}, ~350/243 = 633.738{{c}} (~49/48 = 33.738{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~160/147 = 150.0317{{c}}, ~350/243 = 633.8714{{c}} (~49/48 = 33.7447{{c}})
: [[error map]]: {{val| +0.253 -0.341 +0.438 -0.640 }}
* [[CWE]]: ~160/147 = 150.0000{{c}}, ~350/243 = 633.7791{{c}} (~49/48 = 33.7791{{c}})
: error map: {{val| 0.000 -0.618 +0.140 -1.268 }}


{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}


[[Badness]] (Smith): 0.102295
[[Badness]] (Sintel): 2.59


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}
Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~121/84 = 633.755{{c}} (~49/48 = 33.755{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0233{{c}}, ~121/84 = 633.8533{{c}} (~49/48 = 33.7602{{c}})
* CWE: ~12/11 = 150.0000{{c}}, ~121/84 = 633.7841{{c}} (~49/48 = 33.7841{{c}})


{{Optimal ET sequence|legend=0| 32c, 72, 176, 248, 320 }}
{{Optimal ET sequence|legend=0| 32c, 72, 176, 248, 320 }}


Badness (Smith): 0.030159
Badness (Sintel): 0.997


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}
Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~75/52 = 633.742{{c}} (~49/48 = 33.742{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0247{{c}}, ~75/52 = 633.8469{{c}} (~49/48 = 33.7480{{c}})
* CWE: ~12/11 = 150.000{{c}}, ~75/52 = 633.7616{{c}} (~49/48 = 33.7616{{c}})


{{Optimal ET sequence|legend=0| 72, 176f, 248, 320 }}
{{Optimal ET sequence|legend=0| 72, 176f, 248, 320 }}


Badness (Smith): 0.027632
Badness (Sintel): 1.14


==== Octowerckis ====
==== Octowerckis ====
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Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}
Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~13/9 = 633.8370{{c}} (~49/48 = 33.8370{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0289{{c}}, ~13/9 = 633.9590{{c}} (~49/48 = 33.8435{{c}})
* CWE: ~12/11 = 150.0000{{c}}, ~13/9 = 633.8739{{c}} (~49/48 = 33.8739{{c}})


{{Optimal ET sequence|legend=0| 32cf, 72, 176, 248f }}
{{Optimal ET sequence|legend=0| 32cf, 72, 176, 248f }}


Badness (Smith): 0.030192
Badness (Sintel): 1.25
 
== Bosonic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tridecatonic]].''
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 321489/320000, 589824/588245
 
{{Mapping|legend=1| 26 0 -22 73 | 0 1 2 0 }}
: mapping generators: ~36/35, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~36/35 = 46.1534{{c}}, ~3/2 = 701.2433{{c}}
: [[error map]]: {{val| -0.012 -0.723 +0.775 +0.372 }}
* [[CWE]]: ~36/35 = 46.1538{{c}}, ~3/2 = 701.2451{{c}}
: error map: {{val| 0.000 -0.710 +0.792 +0.405 }}
 
{{Optimal ET sequence|legend=1| 26, …, 104c, 130, 546, 676, 806c }}
 
[[Badness]] (Sintel): 3.94
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 8019/8000, 65536/65219
 
Mapping: {{mapping| 26 0 -22 73 90 | 0 1 2 0 0 }}
 
Optimal tunings:
* WE: ~36/35 = 46.1443{{c}}, ~3/2 = 701.4143{{c}}
* CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.4791{{c}}
 
{{Optimal ET sequence|legend=0| 26, …, 104c, 130 }}
 
Badness (Sintel): 2.16
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 364/363, 441/440, 15379/15360
 
Mapping: {{mapping| 26 0 -22 73 90 55 | 0 1 2 0 0 1 }}
 
Optimal tunings:
* WE: ~36/35 = 46.1469{{c}}, ~3/2 = 701.4410{{c}}
* CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.4873{{c}}
 
{{Optimal ET sequence|legend=0| 26, …, 104c, 130 }}
 
Badness (Sintel): 1.36
 
=== Fermionic ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 78408/78125, 177147/176000
 
Mapping: {{mapping| 26 0 -22 73 -116 | 0 1 2 0 5 }}
 
Optimal tunings:
* WE: ~36/35 = 46.1550{{c}}, ~3/2 = 701.0945{{c}}
* CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.0853{{c}}
 
{{Optimal ET sequence|legend=0| 130, 286, 416, 546 }}
 
Badness (Sintel): 3.00
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 40656/40625, 142884/142805
 
Mapping: {{mapping| 26 0 -22 73 -116 55 | 0 1 2 0 5 1 }}
 
Optimal tunings:
* WE: ~36/35 = 46.1573{{c}}, ~3/2 = 701.0904{{c}}
* CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.0603{{c}}
 
{{Optimal ET sequence|legend=0| 130, 286, 416, 546 }}
 
Badness (Sintel): 1.80


== Essence ==
== Essence ==
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[[Comma list]]: 321489/320000, 823543/820125
[[Comma list]]: 321489/320000, 823543/820125


{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}
{{Mapping|legend=1| 2 -1 -9 -5 | 0 11 36 28 }}
: mapping generators: ~567/400, ~243/196
: mapping generators: ~567/400, ~343/300


[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~243/196 = 372.597{{c}} (~343/300 = 227.403{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~567/400 = 600.0984{{c}}, ~343/300 = 227.4405{{c}}
: [[error map]]: {{val| +0.197 -0.208 +0.659 -0.984 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~343/300 = 227.4104{{c}}
: error map: {{val| 0.000 -0.441 +0.460 -1.335 }}


{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}
{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}


[[Badness]] (Smith): 0.173565
[[Badness]] (Sintel): 4.39


=== 11-limit ===
=== 11-limit ===
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Comma list: 441/440, 8019/8000, 456533/455625
Comma list: 441/440, 8019/8000, 456533/455625


Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}
Mapping: {{mapping| 2 -1 -9 -5 -9 | 0 11 36 28 42 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~150/121 = 372.599{{c}} (~154/135 = 227.401{{c}})
Optimal tunings:
* WE: ~99/70 = 600.0988{{c}}, ~154/135 = 227.4386{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~154/135 = 227.4084{{c}}


{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}


Badness (Smith): 0.046447
Badness (Sintel): 1.54


=== 13-limit ===
=== 13-limit ===
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Comma list: 441/440, 729/728, 847/845, 1001/1000
Comma list: 441/440, 729/728, 847/845, 1001/1000


Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}
Mapping: {{mapping| 2 -1 -9 -5 -9 -7 | 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 tunings:
* WE: ~99/70 = 600.0805{{c}}, ~154/135 = 227.4285{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~154/135 = 227.4040{{c}}


{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}


Badness (Smith): 0.026107
Badness (Sintel): 1.08


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Varunismic temperaments| ]] <!-- main article -->
[[Category:Varunismic temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Varunismic_temperaments"