Varunismic temperaments: Difference between revisions
Switch to Sintel's badness, WE & CWE tunings |
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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) → [[ | * ''[[Narayana]]'' (+65625/65536) → [[Vishnu family #Narayana|Vishnu family]] | ||
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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Badness (Sintel): 1.25 | 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 == | ||