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Cataharry family: Difference between revisions

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The '''cataharry family''' of rank-3 temperaments tempers out the [[cataharry comma]], 19683/19600.
{{Technical data page}}
 
The '''cataharry family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the [[cataharry comma]], 19683/19600.


== Cataharry ==
== Cataharry ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: [[19683/19600]]
[[Comma list]]: [[19683/19600]]


[[Mapping]]: [{{val| 1 0 0 -2 }}, {{val| 0 2 0 9 }}, {{val| 0 0 1 -1 }}]
{{Mapping|legend=1| 1 0 0 -2 | 0 2 0 9 | 0 0 1 -1 }}


Mapping generators: ~2, ~140/81, ~5
: mapping generators: ~2, ~140/81, ~5


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]:  
: [{{monzo| 1 0 0 0 }}, {{monzo| 4/9 0 2/9 2/9 }}, {{monzo| 0 0 1 0 }}, {{monzo| 0 0 0 1 }}]
: {{monzo list| 1 0 0 0 | 4/9 0 2/9 2/9 | 0 0 1 0 | 0 0 0 1 }}
: Eigenmonzos: 2, 8/7, 5/4
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7


{{Val list|legend=1| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
{{Optimal ET sequence|legend=1| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}


[[Badness]]: 0.301 × 10<sup>-3</sup>
[[Badness]]: 0.301 × 10<sup>-3</sup>
Line 22: Line 24:


== Albus ==
== Albus ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 540/539, 8019/8000
[[Comma list]]: 540/539, 8019/8000


[[Mapping]]: [{{val| 1 0 0 -2 6 }}, {{val| 0 2 0 9 -12 }}, {{val| 0 0 1 -1 3 }}]
{{Mapping|legend=1| 1 0 0 -2 6 | 0 2 0 9 -12 | 0 0 1 -1 3 }}


Mapping generators: ~2, ~140/81, ~5
: mapping generators: ~2, ~140/81, ~5


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]
: Eigenmonzos: 2, 11/10, 7/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5


{{Val list|legend=1| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}
{{Optimal ET sequence|legend=1| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}


[[Badness]]: 0.621 × 10<sup>-3</sup>
[[Badness]]: 0.621 × 10<sup>-3</sup>
Line 44: Line 46:
Comma list: 351/350, 540/539, 676/675
Comma list: 351/350, 540/539, 676/675


Mapping: [{{val| 1 0 0 -2 6 -1 }}, {{val| 0 2 0 9 -12 3 }}, {{val| 0 0 1 -1 3 1 }}]
Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}
 
Mapping generators: ~2, ~26/15, ~5


[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
Line 57: Line 57:
* 13- and 15-odd-limit
* 13- and 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]
: Eigenmonzos: 2, 11/10, 7/5
: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5


Vals: {{Val list| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}
{{Optimal ET sequence|legend=1| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}


Badness: 0.560 × 10<sup>-3</sup>
Badness: 0.560 × 10<sup>-3</sup>
Line 70: Line 70:


== Snape ==
== Snape ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 441/440, 19683/19600
[[Comma list]]: 441/440, 19683/19600


[[Mapping]]: [{{val| 1 0 0 -2 -7 }}, {{val| 0 2 0 9 22 }}, {{val| 0 0 1 -1 -3 }}]
{{Mapping|legend=1| 1 0 0 -2 -7 | 0 2 0 9 22 | 0 0 1 -1 -3 }}
 
Mapping generators: ~2, ~140/81, ~5


{{Val list|legend=1| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}
{{Optimal ET sequence|legend=1| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}


[[Badness]]: 0.988 × 10<sup>-3</sup>
[[Badness]]: 0.988 × 10<sup>-3</sup>
Line 87: Line 85:
Comma list: 351/350, 441/440, 676/675
Comma list: 351/350, 441/440, 676/675


Mapping: [{{val| 1 0 0 -2 -7 -1 }}, {{val| 0 2 0 9 22 3 }}, {{val| 0 0 1 -1 -3 1 }}]
Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}
 
Mapping generators: ~2, ~26/15, ~5


Vals: {{Val list| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}
{{Optimal ET sequence|legend=1| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}


Badness: 0.786 × 10<sup>-3</sup>
Badness: 0.786 × 10<sup>-3</sup>


== Hagrid ==
== Hagrid ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 243/242, 9801/9800
[[Comma list]]: 243/242, 9801/9800


[[Mapping]]: [{{val| 2 0 0 -4 -1 }}, {{val| 0 2 0 9 5 }}, {{val| 0 0 1 -1 0 }}]
{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}


Mapping generators: ~99/70, ~140/81, ~5
: mapping generators: ~99/70, ~140/81, ~5


{{Val list|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}


[[Badness]]: 1.116 × 10<sup>-3</sup>
[[Badness]]: 1.116 × 10<sup>-3</sup>
Line 113: Line 109:
Comma list: 243/242, 351/350, 364/363
Comma list: 243/242, 351/350, 364/363


Mapping: [{{val| 2 0 0 -4 -1 -2 }}, {{val| 0 2 0 9 5 3 }}, {{val| 0 0 1 -1 0 1 }}]
Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}


Mapping generators: ~99/70, ~26/15, ~5
: mapping generators: ~99/70, ~26/15, ~5


Vals: {{Val list| 24, 34d, 58, 72, 130 }}
{{Optimal ET sequence|legend=1| 24, 34d, 58, 72, 130 }}


Badness: 0.876 × 10<sup>-3</sup>
Badness: 0.876 × 10<sup>-3</sup>


== Draco ==
== Draco ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 176/175, 19683/19600
[[Comma list]]: 176/175, 19683/19600


[[Mapping]]: [{{val| 1 0 0 -2 -6 }}, {{val| 0 2 0 9 9 }}, {{val| 0 0 1 -1 1 }}]
{{Mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}


{{Val list|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}
{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}


[[Badness]]: 1.934 × 10<sup>-3</sup>
[[Badness]]: 1.934 × 10<sup>-3</sup>
Line 137: Line 133:
Comma list: 176/175, 351/350, 676/675
Comma list: 176/175, 351/350, 676/675


Mapping: [{{val| 1 0 0 -2 -6 -1 }}, {{val| 0 2 0 9 9 3 }}, {{val| 0 0 1 -1 1 1 }}]
Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}


Vals: {{Val list| 19e, 24, 34d, 53, 58, 111, 280cdf }}
{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cdf }}


Badness: 0.999 × 10<sup>-3</sup>
Badness: 0.999 × 10<sup>-3</sup>


[[Category:Regular temperament theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Cataharry family| ]] <!-- main article -->
[[Category:Cataharry family| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Cataharry_family"