Cataharry family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''cataharry family''' of [[ | The '''cataharry family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[cataharry comma]] ({{monzo| -4 9 -2 -2 }}, [[ratio]]: 19683/19600). | ||
== Cataharry == | == Cataharry == | ||
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{{Mapping|legend=1| 1 0 0 -2 | 0 2 0 9 | 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 | ||
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{{Optimal ET sequence|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]] (Smith): 0.301 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7 | [[Projection pair]]s: <code>3 19600/6561 7 1033052339200000000/150094635296999121</code> to 2.5.81/7 | ||
== Albus == | == Albus == | ||
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{{Mapping|legend=1| 1 0 0 -2 6 | 0 2 0 9 -12 | 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 | ||
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{{Optimal ET sequence|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]] (Smith): 0.621 × 10<sup>-3</sup> | ||
=== Madagascar === | === Madagascar === | ||
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: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5 | : unchanged-interval (eigenmonzo) basis: 2.7/5.11/5 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }} | ||
Badness: 0.560 × 10<sup>-3</sup> | Badness (Smith): 0.560 × 10<sup>-3</sup> | ||
Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11 | Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11 | ||
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{{Optimal ET sequence|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]] (Smith): 0.988 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 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 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }} | ||
Badness: 0.786 × 10<sup>-3</sup> | Badness (Smith): 0.786 × 10<sup>-3</sup> | ||
== Hagrid == | == Hagrid == | ||
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{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 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 | ||
{{Optimal ET sequence|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]] (Smith): 1.116 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 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 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 24, 34d, 58, 72, 130 }} | ||
Badness: 0.876 × 10<sup>-3</sup> | Badness (Smith): 0.876 × 10<sup>-3</sup> | ||
== Draco == | == Draco == | ||
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{{Optimal ET sequence|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]] (Smith): 1.934 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 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 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19e, 24, 34d, 53, 58, 111, 280cdf }} | ||
Badness: 0.999 × 10<sup>-3</sup> | Badness (Smith): 0.999 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Cataharry family| ]] <!-- main article --> | [[Category:Cataharry family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||