Cataharry family
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[[toc]] The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600. Comma: 19683/19600 7 and 9 limit minimax [|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 Map: [<1 0 0 -2|, <0 2 0 9|, <0 0 1 -1|] Generators: 2, 140/81, 5 Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717 [[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7 =Albus= Commas: 540/539, 8019/8000 Minimax tuning [|1 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3>, |5 0 7/2 -2 -3/2>, |5 0 5/2 -1 -3/2>, |5 0 5/2 -2 -1/2>] Eigenmonzos: 2, 11/10, 7/5 Map: [<1 0 0 -2 6|, <0 2 0 9 -12|, <0 0 1 -1 3|] Generators: 2, 140/81, 5 Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640 Badness: 0.000621 ==Madagascar== Commas: 351/350, 540/539, 676/675 13 and 15 limit minimax [|1 0 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3 0>, |5 0 7/2 -2 -3/2 0>, |5 0 5/2 -1 -3/2 0>, |5 0 5/2 -2 -1/2 0>, |8 0 11/2 -3 -5/2 0>] Eigenmonzos: 2, 11/10, 7/5 Lattice basis: 15/13 0.3019 26/25 0.9477 Angle(15/13, 26/25) = 81.6476 Map to lattice: [<0 -2 -3 -6 3 -6|, <0 0 -1 1 -3 -1|] Map: [<1 0 0 -2 6 -1|, <0 2 0 9 -12 3|, <0 0 1 -1 3 1|] Generators: 2, 26/15, 5 Edos: 19, 53, 58, 72, 111, 130, 183, 313 Badness: 0.000560 [[Spectrum of a temperament|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 Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3 [[madagascar19]] =Snape= Commas: 19683/19600, 441/440 ==13-limit== Commas: 351/350, 441/440, 729/728 =Hagrid= Commas: 243/242, 9801/9800 ==13-limit== Commas: 243/242, 351/350, 729/728 =Draco= Commas: 19683/19600, 176/175 Map: [<1 0 0 -2 -6|, <0 2 0 9 9|, <0 0 1 -1 1|] EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd Badness: 0.001934 ==13-limit== Commas: 176/175, 351/350, 676/675 Map: [<1 0 0 -2 -6 -1|, <0 2 0 9 9 3|, <0 0 1 -1 1 1|] EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf Badness: 0.000999
Original HTML content:
<html><head><title>Cataharry family</title></head><body><!-- ws:start:WikiTextTocRule:16:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 1em;"><a href="#Albus">Albus</a></div> <!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 2em;"><a href="#Albus-Madagascar">Madagascar</a></div> <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 1em;"><a href="#Snape">Snape</a></div> <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 2em;"><a href="#Snape-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 1em;"><a href="#Hagrid">Hagrid</a></div> <!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 2em;"><a href="#Hagrid-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#Draco">Draco</a></div> <!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#Draco-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --></div> <!-- ws:end:WikiTextTocRule:25 --><br /> The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.<br /> <br /> Comma: 19683/19600<br /> <br /> 7 and 9 limit minimax<br /> [|1 0 0 0>, |4/9 0 2/9 2/9>, <br /> |0 0 1 0>, |0 0 0 1>]<br /> Eigenmonzos: 2, 8/7, 5/4<br /> <br /> Map: [<1 0 0 -2|, <0 2 0 9|, <0 0 1 -1|]<br /> Generators: 2, 140/81, 5<br /> Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Albus"></a><!-- ws:end:WikiTextHeadingRule:0 -->Albus</h1> Commas: 540/539, 8019/8000<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3>, <br /> |5 0 7/2 -2 -3/2>, |5 0 5/2 -1 -3/2>, <br /> |5 0 5/2 -2 -1/2>]<br /> Eigenmonzos: 2, 11/10, 7/5<br /> <br /> Map: [<1 0 0 -2 6|, <0 2 0 9 -12|, <0 0 1 -1 3|]<br /> Generators: 2, 140/81, 5<br /> Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640<br /> Badness: 0.000621<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Albus-Madagascar"></a><!-- ws:end:WikiTextHeadingRule:2 -->Madagascar</h2> Commas: 351/350, 540/539, 676/675<br /> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3 0>, <br /> |5 0 7/2 -2 -3/2 0>, |5 0 5/2 -1 -3/2 0>, <br /> |5 0 5/2 -2 -1/2 0>, |8 0 11/2 -3 -5/2 0>]<br /> Eigenmonzos: 2, 11/10, 7/5<br /> <br /> Lattice basis: 15/13 0.3019 26/25 0.9477<br /> Angle(15/13, 26/25) = 81.6476<br /> Map to lattice: [<0 -2 -3 -6 3 -6|, <0 0 -1 1 -3 -1|]<br /> <br /> Map: [<1 0 0 -2 6 -1|, <0 2 0 9 -12 3|, <0 0 1 -1 3 1|]<br /> Generators: 2, 26/15, 5<br /> Edos: 19, 53, 58, 72, 111, 130, 183, 313<br /> Badness: 0.000560<br /> <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 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<br /> <br /> Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3<br /> <br /> <a class="wiki_link" href="/madagascar19">madagascar19</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Snape"></a><!-- ws:end:WikiTextHeadingRule:4 -->Snape</h1> Commas: 19683/19600, 441/440<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Snape-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 351/350, 441/440, 729/728<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Hagrid"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hagrid</h1> Commas: 243/242, 9801/9800<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Hagrid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h2> Commas: 243/242, 351/350, 729/728<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Draco"></a><!-- ws:end:WikiTextHeadingRule:12 -->Draco</h1> Commas: 19683/19600, 176/175<br /> <br /> Map: [<1 0 0 -2 -6|, <0 2 0 9 9|, <0 0 1 -1 1|]<br /> EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd<br /> Badness: 0.001934<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Draco-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> Commas: 176/175, 351/350, 676/675<br /> <br /> Map: [<1 0 0 -2 -6 -1|, <0 2 0 9 9 3|, <0 0 1 -1 1 1|]<br /> EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf<br /> Badness: 0.000999</body></html>