Porwell family
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The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125. Comma: 6144/6125 7 and 9 limit minimax [|1 0 0 0>, |0 1 0 0>, |11/5 1/5 2/5 -2/5>, |11/5 1/5 -3/5 3/5>] Eigenmonzos: 4/3, 7/5 Map: [<1 0 1 4|, <0 1 1 -1|, <0 0 -2 3|] Generators: 2, 3, 35/32 Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130, 229, 412 Badness: 0.000142 [[Projection pair]]s: 3 6125/2048 to 2.5.7 ==Zeus== Commas: 121/120, 176/175 Minimax tuning [|1 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0>, |22/9 2/9 1/3 -4/9 0>, |22/9 2/9 -2/3 5/9 0>, |10/3 2/3 0 -1/3 0>] Eigenmonzos: 2, 9/7, 7/5 Lattice basis: 11/10, 11/8 Map to lattice: [<0 1 -1 2 0|, <0 1 1 -1 1|] Angle(11/10, 11/8) = 87.464 degrees Map: [<1 0 1 4 2|, <0 1 1 -1 1|, <0 0 -2 3 1|] Generators: 2, 3, 11/10 EDOs: 6, 7, 9, 15, 22, 31, 46, 53, 68, 77, 99 Badness: 0.000400 Zeus11[22] [[Hobbits|hobbit]] [[transversal]] 33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3, 11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4, 11/6, 15/8, 64/33, 2 Zeus11[24] hobbit transversal 33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3, 11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9, 11/6, 15/8, 64/33, 2 ===Tridecimal Zeus=== Commas: 121/120, 176/175, 351/350 13-limit minimax [|1 0 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0 0>, |22/9 2/9 1/3 -4/9 0 0>, |22/9 2/9 -2/3 5/9 0 0>, |10/3 2/3 0 -1/3 0 0>, |14/3 -8/3 1 1/3 0 0>] Eigenmonzos: 2, 9/7, 7/5 15-limit minimax [|1 0 0 0 0 0>, |0 1 0 0 0 0>, |11/5 1/5 2/5 -2/5 0 0>,|11/5 1/5 -3/5 3/5 0 0>, |13/5 3/5 1/5 -1/5 0 0>, |38/5 -12/5 1/5 -1/5 0 0>] Eigenmonzos: 2, 4/3, 7/5 Lattice basis: 11/10 length 0.7898 11/8 length 1.002 Angle(11/10, 11/8) = 106.7439 degrees Map to lattice: [<0 1 -1 2 0 -3|, <0 1 1 -1 1 -2|] Map: [<1 0 1 4 2 7|, <0 1 1 -1 1 -2|, <0 0 -2 3 -1 -1|] Generators: 2, 3, 11/10 Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130, 229, 282, 381, 412 Badness: 0.000934 Zeus13[22] hobbit transversal 260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2 ===Tinia=== Commas: 66/65, 121/120, 176/175 Map: [<1 0 1 4 2 2|, <0 1 1 -1 1 1|, <0 0 -2 3 -1 -1|] EDOs: 7, 9, 15, 24, 31 Badness: 0.000808 ==Jupiter== Commas: 540/539, 5632/5625 Map: [<1 0 1 4 -5|, <0 1 1 -1 6|, <0 0 2 -3 8|] EDOs: 9, 22, 31, 53, 108, 121, 130, 152, 282 Badness: 0.000562
Original HTML content:
<html><head><title>Porwell family</title></head><body>The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.<br /> <br /> Comma: 6144/6125<br /> <br /> 7 and 9 limit minimax<br /> [|1 0 0 0>, |0 1 0 0>, |11/5 1/5 2/5 -2/5>, <br /> |11/5 1/5 -3/5 3/5>]<br /> Eigenmonzos: 4/3, 7/5<br /> <br /> Map: [<1 0 1 4|, <0 1 1 -1|, <0 0 -2 3|]<br /> Generators: 2, 3, 35/32<br /> Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130, 229, 412<br /> Badness: 0.000142<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 3 6125/2048 to 2.5.7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Zeus"></a><!-- ws:end:WikiTextHeadingRule:0 -->Zeus</h2> Commas: 121/120, 176/175<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0>, <br /> |22/9 2/9 1/3 -4/9 0>, |22/9 2/9 -2/3 5/9 0>, <br /> |10/3 2/3 0 -1/3 0>]<br /> Eigenmonzos: 2, 9/7, 7/5<br /> <br /> Lattice basis: 11/10, 11/8<br /> Map to lattice: [<0 1 -1 2 0|, <0 1 1 -1 1|]<br /> Angle(11/10, 11/8) = 87.464 degrees<br /> <br /> Map: [<1 0 1 4 2|, <0 1 1 -1 1|, <0 0 -2 3 1|]<br /> Generators: 2, 3, 11/10<br /> EDOs: 6, 7, 9, 15, 22, 31, 46, 53, 68, 77, 99<br /> Badness: 0.000400<br /> <br /> Zeus11[22] <a class="wiki_link" href="/Hobbits">hobbit</a> <a class="wiki_link" href="/transversal">transversal</a><br /> 33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3, <br /> 11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4, <br /> 11/6, 15/8, 64/33, 2<br /> Zeus11[24] hobbit transversal<br /> 33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,<br /> 11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9, <br /> 11/6, 15/8, 64/33, 2<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Zeus-Tridecimal Zeus"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tridecimal Zeus</h3> Commas: 121/120, 176/175, 351/350<br /> <br /> 13-limit minimax<br /> [|1 0 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0 0>, <br /> |22/9 2/9 1/3 -4/9 0 0>, |22/9 2/9 -2/3 5/9 0 0>, <br /> |10/3 2/3 0 -1/3 0 0>, |14/3 -8/3 1 1/3 0 0>]<br /> Eigenmonzos: 2, 9/7, 7/5<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |0 1 0 0 0 0>, <br /> |11/5 1/5 2/5 -2/5 0 0>,|11/5 1/5 -3/5 3/5 0 0>, <br /> |13/5 3/5 1/5 -1/5 0 0>, |38/5 -12/5 1/5 -1/5 0 0>]<br /> Eigenmonzos: 2, 4/3, 7/5<br /> <br /> Lattice basis: 11/10 length 0.7898 11/8 length 1.002<br /> Angle(11/10, 11/8) = 106.7439 degrees<br /> Map to lattice: [<0 1 -1 2 0 -3|, <0 1 1 -1 1 -2|]<br /> <br /> Map: [<1 0 1 4 2 7|, <0 1 1 -1 1 -2|, <0 0 -2 3 -1 -1|]<br /> Generators: 2, 3, 11/10<br /> Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130, 229, 282, 381, 412<br /> Badness: 0.000934<br /> <br /> Zeus13[22] hobbit transversal<br /> 260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Zeus-Tinia"></a><!-- ws:end:WikiTextHeadingRule:4 -->Tinia</h3> Commas: 66/65, 121/120, 176/175<br /> <br /> Map: [<1 0 1 4 2 2|, <0 1 1 -1 1 1|, <0 0 -2 3 -1 -1|]<br /> EDOs: 7, 9, 15, 24, 31<br /> Badness: 0.000808<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Jupiter"></a><!-- ws:end:WikiTextHeadingRule:6 -->Jupiter</h2> Commas: 540/539, 5632/5625<br /> <br /> Map: [<1 0 1 4 -5|, <0 1 1 -1 6|, <0 0 2 -3 8|]<br /> EDOs: 9, 22, 31, 53, 108, 121, 130, 152, 282<br /> Badness: 0.000562</body></html>