Gamelismic family
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//Gamelismic temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024. ===Vital statistics=== [[Comma]] c = 1029/1024 7-limit minimax tuning: 3, 5, and 7 1/4c flat 9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat TOP-RMS: <1200.486 1901.833 2786.314 3367.676| [[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5) Angle(8/7, 5/4) = 90 degrees Map to lattice: [<0 3 0 -1|, <0 0 1 0|] [[edo|EDOs]]: [[118edo|118]], [[159edo|159]] ==11-limit temperaments== ===Portent=== Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440. [[Comma|Commas]]: c = 1029/1024, e = 385/384 Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |39/14 4/7 1/2 -2/7 -1/2>, |20/7 -2/7 0 1/7 0>, |39/14 4/7 -1/2 -2/7 1/2>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7 [[Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931 Angle(8/7, 12/11) = 86.657 degrees Map to lattice: [<0 3 1 -1 3|, <0 0 1 0 -1|] Map: [<1 1 0 3 5|, <0 3 0 -1 4| <0 0 1 0 -1|] [[Generator|Generators]]: 2, 8/7, 5 [[edo|EDOs]]: [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]]
Original HTML content:
<html><head><title>Gamelismic family</title></head><body><em>Gamelismic temperament</em> is the rank three <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a> tempering out 1029/1024. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3> <a class="wiki_link" href="/Comma">Comma</a> c = 1029/1024<br /> <br /> 7-limit minimax tuning: 3, 5, and 7 1/4c flat<br /> 9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat<br /> TOP-RMS: <1200.486 1901.833 2786.314 3367.676|<br /> <a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.5192, 5/4 length = log2(5)<br /> Angle(8/7, 5/4) = 90 degrees<br /> Map to lattice: [<0 3 0 -1|, <0 0 1 0|] <br /> <br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-11-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit temperaments</h2> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-11-limit temperaments-Portent"></a><!-- ws:end:WikiTextHeadingRule:4 -->Portent</h3> Portent has a <a class="wiki_link" href="/Normal%20lists">normal comma list</a> [1029/1024, 385/384] and also tempers out 441/440. <br /> <br /> <a class="wiki_link" href="/Comma">Commas</a>: c = 1029/1024, e = 385/384<br /> <br /> Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat<br /> [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, <br /> |39/14 4/7 1/2 -2/7 -1/2>,<br /> |20/7 -2/7 0 1/7 0>, <br /> |39/14 4/7 -1/2 -2/7 1/2>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 9/7<br /> <br /> <a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.46467, 12/11 length 1.931<br /> Angle(8/7, 12/11) = 86.657 degrees<br /> Map to lattice: [<0 3 1 -1 3|, <0 0 1 0 -1|]<br /> <br /> Map: [<1 1 0 3 5|, <0 3 0 -1 4| <0 0 1 0 -1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 8/7, 5<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a></body></html>