Gamelismic family
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[[toc|flat]] =Gamelan= //Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024. [[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|] Map: [<1 1 0 3|, <0 3 0 -1|,<0 0 1 0|] [[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, 118, [[118edo|118]], [[159edo|159]], 190 Badness: 0.000176 [[Projection pair]]: 3 1024/343 to 2.5.7 =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 Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190 Badness: 0.000234 Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7 ==Portending== Commas: 325/324, 364/363, 441/440 Map: [<1 1 0 3 5 6|, <0 3 0 -1 4 12| <0 0 1 0 -1 -2|] EDOs: 15, 26, 41, 46, 72, 87, 159 Badness: 0.000627 ==Portentous== Commas: 385/384, 441/440, 625/624 Map: [<1 1 0 3 5 -5|, <0 3 0 -1 4 -3| <0 0 1 0 -1 4|] EDOs: 15, 31, 56, 72, 87, 103, 159, 190 Badness: 0.000662 ==Ominous== Commas: 351/350, 385/384, 441/440 Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 -10| <0 0 1 0 -1 2|] EDOs: 26, 31, 46, 72, 103, 149 Badness: 0.000751 ===17-limit=== Commas: 273/272, 351/350, 441/440, 561/560 Minimax tuning [|1 0 0 0 0 0 0>, |7/4 9/10 0 0 -3/10 -3/20 0>, |5/2 7/5 0 0 -4/5 1/10 0>, |11/4 -3/10 0 0 1/10 1/20 0>, |7/2 -1/5 0 0 2/5 -3/10 0>, |7/2 -1/5 0 0 -3/5 7/10 0>, |4 2/5 0 0 -4/5 3/5 0>] Eigenmonzos: 2, 13/11, 11/9 Lattice basis: 8/7 0.3859 6/5 1.1303 Angle(8/7, 6/5) = 98.6015 Map to lattice: [<0 1 1 0 0 -1 0|, <0 -1 -1 0 -1 2 1|] Map: [<1 1 0 3 5 1 1|, <0 3 0 -1 4 -10 -8|, <0 0 1 0 -1 2 2|] Generators: 2, 8/7, 5 EDOs: 26, 31, 46, 72, 103, 149 Badness: 0.000612 ==Momentous== Commas: 196/195, 352/351, 385/384 Map: [<1 1 0 3 5 7|, <0 3 0 -4 1 -5|, <0 0 1 0 -1 -1|] EDOs: 10, 31, 41, 46, 77, 87, 118, 164 Badness: 0.000832 ==Foreboding== Commas: 105/104, 144/143, 275/273 Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 2|, <0 0 1 0 -1 1|] [[edo|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]] Badness: 0.000873
Original HTML content:
<html><head><title>Gamelismic family</title></head><body><!-- ws:start:WikiTextTocRule:16:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Gamelan">Gamelan</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Portent">Portent</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> <!-- ws:end:WikiTextTocRule:25 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Gamelan"></a><!-- ws:end:WikiTextHeadingRule:0 -->Gamelan</h1> <em>Gamelan 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 /> <br /> <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 /> Map: [<1 1 0 3|, <0 3 0 -1|,<0 0 1 0|]<br /> <a class="wiki_link" href="/edo">EDOs</a>: 5, 10, 15, 26, 31, 41, 72, 118, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, 190<br /> Badness: 0.000176<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 3 1024/343 to 2.5.7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Portent"></a><!-- ws:end:WikiTextHeadingRule:2 -->Portent</h1> 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 /> Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190<br /> Badness: 0.000234<br /> <br /> Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Portent-Portending"></a><!-- ws:end:WikiTextHeadingRule:4 -->Portending</h2> Commas: 325/324, 364/363, 441/440<br /> <br /> Map: [<1 1 0 3 5 6|, <0 3 0 -1 4 12| <0 0 1 0 -1 -2|]<br /> EDOs: 15, 26, 41, 46, 72, 87, 159<br /> Badness: 0.000627<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Portent-Portentous"></a><!-- ws:end:WikiTextHeadingRule:6 -->Portentous</h2> Commas: 385/384, 441/440, 625/624<br /> <br /> Map: [<1 1 0 3 5 -5|, <0 3 0 -1 4 -3| <0 0 1 0 -1 4|]<br /> EDOs: 15, 31, 56, 72, 87, 103, 159, 190<br /> Badness: 0.000662<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Portent-Ominous"></a><!-- ws:end:WikiTextHeadingRule:8 -->Ominous</h2> Commas: 351/350, 385/384, 441/440<br /> <br /> Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 -10| <0 0 1 0 -1 2|]<br /> EDOs: 26, 31, 46, 72, 103, 149<br /> Badness: 0.000751<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Portent-Ominous-17-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->17-limit</h3> Commas: 273/272, 351/350, 441/440, 561/560<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0 0 0>, <br /> |7/4 9/10 0 0 -3/10 -3/20 0>, <br /> |5/2 7/5 0 0 -4/5 1/10 0>, <br /> |11/4 -3/10 0 0 1/10 1/20 0>, <br /> |7/2 -1/5 0 0 2/5 -3/10 0>, <br /> |7/2 -1/5 0 0 -3/5 7/10 0>, <br /> |4 2/5 0 0 -4/5 3/5 0>]<br /> Eigenmonzos: 2, 13/11, 11/9<br /> <br /> Lattice basis: 8/7 0.3859 6/5 1.1303<br /> Angle(8/7, 6/5) = 98.6015<br /> Map to lattice: [<0 1 1 0 0 -1 0|, <0 -1 -1 0 -1 2 1|]<br /> <br /> Map: [<1 1 0 3 5 1 1|, <0 3 0 -1 4 -10 -8|, <br /> <0 0 1 0 -1 2 2|]<br /> Generators: 2, 8/7, 5<br /> EDOs: 26, 31, 46, 72, 103, 149<br /> Badness: 0.000612<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Portent-Momentous"></a><!-- ws:end:WikiTextHeadingRule:12 -->Momentous</h2> Commas: 196/195, 352/351, 385/384<br /> <br /> Map: [<1 1 0 3 5 7|, <0 3 0 -4 1 -5|, <0 0 1 0 -1 -1|]<br /> EDOs: 10, 31, 41, 46, 77, 87, 118, 164<br /> Badness: 0.000832<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Portent-Foreboding"></a><!-- ws:end:WikiTextHeadingRule:14 -->Foreboding</h2> Commas: 105/104, 144/143, 275/273<br /> <br /> Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 2|, <0 0 1 0 -1 1|]<br /> <a class="wiki_link" href="/edo">EDOs</a>: 5, 10, 15, 26, 31, 41, <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><br /> Badness: 0.000873</body></html>