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Gamelismic family: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 149679259 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 160294287 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-20 06:57:18 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-03 15:19:10 UTC</tt>.<br>
: The original revision id was <tt>149679259</tt>.<br>
: The original revision id was <tt>160294287</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//Gamelismic temperament// is the rank three [[7-limit]] [[temperament]] tempering out 1029/1024. It has a [[Minkowski reduced generator basis]] given by the tempered versions of [8/7, 2, 5] (in that order.) The vals [&lt;0 3 0 -1|, &lt;1 1 0 3|, &lt;0 0 1 0|] map 7-limit just intonation to the three basis elements, which may be tuned to [[118edo]] as [23/118, 118/118, 274/118].
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//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: &lt;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: [&lt;0 3 0 -1|, &lt;0 0 1 0|]  
EDOs: 118, 159


==11-limit temperaments==
==11-limit temperaments==


===Prodigy===
===Prodigy===
Prodigy has normal [[comma]] list [1029/1024, 385/384] and also tempers out 441/440. It has a Minkowski generator basis [2, 8/7, 12/11], which may be mapped from the [[11-limit]] by [&lt;1 1 2 3 3|, &lt;0 3 1 -1 3|,  &lt;0 0 1 0 -1|]. Once again [[118edo]] is a good tuning choice, and [[159edo]] is another one. </pre></div>
Prodigy has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440. It has a Minkowski generator basis [2, 8/7, 12/11], which may be mapped from the [[11-limit]] by [&lt;1 1 2 3 3|, &lt;0 3 1 -1 3|,  &lt;0 0 1 0 -1|]. Once again [[118edo]] is a good tuning choice, and [[159edo]] is another one. </pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gamelismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Gamelismic temperament&lt;/em&gt; is the rank three &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/temperament"&gt;temperament&lt;/a&gt; tempering out 1029/1024. It has a &lt;a class="wiki_link" href="/Minkowski%20reduced%20generator%20basis"&gt;Minkowski reduced generator basis&lt;/a&gt; given by the tempered versions of [8/7, 2, 5] (in that order.) The vals [&amp;lt;0 3 0 -1|, &amp;lt;1 1 0 3|, &amp;lt;0 0 1 0|] map 7-limit just intonation to the three basis elements, which may be tuned to &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; as [23/118, 118/118, 274/118].&lt;br /&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gamelismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Gamelismic temperament&lt;/em&gt; is the rank three &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt; tempering out 1029/1024. &lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h3&gt;
Comma c = 1029/1024&lt;br /&gt;
7-limit minimax tuning: 3, 5, and 7 1/4c flat&lt;br /&gt;
9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat&lt;br /&gt;
TOP-RMS: &amp;lt;1200.486 1901.833 2786.314 3367.676|&lt;br /&gt;
Minkowski lattice basis: 8/7 length 0.5192, 5/4 length = log2(5)&lt;br /&gt;
angle(8/7, 5/4) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 3 0 -1|, &amp;lt;0 0 1 0|] &lt;br /&gt;
EDOs: 118, 159&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-11-limit temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11-limit temperaments&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-11-limit temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit temperaments&lt;/h2&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-11-limit temperaments-Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Prodigy&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-11-limit temperaments-Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Prodigy&lt;/h3&gt;
Prodigy has normal &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; list [1029/1024, 385/384] and also tempers out 441/440. It has a Minkowski generator basis [2, 8/7, 12/11], which may be mapped from the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; by [&amp;lt;1 1 2 3 3|, &amp;lt;0 3 1 -1 3|,  &amp;lt;0 0 1 0 -1|]. Once again &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; is a good tuning choice, and &lt;a class="wiki_link" href="/159edo"&gt;159edo&lt;/a&gt; is another one.&lt;/body&gt;&lt;/html&gt;</pre></div>
Prodigy has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; [1029/1024, 385/384] and also tempers out 441/440. It has a Minkowski generator basis [2, 8/7, 12/11], which may be mapped from the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; by [&amp;lt;1 1 2 3 3|, &amp;lt;0 3 1 -1 3|,  &amp;lt;0 0 1 0 -1|]. Once again &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; is a good tuning choice, and &lt;a class="wiki_link" href="/159edo"&gt;159edo&lt;/a&gt; is another one.&lt;/body&gt;&lt;/html&gt;</pre></div>
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