Gamelismic family: Difference between revisions

Revision as of 16:40, 3 September 2010

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2010-09-03 16:40:07 UTC.

The original revision id was 160308089.

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Original Wikitext content:

//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|] 
EDOs: 118, 159

==11-limit temperaments==

===Prodigy===
Prodigy has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440. 

Commas c = 1029/1024, e = 385/384
Minimax:  3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat
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|]
EDOs 118, 159

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:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3>
Comma c = 1029/1024<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: &lt;1200.486 1901.833 2786.314 3367.676|<br />
Minkowski lattice basis: 8/7 length 0.5192, 5/4 length = log2(5)<br />
angle(8/7, 5/4) = 90 degrees<br />
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|] <br />
EDOs: 118, 159<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-11-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit temperaments</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-11-limit temperaments-Prodigy"></a><!-- ws:end:WikiTextHeadingRule:4 -->Prodigy</h3>
Prodigy 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 />
Commas c = 1029/1024, e = 385/384<br />
Minimax:  3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat<br />
Minkowski lattice basis: <br />
8/7 length 0.46467, 12/11 length 1.931<br />
angle(8/7, 12/11) = 86.657 degrees<br />
Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]<br />
EDOs 118, 159</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-03 15:19:10 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-03 16:40:07 UTC</tt>.<br>
-: The original revision id was <tt>160294287</tt>.<br>
+: The original revision id was <tt>160308089</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>
@@ Line 21: / Line 21: @@
 ===Prodigy===
-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>
+Prodigy has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
+Commas c = 1029/1024, e = 385/384
+Minimax:  3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat
+Minkowski lattice basis:
+/7 length 0.46467, 12/11 length 1.931
+angle(8/7, 12/11) = 86.657 degrees
+Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]
+EDOs 118, 159</pre></div>
 <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="/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;
@@ Line 38: / Line 46: @@
 &lt;br /&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 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>
+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. &lt;br /&gt;
+&lt;br /&gt;
+Commas c = 1029/1024, e = 385/384&lt;br /&gt;
+Minimax:  3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat&lt;br /&gt;
+Minkowski lattice basis: &lt;br /&gt;
+/7 length 0.46467, 12/11 length 1.931&lt;br /&gt;
+angle(8/7, 12/11) = 86.657 degrees&lt;br /&gt;
+Map to lattice: [&amp;lt;0 3 1 -1 3|, &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
+EDOs 118, 159&lt;/body&gt;&lt;/html&gt;</pre></div>

Gamelismic family: Difference between revisions

Revision as of 16:40, 3 September 2010

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