Bug family: Difference between revisions

Revision as of 00:04, 6 January 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-01-06 00:04:11 UTC.

The original revision id was 191305922.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or one step of [[9edo]]. The monzo for 27/25 is |0 3 -2>, the dual of which is <<2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.

Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the [[Ragismic microtemperaments|ennealimmal]] tempering is, we can reconstruct 7-limit JI.

==Bug==
Comma: 27/25

[[POTE tuning|POTE temperament]]: 260.388

Map: [<1 0 0|, <0 2 3|]
EDOs: 4, 5, 9, 14, 23, 106
Badness: 0.0328

==Beep==
Commas: 21/20, 27/25

[[POTE tuning|POTE temperament]]: 263.395

Map: [<1 0 0 2|, <0 2 3 1|]
Wedgie: <<2 3 1 0 -4 -6||
EDOs: 4, 5, 9, 32, 41
Badness: 0.0186

===Pentoid===
Commas: 21/20, 27/25, 99/98

[[POTE tuning|POTE temperament]]: 264.312

Map: [<1 0 0 2 5|, <0 2 3 1 -2|]
EDOs: 4, 5, 9, 50, 59
Badness: 0.0226

Original HTML content:

<html><head><title>Bug family</title></head><body>The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or one step of <a class="wiki_link" href="/9edo">9edo</a>. The monzo for 27/25 is |0 3 -2&gt;, the dual of which is &lt;&lt;2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;5 temperament, and <a class="wiki_link" href="/14edo">14edo</a> is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.<br />
<br />
Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the <a class="wiki_link" href="/Ragismic%20microtemperaments">ennealimmal</a> tempering is, we can reconstruct 7-limit JI.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Bug"></a><!-- ws:end:WikiTextHeadingRule:0 -->Bug</h2>
Comma: 27/25<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 260.388<br />
<br />
Map: [&lt;1 0 0|, &lt;0 2 3|]<br />
EDOs: 4, 5, 9, 14, 23, 106<br />
Badness: 0.0328<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Beep"></a><!-- ws:end:WikiTextHeadingRule:2 -->Beep</h2>
Commas: 21/20, 27/25<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.395<br />
<br />
Map: [&lt;1 0 0 2|, &lt;0 2 3 1|]<br />
Wedgie: &lt;&lt;2 3 1 0 -4 -6||<br />
EDOs: 4, 5, 9, 32, 41<br />
Badness: 0.0186<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Beep-Pentoid"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentoid</h3>
Commas: 21/20, 27/25, 99/98<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 264.312<br />
<br />
Map: [&lt;1 0 0 2 5|, &lt;0 2 3 1 -2|]<br />
EDOs: 4, 5, 9, 50, 59<br />
Badness: 0.0226</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>2010-12-29 17:38:31 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-06 00:04:11 UTC</tt>.<br>
-: The original revision id was <tt>190234182</tt>.<br>
+: The original revision id was <tt>191305922</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 17: / Line 17: @@
 Map: [&lt;1 0 0|, &lt;0 2 3|]
 EDOs: 4, 5, 9, 14, 23, 106
+Badness: 0.0328
 ==Beep==
@@ Line 23: / Line 24: @@
 [[POTE tuning|POTE temperament]]: 263.395
-Map: [&lt;1 0 02 2|, &lt;0 2 3 1|]
+Map: [&lt;1 0 0 2|, &lt;0 2 3 1|]
 Wedgie: &lt;&lt;2 3 1 0 -4 -6||
 EDOs: 4, 5, 9, 32, 41
+Badness: 0.0186
+===Pentoid===
+Commas: 21/20, 27/25, 99/98
+[[POTE tuning|POTE temperament]]: 264.312
+Map: [&lt;1 0 0 2 5|, &lt;0 2 3 1 -2|]
+EDOs: 4, 5, 9, 50, 59
+Badness: 0.0226
 </pre></div>
 <h4>Original HTML content:</h4>
@@ Line 40: / Line 50: @@
 Map: [&amp;lt;1 0 0|, &amp;lt;0 2 3|]&lt;br /&gt;
 EDOs: 4, 5, 9, 14, 23, 106&lt;br /&gt;
+Badness: 0.0328&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Beep"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Beep&lt;/h2&gt;
@@ Line 46: / Line 57: @@
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.395&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 0 02 2|, &amp;lt;0 2 3 1|]&lt;br /&gt;
+Map: [&amp;lt;1 0 0 2|, &amp;lt;0 2 3 1|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;2 3 1 0 -4 -6||&lt;br /&gt;
-EDOs: 4, 5, 9, 32, 41&lt;/body&gt;&lt;/html&gt;</pre></div>
+EDOs: 4, 5, 9, 32, 41&lt;br /&gt;
+Badness: 0.0186&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Beep-Pentoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pentoid&lt;/h3&gt;
+Commas: 21/20, 27/25, 99/98&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 264.312&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 0 2 5|, &amp;lt;0 2 3 1 -2|]&lt;br /&gt;
+EDOs: 4, 5, 9, 50, 59&lt;br /&gt;
+Badness: 0.0226&lt;/body&gt;&lt;/html&gt;</pre></div>

Bug family: Difference between revisions

Revision as of 00:04, 6 January 2011

IMPORTED REVISION FROM WIKISPACES

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