Tree of rank two temperaments: Difference between revisions

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<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>2011-11-~~28 22~~:58:25 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-29 01:03:40 UTC</tt>.<br>

: The original revision id was <tt>~~279974976~~</tt>.<br>

: The original revision id was <tt>280000682</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>

<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">|-15 8 1> [[Helmholtz node|helmholtz]] 4.25910

<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">=The temperament tree=

Using the [[Normal lists|normal comma list]] it is possible to define a [[http://en.wikipedia.org/wiki/Tree_structure|tree]] of temperaments of a given rank. Below is given the top level of a tree for rank two temperaments in the form of a 5-limit monzo, followed by a link to a 7-limit node of the tree. This in turn may be followed, via the hyperlinks, to further nodes in higher prime limits. Temperaments are denoted via names, wedgies, and the normal comma list. The wedgies, for those with the proper software, can be used to do all of the basic regular temperament operations, and their presence allows them to be searched for using the "Search Wiki" function. By putting together the commas in the normal list, Graham Breed's [[http://x31eq.com/temper/|temperament finder]] gives an alternative to wedgies for finding the properties of the temperament. The number at the end of the row is a logflat badness measure (1000 times wedgie badness.) The branches near the top tend to favor the 5-limit part of the temperament in terms of complexity, while those near the bottom tend to favor higher limits after the links are followed to those limits.

=The 5-limit top branches=

|-15 8 1> [[Helmholtz node|helmholtz]] 4.25910

|-4 4 -1> [[Meantone node|meantone]] 7.38134

|-3 -1 2> [[Dicot node|dicot]] 13.02798

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</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"><html><head><title>Tree of rank two temperaments</title></head><body>|-15 8 1&gt; <a class="wiki_link" href="/Helmholtz%20node">helmholtz</a> 4.25910<br />

<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"><html><head><title>Tree of rank two temperaments</title></head><body><h1 id="toc0"><a name="The temperament tree"></a>The temperament tree</h1>

Using the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> it is possible to define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tree_structure" rel="nofollow">tree</a> of temperaments of a given rank. Below is given the top level of a tree for rank two temperaments in the form of a 5-limit monzo, followed by a link to a 7-limit node of the tree. This in turn may be followed, via the hyperlinks, to further nodes in higher prime limits. Temperaments are denoted via names, wedgies, and the normal comma list. The wedgies, for those with the proper software, can be used to do all of the basic regular temperament operations, and their presence allows them to be searched for using the &quot;Search Wiki&quot; function. By putting together the commas in the normal list, Graham Breed's <a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow">temperament finder</a> gives an alternative to wedgies for finding the properties of the temperament. The number at the end of the row is a logflat badness measure (1000 times wedgie badness.) The branches near the top tend to favor the 5-limit part of the temperament in terms of complexity, while those near the bottom tend to favor higher limits after the links are followed to those limits.<br />

<br />

<h1 id="toc1"><a name="The 5-limit top branches"></a>The 5-limit top branches</h1>

|-15 8 1&gt; <a class="wiki_link" href="/Helmholtz%20node">helmholtz</a> 4.25910<br />

|-4 4 -1&gt; <a class="wiki_link" href="/Meantone%20node">meantone</a> 7.38134<br />

|-3 -1 2&gt; <a class="wiki_link" href="/Dicot%20node">dicot</a> 13.02798<br />

@@ 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>2011-11-28 22:58:25 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-29 01:03:40 UTC</tt>.<br>
-: The original revision id was <tt>279974976</tt>.<br>
+: The original revision id was <tt>280000682</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>
 <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">|-15 8 1&gt; [[Helmholtz node|helmholtz]] 4.25910
+<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">=The temperament tree=
+Using the [[Normal lists|normal comma list]] it is possible to define a [[http://en.wikipedia.org/wiki/Tree_structure|tree]] of temperaments of a given rank. Below is given the top level of a tree for rank two temperaments in the form of a 5-limit monzo, followed by a link to a 7-limit node of the tree. This in turn may be followed, via the hyperlinks, to further nodes in higher prime limits. Temperaments are denoted via names, wedgies, and the normal comma list. The wedgies, for those with the proper software, can be used to do all of the basic regular temperament operations, and their presence allows them to be searched for using the "Search Wiki" function. By putting together the commas in the normal list, Graham Breed's [[http://x31eq.com/temper/|temperament finder]] gives an alternative to wedgies for finding the properties of the temperament. The number at the end of the row is a logflat badness measure (1000 times wedgie badness.) The branches near the top tend to favor the 5-limit part of the temperament in terms of complexity, while those near the bottom tend to favor higher limits after the links are followed to those limits.
+=The 5-limit top branches=
+|-15 8 1&gt; [[Helmholtz node|helmholtz]] 4.25910
 |-4 4 -1&gt; [[Meantone node|meantone]] 7.38134
 |-3 -1 2&gt; [[Dicot node|dicot]] 13.02798
@@ Line 68: / Line 72: @@
 </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;Tree of rank two temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;|-15 8 1&amp;gt; &lt;a class="wiki_link" href="/Helmholtz%20node"&gt;helmholtz&lt;/a&gt; 4.25910&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;Tree of rank two temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="The temperament tree"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;The temperament tree&lt;/h1&gt;
+Using the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; it is possible to define a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tree_structure" rel="nofollow"&gt;tree&lt;/a&gt; of temperaments of a given rank. Below is given the top level of a tree for rank two temperaments in the form of a 5-limit monzo, followed by a link to a 7-limit node of the tree. This in turn may be followed, via the hyperlinks, to further nodes in higher prime limits. Temperaments are denoted via names, wedgies, and the normal comma list. The wedgies, for those with the proper software, can be used to do all of the basic regular temperament operations, and their presence allows them to be searched for using the &amp;quot;Search Wiki&amp;quot; function. By putting together the commas in the normal list, Graham Breed's &lt;a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow"&gt;temperament finder&lt;/a&gt; gives an alternative to wedgies for finding the properties of the temperament. The number at the end of the row is a logflat badness measure (1000 times wedgie badness.) The branches near the top tend to favor the 5-limit part of the temperament in terms of complexity, while those near the bottom tend to favor higher limits after the links are followed to those limits.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="The 5-limit top branches"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;The 5-limit top branches&lt;/h1&gt;
+|-15 8 1&amp;gt; &lt;a class="wiki_link" href="/Helmholtz%20node"&gt;helmholtz&lt;/a&gt; 4.25910&lt;br /&gt;
 |-4 4 -1&amp;gt; &lt;a class="wiki_link" href="/Meantone%20node"&gt;meantone&lt;/a&gt; 7.38134&lt;br /&gt;
 |-3 -1 2&amp;gt; &lt;a class="wiki_link" href="/Dicot%20node"&gt;dicot&lt;/a&gt; 13.02798&lt;br /&gt;