Cangwu badness: 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2013~~-11-~~12 03~~:24:40 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-18 14:09:32 UTC</tt>.<br>

: The original revision id was <tt>~~468224298~~</tt>.<br>

: The original revision id was <tt>509656698</tt>.<br>

: The revision comment was: <tt>~~backlink to badness node~~</tt><br>

: The revision comment was: <tt></tt><br>

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<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">//Cangwu badness// is a polynomial function [[badness]] measure; the name stems from Cangwu Green Park, Lianyungang, China, where [[Graham Breed]] thought it up. It is defined in terms of a matrix determinant as

[[image:mathhazard.jpg align="center"]]

//Cangwu badness// is a polynomial function [[badness]] measure; the name stems from Cangwu Green Park, Lianyungang, China, where [[Graham Breed]] thought it up. It is defined in terms of a matrix determinant as

[[math]]

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Some 7-limit examples are beep, meantone, miracle, pontiac and ennealimmal.

If two temperaments of the same rank are such that neither dominants the other, we may subtract one Cangwu badness polynomial from the other and find the positive root of the result. This gives a value of the parameter 'x' at which the two temperaments are rated equal in badness, which can be applied to rate other temperaments by badness. For example, if 5-limit father and helmholtz are made equally bad, then meantone, augmented, dicot, porcupine, srutal, diminished, magic, hanson and mavila, in that order, rate as better.

If two temperaments of the same rank are such that neither dominants the other, we may subtract one Cangwu badness polynomial from the other and find the positive root of the result. This gives a value of the parameter 'x' at which the two temperaments are rated equal in badness, which can be applied to rate other temperaments by badness. For example, if 5-limit father and helmholtz are made equally bad, then meantone, augmented, dicot, porcupine, srutal, diminished, magic, hanson and mavila, in that order, rate as better.</pre></div>

</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>Cangwu badness</title></head><body><em>Cangwu badness</em> is a polynomial function <a class="wiki_link" href="/badness">badness</a> measure; the name stems from Cangwu Green Park, Lianyungang, China, where <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a> thought it up. It is defined in terms of a matrix determinant as<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>Cangwu badness</title></head><body><br />

<div style="text-align: center"><img src="/file/view/mathhazard.jpg" alt="mathhazard.jpg" title="mathhazard.jpg" /></div><em>Cangwu badness</em> is a polynomial function <a class="wiki_link" href="/badness">badness</a> measure; the name stems from Cangwu Green Park, Lianyungang, China, where <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a> thought it up. It is defined in terms of a matrix determinant as<br />

<br />

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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:xenwolf|xenwolf]] and made on <tt>2013-11-12 03:24:40 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-18 14:09:32 UTC</tt>.<br>
-: The original revision id was <tt>468224298</tt>.<br>
+: The original revision id was <tt>509656698</tt>.<br>
-: The revision comment was: <tt>backlink to badness node</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">//Cangwu badness// is a polynomial function [[badness]] measure; the name stems from Cangwu Green Park, Lianyungang, China, where [[Graham Breed]] thought it up. It is defined in terms of a matrix determinant as
+<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">
+[[image:mathhazard.jpg align="center"]]
+//Cangwu badness// is a polynomial function [[badness]] measure; the name stems from Cangwu Green Park, Lianyungang, China, where [[Graham Breed]] thought it up. It is defined in terms of a matrix determinant as
 [[math]]
@@ Line 36: / Line 38: @@
 Some 7-limit examples are beep, meantone, miracle, pontiac and ennealimmal.
-If two temperaments of the same rank are such that neither dominants the other, we may subtract one Cangwu badness polynomial from the other and find the positive root of the result. This gives a value of the parameter 'x' at which the two temperaments are rated equal in badness, which can be applied to rate other temperaments by badness. For example, if 5-limit father and helmholtz are made equally bad, then meantone, augmented, dicot, porcupine, srutal, diminished, magic, hanson and mavila, in that order, rate as better.
+If two temperaments of the same rank are such that neither dominants the other, we may subtract one Cangwu badness polynomial from the other and find the positive root of the result. This gives a value of the parameter 'x' at which the two temperaments are rated equal in badness, which can be applied to rate other temperaments by badness. For example, if 5-limit father and helmholtz are made equally bad, then meantone, augmented, dicot, porcupine, srutal, diminished, magic, hanson and mavila, in that order, rate as better.</pre></div>
-</pre></div>
 <h4>Original HTML content:</h4>
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+<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;Cangwu badness&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
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