Tenney norm: Difference between revisions

Wikispaces>xenwolf
**Imported revision 238544007 - Original comment: **
Wikispaces>xenwolf
**Imported revision 238544727 - 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>2011-06-24 04:53:25 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-24 05:03:05 UTC</tt>.<br>
: The original revision id was <tt>238544007</tt>.<br>
: The original revision id was <tt>238544727</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">If p/q is a positive rational number reduced to its lowest terms, then the **Tenney height**, named for [[James Tenney]] who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 ([[log2]]), of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals.
<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">If p/q is a positive rational number reduced to its lowest terms, then the **Tenney height**, named for [[James Tenney]] who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 ([[log2]]), of the height. In either form it is widely used as a [[measure of inharmonicity]] and/or complexity for intervals.


The [[Tenney Height|Tenney height]] of a [[monzo]] is given by
The [[Tenney Height|Tenney height]] of a [[monzo]] is given by
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<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;Tenney Height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If p/q is a positive rational number reduced to its lowest terms, then the &lt;strong&gt;Tenney height&lt;/strong&gt;, named for &lt;a class="wiki_link" href="/James%20Tenney"&gt;James Tenney&lt;/a&gt; who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 (&lt;a class="wiki_link" href="/log2"&gt;log2&lt;/a&gt;), of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals.&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;Tenney Height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If p/q is a positive rational number reduced to its lowest terms, then the &lt;strong&gt;Tenney height&lt;/strong&gt;, named for &lt;a class="wiki_link" href="/James%20Tenney"&gt;James Tenney&lt;/a&gt; who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 (&lt;a class="wiki_link" href="/log2"&gt;log2&lt;/a&gt;), of the height. In either form it is widely used as a &lt;a class="wiki_link" href="/measure%20of%20inharmonicity"&gt;measure of inharmonicity&lt;/a&gt; and/or complexity for intervals.&lt;br /&gt;
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The &lt;a class="wiki_link" href="/Tenney%20Height"&gt;Tenney height&lt;/a&gt; of a &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is given by&lt;br /&gt;
The &lt;a class="wiki_link" href="/Tenney%20Height"&gt;Tenney height&lt;/a&gt; of a &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is given by&lt;br /&gt;
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&lt;em&gt;see also discussion on &lt;!-- ws:start:WikiTextUrlRule:100:http://lumma.org/music/theory/TuningFAQ.txt --&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/TuningFAQ.txt" rel="nofollow"&gt;http://lumma.org/music/theory/TuningFAQ.txt&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:100 --&gt; section CONSONANCE AND DISSONANCE&lt;/em&gt; &lt;strong&gt;&amp;lt;-- Error 404 - File not Found&lt;/strong&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;em&gt;see also discussion on &lt;!-- ws:start:WikiTextUrlRule:101:http://lumma.org/music/theory/TuningFAQ.txt --&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/TuningFAQ.txt" rel="nofollow"&gt;http://lumma.org/music/theory/TuningFAQ.txt&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:101 --&gt; section CONSONANCE AND DISSONANCE&lt;/em&gt; &lt;strong&gt;&amp;lt;-- Error 404 - File not Found&lt;/strong&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>