Tenney norm: Difference between revisions
Wikispaces>xenwolf **Imported revision 249502925 - Original comment: ** |
Wikispaces>guest **Imported revision 249667084 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-08-31 09:26:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>249667084</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> | ||
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[[code]] | [[code]] | ||
==Examples== | ==Examples==|| **interval name** || **frequency ratio** || **ket vector** || **log2 (Benedetti Height)** || | ||
|| **interval name** || **frequency ratio** || **ket vector** || ** | |||
|| prime || 1/1 || |0> || 0 || | || prime || 1/1 || |0> || 0 || | ||
|| octave || 2/1 || |1> || 1 || | || octave || 2/1 || |1> || 1 || | ||
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The name //Tenney height// stems from the fact that [[James Tenney]] proposed it. The //Benedetti height//, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician [[http://www.webcitation.org/6076Lm8r4|Giovanni Battista Benedetti]]. | The name //Tenney height// stems from the fact that [[James Tenney]] proposed it. The //Benedetti height//, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician [[http://www.webcitation.org/6076Lm8r4|Giovanni Battista Benedetti]]. | ||
//See also, discussion at http://lumma.org/tuning/faq/#heights// </pre></div> | //See also, discussion at http://lumma.org/tuning/faq/#heights//</pre></div> | ||
<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"><html><head><title>Tenney Height</title></head><body>If p/q is a positive rational number reduced to its lowest terms, then the <a class="wiki_link" href="/Benedetti%20height">Benedetti height</a> is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 (<a class="wiki_link" href="/log2">log2</a>), of the Benedetti height, leading to Tenney height. In either form it is widely used as a <a class="wiki_link" href="/measure%20of%20inharmonicity">measure of inharmonicity</a> and/or complexity for intervals.<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>Tenney Height</title></head><body>If p/q is a positive rational number reduced to its lowest terms, then the <a class="wiki_link" href="/Benedetti%20height">Benedetti height</a> is the integer pq. Often it is more convenient instead to take the logarithm, usually base 2 (<a class="wiki_link" href="/log2">log2</a>), of the Benedetti height, leading to Tenney height. In either form it is widely used as a <a class="wiki_link" href="/measure%20of%20inharmonicity">measure of inharmonicity</a> and/or complexity for intervals.<br /> | ||
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<!-- ws:end:WikiTextCodeRule:0 --><br /> | <!-- ws:end:WikiTextCodeRule:0 --><br /> | ||
< | ==Examples==|| <strong>interval name</strong> || <strong>frequency ratio</strong> || <strong>ket vector</strong> || <strong>log2 (Benedetti Height)</strong> ||<br /> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>prime<br /> | <td>prime<br /> | ||
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The name <em>Tenney height</em> stems from the fact that <a class="wiki_link" href="/James%20Tenney">James Tenney</a> proposed it. The <em>Benedetti height</em>, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician <a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow">Giovanni Battista Benedetti</a>.<br /> | The name <em>Tenney height</em> stems from the fact that <a class="wiki_link" href="/James%20Tenney">James Tenney</a> proposed it. The <em>Benedetti height</em>, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician <a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow">Giovanni Battista Benedetti</a>.<br /> | ||
<br /> | <br /> | ||
<em>See also, discussion at <!-- ws:start:WikiTextUrlRule: | <em>See also, discussion at <!-- ws:start:WikiTextUrlRule:87:http://lumma.org/tuning/faq/#heights --><a class="wiki_link_ext" href="http://lumma.org/tuning/faq/#heights" rel="nofollow">http://lumma.org/tuning/faq/#heights</a><!-- ws:end:WikiTextUrlRule:87 --></em></body></html></pre></div> | ||