Tenney norm: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-12 04:01:17 UTC</tt>.<br>

: The original revision id was <tt>240952357</tt>.<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;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** 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

|| **interval name** || **frequency ratio** || **ket vector** || **log2(Tenney Height)** ||

The name //Tenney height// stems from the fact that [[James Tenney]] proposed it. However, it has been proposed that it should be called //Benedetti height//, since the first person to propose it as a consonance measure seems to have been Renaissance scientist and mathematician [[http://www.webcitation.org/6076Lm8r4|Giovanni Battista Benedetti]].

<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; 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;

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;

         &lt;td&gt;&lt;strong&gt;log2(Tenney Height)&lt;/strong&gt;&lt;br /&gt;

The name &lt;em&gt;Tenney height&lt;/em&gt; stems from the fact that &lt;a class="wiki_link" href="/James%20Tenney"&gt;James Tenney&lt;/a&gt; proposed it. However, it has been proposed that it should be called &lt;em&gt;Benedetti height&lt;/em&gt;, since the first person to propose it as a consonance measure seems to have been Renaissance scientist and mathematician &lt;a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow"&gt;Giovanni Battista Benedetti&lt;/a&gt;.&lt;br /&gt;