Benedetti height
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Original Wikitext content:
The //Benedetti height// of a positive rational number N/D reduced to lowest terms (no common factor between N and D) is equal to N*D, the product of the numerator and denominator. The logarithm base two of the Benedetti height is the [[Tenney height]], or Tenney norm. The name is based on the fact that the scientist, mathematician and music theorist [[http://www.webcitation.org/6076Lm8r4|Giovanni Battista Benedetti]] first proposed it as a measure of inharmonicity. It may be the first number-theoretic [[height]] function ever defined for any purpose. See also [[Kees Height|Kees Height.]] =Examples= ||= Interval ||= Benedetti height ||= Tenney height || || 3/2 || 6 || 2.585 || || 6/5 || 30 || 4.907 || || 9/7 || 63 || 5.977 || || 13/11 || 143 || 7.160 ||
Original HTML content:
<html><head><title>Benedetti height</title></head><body>The <em>Benedetti height</em> of a positive rational number N/D reduced to lowest terms (no common factor between N and D) is equal to N*D, the product of the numerator and denominator. The logarithm base two of the Benedetti height is the <a class="wiki_link" href="/Tenney%20height">Tenney height</a>, or Tenney norm. The name is based on the fact that the scientist, mathematician and music theorist <a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow">Giovanni Battista Benedetti</a> first proposed it as a measure of inharmonicity. It may be the first number-theoretic <a class="wiki_link" href="/height">height</a> function ever defined for any purpose.<br />
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See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br />
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<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1>
<table class="wiki_table">
<tr>
<td style="text-align: center;">Interval<br />
</td>
<td style="text-align: center;">Benedetti height<br />
</td>
<td style="text-align: center;">Tenney height<br />
</td>
</tr>
<tr>
<td>3/2<br />
</td>
<td>6<br />
</td>
<td>2.585<br />
</td>
</tr>
<tr>
<td>6/5<br />
</td>
<td>30<br />
</td>
<td>4.907<br />
</td>
</tr>
<tr>
<td>9/7<br />
</td>
<td>63<br />
</td>
<td>5.977<br />
</td>
</tr>
<tr>
<td>13/11<br />
</td>
<td>143<br />
</td>
<td>7.160<br />
</td>
</tr>
</table>
</body></html>