Benedetti height: Difference between revisions
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Wikispaces>clumma **Imported revision 540068900 - Original comment: ** |
Wikispaces>clumma **Imported revision 588205005 - 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:clumma|clumma]] and made on <tt> | : This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:08:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588205005</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">The //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;white-space: pre-wrap ! important" class="old-revision-html">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.]] | See also [[Kees Height|Kees Height.]] | ||
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</pre></div> | </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>Benedetti height</title></head><body>The <em>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"><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 /> | ||
<br /> | <br /> | ||
See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br /> | See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br /> | ||
Revision as of 14:08, 27 July 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author clumma and made on 2016-07-27 14:08:45 UTC.
- The original revision id was 588205005.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 />
<br />
See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br />
<br />
<!-- 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>