Benedetti height: Difference between revisions
Wikispaces>Omegatron **Imported revision 520874452 - Original comment: ** |
Wikispaces>clumma **Imported revision 540068900 - 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:clumma|clumma]] and made on <tt>2015-02-06 23:26:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540068900</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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=Examples= | =Examples= | ||
|| | ||= Interval ||= Benedetti height ||= Tenney height || | ||
|| 3/2 || 6 || 2.585 || | || 3/2 || 6 || 2.585 || | ||
|| 6/5 || 30 || 4.907 || | || 6/5 || 30 || 4.907 || | ||
|| 9/7 || 63 || 5.977 || | || 9/7 || 63 || 5.977 || | ||
|| 13/11 || 143 || 7.160 ||</pre></div> | || 13/11 || 143 || 7.160 || | ||
</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 <a class="wiki_link" href="/height">height</a> </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 height function ever defined for any purpose.<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>Benedetti height</title></head><body>The <em>Benedetti <a class="wiki_link" href="/height">height</a> </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 height function ever defined for any purpose.<br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <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> | ||
<tr> | <tr> | ||