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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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|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|height]] function ever defined for any purpose. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:08:57 UTC</tt>.<br>
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| : The original revision id was <tt>588205047</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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.
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| See also [[Kees Height|Kees Height.]] | | See also [[Kees_Height|Kees Height.]] |
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| =Examples= | | =Examples= |
| ||= Interval ||= Benedetti height ||= Tenney height ||
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| || 3/2 || 6 || 2.585 ||
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| || 6/5 || 30 || 4.907 ||
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| || 9/7 || 63 || 5.977 ||
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| || 13/11 || 143 || 7.160 ||
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| </pre></div>
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| <h4>Original HTML content:</h4>
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| <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 />
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| <br />
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| See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1>
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| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td style="text-align: center;">Interval<br />
| | | style="text-align:center;" | Interval |
| </td>
| | | style="text-align:center;" | Benedetti height |
| <td style="text-align: center;">Benedetti height<br />
| | | style="text-align:center;" | Tenney height |
| </td>
| | |- |
| <td style="text-align: center;">Tenney height<br />
| | | | 3/2 |
| </td>
| | | | 6 |
| </tr>
| | | | 2.585 |
| <tr>
| | |- |
| <td>3/2<br />
| | | | 6/5 |
| </td>
| | | | 30 |
| <td>6<br />
| | | | 4.907 |
| </td>
| | |- |
| <td>2.585<br />
| | | | 9/7 |
| </td>
| | | | 63 |
| </tr>
| | | | 5.977 |
| <tr>
| | |- |
| <td>6/5<br />
| | | | 13/11 |
| </td>
| | | | 143 |
| <td>30<br />
| | | | 7.160 |
| </td>
| | |} |
| <td>4.907<br />
| | [[Category:benedetti]] |
| </td>
| | [[Category:definition]] |
| </tr>
| | [[Category:height]] |
| <tr>
| | [[Category:measure]] |
| <td>9/7<br />
| | [[Category:psychoacoustics]] |
| </td>
| | [[Category:tenney]] |
| <td>63<br />
| | [[Category:theory]] |
| </td>
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| <td>5.977<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13/11<br />
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| </td>
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| <td>143<br />
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| </td>
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| <td>7.160<br />
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| </td>
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| </tr>
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| </table>
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| </body></html></pre></div>
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