Benedetti height: Difference between revisions

Revision as of 17:52, 4 September 2014

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Omegatron and made on 2014-09-04 17:52:08 UTC.

The original revision id was 520874452.

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 <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 />
<br />
See also <a class="wiki_link" href="/Kees%20Height">Kees Height.</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1>
 

<table class="wiki_table">
    <tr>
        <th>interval<br />
</th>
        <th>Benedetti height<br />
</th>
        <th>Tenney height<br />
</th>
    </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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-23 17:51:48 UTC</tt>.<br>
+: This revision was by author [[User:Omegatron|Omegatron]] and made on <tt>2014-09-04 17:52:08 UTC</tt>.<br>
-: The original revision id was <tt>504155460</tt>.<br>
+: The original revision id was <tt>520874452</tt>.<br>
-: The revision comment was: <tt>added examples</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>
 <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 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.
+<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.]]
@@ Line 17: / Line 17: @@
 || 13/11 || 143 || 7.160 ||</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Benedetti height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;Benedetti height&lt;/em&gt; 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 &lt;a class="wiki_link" href="/Tenney%20height"&gt;Tenney height&lt;/a&gt;, or Tenney norm. The name is based on the fact that the scientist, mathematician and music theorist &lt;a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow"&gt;Giovanni Battista Benedetti&lt;/a&gt; first proposed it as a measure of inharmonicity. It may be the first number theoretic height function ever defined for any purpose.&lt;br /&gt;
+<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;Benedetti height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;Benedetti &lt;a class="wiki_link" href="/height"&gt;height&lt;/a&gt; &lt;/em&gt; 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 &lt;a class="wiki_link" href="/Tenney%20height"&gt;Tenney height&lt;/a&gt;, or Tenney norm. The name is based on the fact that the scientist, mathematician and music theorist &lt;a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow"&gt;Giovanni Battista Benedetti&lt;/a&gt; first proposed it as a measure of inharmonicity. It may be the first number theoretic height function ever defined for any purpose.&lt;br /&gt;
 &lt;br /&gt;
 See also &lt;a class="wiki_link" href="/Kees%20Height"&gt;Kees Height.&lt;/a&gt;&lt;br /&gt;

Benedetti height: Difference between revisions

Revision as of 17:52, 4 September 2014

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search