Tenney norm: Difference between revisions
Wikispaces>xenwolf **Imported revision 249676220 - Original comment: repair table** |
Wikispaces>MartinGough **Imported revision 440365758 - 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:MartinGough|MartinGough]] and made on <tt>2013-07-03 11:41:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>440365758</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
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The //Tenney height// of a [[monzo]] is given by | The //Tenney height// of a [[monzo]] is given by | ||
[[code]] | [[code]] | ||
|| |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p) |ep| = log2(|e2| * |e3| * ... * |ep|) | || |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p)|ep| = log2(2^|e2| * 3^|e3| * ... * p^|ep|) | ||
[[code]] | [[code]] | ||
==Examples== | ==Examples==|| **interval name** || **frequency ratio** || **ket vector** || **log2 (Benedetti Height)** || | ||
|| **interval name** || **frequency ratio** || **ket vector** || **log2 (Benedetti Height)** || | |||
|| prime || 1/1 || |0> || 0 || | || prime || 1/1 || |0> || 0 || | ||
|| octave || 2/1 || |1> || 1 || | || octave || 2/1 || |1> || 1 || | ||
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The <em>Tenney height</em> of a <a class="wiki_link" href="/monzo">monzo</a> is given by<br /> | The <em>Tenney height</em> of a <a class="wiki_link" href="/monzo">monzo</a> is given by<br /> | ||
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&lt;pre class=&quot;text&quot;&gt;|| |e2 e3 ... ep&amp;gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep| = log2(|e2| * |e3| * ... * |ep|)&lt;/pre&gt; | &lt;pre class=&quot;text&quot;&gt;|| |e2 e3 ... ep&amp;gt; || = |e2| + log2(3)|e3| + ... + log2(p)|ep| = log2(2^|e2| * 3^|e3| * ... * p^|ep|)&lt;/pre&gt; | ||
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<style type="text/css"><!-- | <style type="text/css"><!-- | ||
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</style><pre class="text">|| |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep| = log2(|e2| * |e3| * ... * |ep|)</pre> | </style><pre class="text">|| |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p)|ep| = log2(2^|e2| * 3^|e3| * ... * p^|ep|)</pre> | ||
<!-- ws:end:WikiTextCodeRule:0 --><br /> | <!-- ws:end:WikiTextCodeRule:0 --><br /> | ||
< | ==Examples==|| <strong>interval name</strong> || <strong>frequency ratio</strong> || <strong>ket vector</strong> || <strong>log2 (Benedetti Height)</strong> ||<br /> | ||
<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>prime<br /> | <td>prime<br /> | ||
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The name <em>Tenney height</em> stems from the fact that <a class="wiki_link" href="/James%20Tenney">James Tenney</a> proposed it. The <em>Benedetti height</em>, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician <a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow">Giovanni Battista Benedetti</a>.<br /> | The name <em>Tenney height</em> stems from the fact that <a class="wiki_link" href="/James%20Tenney">James Tenney</a> proposed it. The <em>Benedetti height</em>, the product of the numerator and denominator, was first proposed as a consonance measure by the Renaissance scientist and mathematician <a class="wiki_link_ext" href="http://www.webcitation.org/6076Lm8r4" rel="nofollow">Giovanni Battista Benedetti</a>.<br /> | ||
<br /> | <br /> | ||
<em>See also, discussion at <!-- ws:start:WikiTextUrlRule: | <em>See also, discussion at <!-- ws:start:WikiTextUrlRule:87:http://lumma.org/tuning/faq/#heights --><a class="wiki_link_ext" href="http://lumma.org/tuning/faq/#heights" rel="nofollow">http://lumma.org/tuning/faq/#heights</a><!-- ws:end:WikiTextUrlRule:87 --></em></body></html></pre></div> | ||