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Tenney norm: Difference between revisions

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VisualWikitext
Wikispaces>xenwolf
**Imported revision 146157510 - Original comment: **
Wikispaces>xenwolf
**Imported revision 146159623 - Original comment: added example**
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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:xenwolf|xenwolf]] and made on <tt>2010-06-01 03:07:44 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-01 03:27:49 UTC</tt>.<br>
: The original revision id was <tt>146157510</tt>.<br>
: The original revision id was <tt>146159623</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>added example</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|Tenney height]] of a [[monzo]] is given by
The [[Tenney Height|Tenney height]] of a [[monzo]] is given by
[[code type=text]]
|| |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|
[[code]]
==examples==
I tried to make it more understabable (for me?) using a few examples (maybe not perfect)


|| |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|
|| **interval name** || **frequency ratio** || **ket vector** || **Tenney Height** ||
|| prime || 1/1 || |.&gt; || 0 ||
|| octave || 2/1 || |1&gt; ||  1 ||
|| just perfect fifth || 3/2 || |-1 1&gt; || ca 2.585 ||
|| just major third || 5/4 || |-2 0 1&gt; || ca 4.322 ||
|| harmonic seventh || 7/4 || |-2 0 0 1&gt; || ca 4.807 ||




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&lt;br /&gt;
&lt;br /&gt;
The &lt;a class="wiki_link" href="/Tenney%20Height"&gt;Tenney height&lt;/a&gt; of a &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is given by&lt;br /&gt;
The &lt;a class="wiki_link" href="/Tenney%20Height"&gt;Tenney height&lt;/a&gt; of a &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is given by&lt;br /&gt;
&lt;!-- ws:start:WikiTextCodeRule:0:
&amp;lt;pre class=&amp;quot;text&amp;quot;&amp;gt;|| |e2 e3 ... ep&amp;amp;gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|&amp;lt;/pre&amp;gt;
--&gt;
&lt;style type="text/css"&gt;&lt;!--
/**
* GeSHi (C) 2004 - 2007 Nigel McNie, 2007 - 2008 Benny Baumann
* (http://qbnz.com/highlighter/ and http://geshi.org/)
*/
.text  {font-family:monospace;}
.text .imp {font-weight: bold; color: red;}
.text span.xtra { display:block; }
--&gt;
&lt;/style&gt;&lt;pre class="text"&gt;|| |e2 e3 ... ep&amp;gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|&lt;/pre&gt;
&lt;!-- ws:end:WikiTextCodeRule:0 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;examples&lt;/h2&gt;
I tried to make it more understabable (for me?) using a few examples (maybe not perfect)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
|| |e2 e3 ... ep&amp;gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;interval name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;frequency ratio&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;ket vector&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Tenney Height&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|.&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;just perfect fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ca 2.585&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;just major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ca 4.322&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;harmonic seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 0 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ca 4.807&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;see also discussion on &lt;!-- ws:start:WikiTextUrlRule:10:http://lumma.org/music/theory/TuningFAQ.txt --&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/TuningFAQ.txt" rel="nofollow"&gt;http://lumma.org/music/theory/TuningFAQ.txt&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:10 --&gt; section CONSONANCE AND DISSONANCE&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;em&gt;see also discussion on &lt;!-- ws:start:WikiTextUrlRule:100:http://lumma.org/music/theory/TuningFAQ.txt --&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/TuningFAQ.txt" rel="nofollow"&gt;http://lumma.org/music/theory/TuningFAQ.txt&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:100 --&gt; section CONSONANCE AND DISSONANCE&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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