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Monzos and interval space: Difference between revisions

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**Imported revision 250559138 - Original comment: Reverted to Jun 25, 2011 5:32 pm: reverting to last edit by xenjacob**
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**Imported revision 278344806 - 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>
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: This revision was by author [[User:clumma|clumma]] and made on <tt>2011-09-03 22:53:36 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-22 21:02:23 UTC</tt>.<br>
: The original revision id was <tt>250559138</tt>.<br>
: The original revision id was <tt>278344806</tt>.<br>
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<h4>Original Wikitext content:</h4>
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==Example==  
==Example==  
The 5-limit interval 16/15 factors as 2^4 3^(-1) 5^(-1), so it has a monzo representation of |4 -1 -1&gt;. In weighted coordinates, that becomes |4 -log2(3) -log2(5)&gt;, approximately |4 -1.585 -2.322&gt;. The TE norm is therefore sqrt(1^2 + log2(3)^2 + log2(5)^2) ~ sqrt(23.903) = 4.889.
The 5-limit interval 16/15 factors as 2^4 3^(-1) 5^(-1), so it has a monzo representation of |4 -1 -1&gt;. In weighted coordinates, that becomes |4 -log2(3) -log2(5)&gt;, approximately |4 -1.585 -2.322&gt;. The TE norm is therefore √(1^2 + log2(3)^2 + log2(5)^2) ≅ √23.903 ≅ 4.889.


//see also [[Fractional monzos]], [[Vals and Tuning Space]]...//</pre></div>
//see also [[Fractional monzos]], [[Vals and Tuning Space]]...//</pre></div>
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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Example"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Example&lt;/h2&gt;
  The 5-limit interval 16/15 factors as 2^4 3^(-1) 5^(-1), so it has a monzo representation of |4 -1 -1&amp;gt;. In weighted coordinates, that becomes |4 -log2(3) -log2(5)&amp;gt;, approximately |4 -1.585 -2.322&amp;gt;. The TE norm is therefore sqrt(1^2 + log2(3)^2 + log2(5)^2) ~ sqrt(23.903) = 4.889.&lt;br /&gt;
  The 5-limit interval 16/15 factors as 2^4 3^(-1) 5^(-1), so it has a monzo representation of |4 -1 -1&amp;gt;. In weighted coordinates, that becomes |4 -log2(3) -log2(5)&amp;gt;, approximately |4 -1.585 -2.322&amp;gt;. The TE norm is therefore √(1^2 + log2(3)^2 + log2(5)^2) ≅ √23.903 ≅ 4.889.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;see also &lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;, &lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;...&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;em&gt;see also &lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;, &lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;...&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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