Monzos and interval space: Difference between revisions
Wikispaces>genewardsmith **Imported revision 175439685 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 196642622 - Original comment: ** |
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and if the coordinates are the weighted interval space coordinates, then the TE norm is the [[http://mathworld.wolfram.com/L2-Norm.html|standard Euclidean, or L2, norm]]. | and if the coordinates are the weighted interval space coordinates, then the TE norm is the [[http://mathworld.wolfram.com/L2-Norm.html|standard Euclidean, or L2, norm]]. | ||
==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>. In weighted coordinates, that becomes |4 -log2(3) -log2(5)> = |4 -1.585 -2.322>. The TE norm is therefore sqrt(1^2 + log2(3)^2 + log2(5)^2) = sqrt(23.903) = 4.889. | |||
//see also [[Fractional monzos]]...//</pre></div> | //see also [[Fractional monzos]]...//</pre></div> | ||
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and if the coordinates are the weighted interval space coordinates, then the TE norm is the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/L2-Norm.html" rel="nofollow">standard Euclidean, or L2, norm</a>.<br /> | and if the coordinates are the weighted interval space coordinates, then the TE norm is the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/L2-Norm.html" rel="nofollow">standard Euclidean, or L2, norm</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Example"></a><!-- ws:end:WikiTextHeadingRule:0 -->Example</h2> | |||
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; <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x|4 -1.585 -2.322&gt;. The TE norm is therefore sqrt(1^2 + log2(3)^2 + log2(5)^2)"></a><!-- ws:end:WikiTextHeadingRule:2 --> |4 -1.585 -2.322&gt;. The TE norm is therefore sqrt(1^2 + log2(3)^2 + log2(5)^2) </h1> | |||
sqrt(23.903) = 4.889.<br /> | |||
<br /> | <br /> | ||
<em>see also <a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a>...</em></body></html></pre></div> | <em>see also <a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a>...</em></body></html></pre></div> | ||