Monzos and interval space: Difference between revisions
Wikispaces>genewardsmith **Imported revision 196642622 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 196643650 - Original comment: ** |
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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-27 16: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-27 16:47:56 UTC</tt>.<br> | ||
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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>. In weighted coordinates, that becomes |4 -log2(3) -log2(5)> | 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)>, approximately |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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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Example"></a><!-- ws:end:WikiTextHeadingRule:0 -->Example</h2> | <!-- 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; | 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.<br /> | ||
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<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> | ||