Patent val
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2011-06-13 04:59:38 UTC.
- The original revision id was 236182350.
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Original Wikitext content:
Given N-edo, the equal division of the octave into N parts, we may for any prime p find a corresponding p-limit val in a canonical manner by [[http://en.wikipedia.org/wiki/Scalar_multiplication|scalar multiplying]] <1 log2(3) log2(5) ... log(p)| by N and rounding to the nearest integer. In general this is not guaranteed to be the most accurate available val, but if N-edo has enough relative accuracy in the p-limit, it will be. The name //patent// comes from the fact that "patent" in one sense of the word is a synonym for "obvious"; the patent val may or may not be the best choice but it's the obvious choice. == Example == multiplying 12 times <1 1.585 2.322 2.807 3.459| yields <12 19.020 27.863 33.688 41.513|, rounded to <12 19 28 34 42|, which is the **11-limit patent val for [[12edo]]**.
Original HTML content:
<html><head><title>Patent val</title></head><body>Given N-edo, the equal division of the octave into N parts, we may for any prime p find a corresponding p-limit val in a canonical manner by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scalar_multiplication" rel="nofollow">scalar multiplying</a> <1 log2(3) log2(5) ... log(p)| by N and rounding to the nearest integer. In general this is not guaranteed to be the most accurate available val, but if N-edo has enough relative accuracy in the p-limit, it will be. The name <em>patent</em> comes from the fact that "patent" in one sense of the word is a synonym for "obvious"; the patent val may or may not be the best choice but it's the obvious choice.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Example"></a><!-- ws:end:WikiTextHeadingRule:0 --> Example </h2> multiplying 12 times <1 1.585 2.322 2.807 3.459| <br /> yields <12 19.020 27.863 33.688 41.513|, <br /> rounded to <12 19 28 34 42|, <br /> which is the <strong>11-limit patent val for <a class="wiki_link" href="/12edo">12edo</a></strong>.</body></html>