TOP tuning: Difference between revisions
Wikispaces>genewardsmith **Imported revision 548716694 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 548731802 - 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> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-04-26 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-04-26 16:12:19 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>548731802</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></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> | ||
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=Extrinsic primes tuning= | =Extrinsic primes tuning= | ||
For a temperament with both intrinsic and extrinsic primes, we may find the set of TOP tunings by first computing the tuning of the intrinsic primes. Then if r is an extrinsic prime, the tuning may be anything in the range where APE(r) | For a temperament with both intrinsic and extrinsic primes, we may find the set of TOP tunings by first computing the tuning of the intrinsic primes. Then if r is an extrinsic prime, the tuning may be anything in the range where APE(r) ≤ E. The limit of the [[Lp tuning]] as p tends to 1 and the centroid of the region of TOP tunings both lead to choosing the JI tuning for r.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>TOP tuning</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Proportional error"></a><!-- ws:end:WikiTextHeadingRule:0 -->Proportional error</h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>TOP tuning</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Proportional error"></a><!-- ws:end:WikiTextHeadingRule:0 -->Proportional error</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Extrinsic primes tuning"></a><!-- ws:end:WikiTextHeadingRule:6 -->Extrinsic primes tuning</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Extrinsic primes tuning"></a><!-- ws:end:WikiTextHeadingRule:6 -->Extrinsic primes tuning</h1> | ||
For a temperament with both intrinsic and extrinsic primes, we may find the set of TOP tunings by first computing the tuning of the intrinsic primes. Then if r is an extrinsic prime, the tuning may be anything in the range where APE(r) | For a temperament with both intrinsic and extrinsic primes, we may find the set of TOP tunings by first computing the tuning of the intrinsic primes. Then if r is an extrinsic prime, the tuning may be anything in the range where APE(r) ≤ E. The limit of the <a class="wiki_link" href="/Lp%20tuning">Lp tuning</a> as p tends to 1 and the centroid of the region of TOP tunings both lead to choosing the JI tuning for r.</body></html></pre></div> | ||