Kees semi-height: Difference between revisions
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Wikispaces>phylingual **Imported revision 344989860 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 345051804 - Original comment: Reverted to Jun 12, 2012 2:32 pm: It's not the same as thee odd limit** |
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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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-13 12:17:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>345051804</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Reverted to Jun 12, 2012 2:32 pm: It's not the same as thee odd limit</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">Given a ratio of positive integers p/q, the //kees height// is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b) | <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;white-space: pre-wrap ! important" class="old-revision-html">Given a ratio of positive integers p/q, the //kees height// is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b). The kees "expressibility" is then the logarithm of the kees height. | ||
The point of kees height is to serve as a metric/height on JI pitch classes corresponding to [[benedetti height]] on pitches. The measure was proposed by [[Kees van Prooijen]]. | The point of kees height is to serve as a metric/height on JI pitch classes corresponding to [[benedetti height]] on pitches. The measure was proposed by [[Kees van Prooijen]]. | ||
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[[http://www.kees.cc/tuning/perbl.html|Kees tuning pages]]</pre></div> | [[http://www.kees.cc/tuning/perbl.html|Kees tuning pages]]</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>Kees Height</title></head><body>Given a ratio of positive integers p/q, the <em>kees height</em> is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b) | <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>Kees Height</title></head><body>Given a ratio of positive integers p/q, the <em>kees height</em> is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b). The kees &quot;expressibility&quot; is then the logarithm of the kees height. <br /> | ||
<br /> | <br /> | ||
The point of kees height is to serve as a metric/height on JI pitch classes corresponding to <a class="wiki_link" href="/benedetti%20height">benedetti height</a> on pitches. The measure was proposed by <a class="wiki_link" href="/Kees%20van%20Prooijen">Kees van Prooijen</a>.<br /> | The point of kees height is to serve as a metric/height on JI pitch classes corresponding to <a class="wiki_link" href="/benedetti%20height">benedetti height</a> on pitches. The measure was proposed by <a class="wiki_link" href="/Kees%20van%20Prooijen">Kees van Prooijen</a>.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow">Kees tuning pages</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow">Kees tuning pages</a></body></html></pre></div> | ||
Revision as of 12:17, 13 June 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-06-13 12:17:26 UTC.
- The original revision id was 345051804.
- The revision comment was: Reverted to Jun 12, 2012 2:32 pm: It's not the same as thee odd limit
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
Given a ratio of positive integers p/q, the //kees height// is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b). The kees "expressibility" is then the logarithm of the kees height. The point of kees height is to serve as a metric/height on JI pitch classes corresponding to [[benedetti height]] on pitches. The measure was proposed by [[Kees van Prooijen]]. [[http://www.kees.cc/tuning/perbl.html|Kees tuning pages]]
Original HTML content:
<html><head><title>Kees Height</title></head><body>Given a ratio of positive integers p/q, the <em>kees height</em> is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b). The kees "expressibility" is then the logarithm of the kees height. <br /> <br /> The point of kees height is to serve as a metric/height on JI pitch classes corresponding to <a class="wiki_link" href="/benedetti%20height">benedetti height</a> on pitches. The measure was proposed by <a class="wiki_link" href="/Kees%20van%20Prooijen">Kees van Prooijen</a>.<br /> <br /> <a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow">Kees tuning pages</a></body></html>