Kees semi-height: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 345051804 - Original comment: Reverted to Jun 12, 2012 2:32 pm: It's not the same as thee odd limit** |
Wikispaces>genewardsmith **Imported revision 345141894 - 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>2012-06-13 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-13 17:45:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>345141894</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<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). The kees "expressibility" is then the logarithm of the kees height. | <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 set of JI intervals with kees height less than or equal to a odd integer q comprises the [[Odd limit|q odd limit]] | ||
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). The kees &quot;expressibility&quot; is then the logarithm of the kees height. <br /> | <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. The set of JI intervals with kees height less than or equal to a odd integer q comprises the <a class="wiki_link" href="/Odd%20limit">q odd limit</a><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 17:45, 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 17:45:01 UTC.
- The original revision id was 345141894.
- The revision comment was:
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 set of JI intervals with kees height less than or equal to a odd integer q comprises the [[Odd limit|q odd limit]] 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. The set of JI intervals with kees height less than or equal to a odd integer q comprises the <a class="wiki_link" href="/Odd%20limit">q odd limit</a><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>