Kees semi-height
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 2013-12-30 10:42:25 UTC.
- The original revision id was 479870430.
- 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 base two of the Kees height. The set of JI intervals with kees height less than or equal to an odd integer q comprises the [[Odd limit|q odd limit]] The point of kees height is to serve as a metric/height on [[Pitch class|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]] == Examples == ||= **interval** ||= **kees height** || ||= 5/3 ||= 5 || ||= 4/3 ||= 3 || ||= 2/1 ||= 1 ||
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 base two of the Kees height. The set of JI intervals with kees height less than or equal to an odd integer q comprises the <a class="wiki_link" href="/Odd%20limit">q odd limit</a><br />
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The point of kees height is to serve as a metric/height on <a class="wiki_link" href="/Pitch%20class">JI pitch classes</a> 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 />
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<a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow">Kees tuning pages</a><br />
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<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 --> Examples </h2>
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<td style="text-align: center;"><strong>interval</strong><br />
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<td style="text-align: center;"><strong>kees height</strong><br />
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<td style="text-align: center;">5/3<br />
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<td style="text-align: center;">5<br />
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<td style="text-align: center;">4/3<br />
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<td style="text-align: center;">3<br />
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<td style="text-align: center;">2/1<br />
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<td style="text-align: center;">1<br />
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