Kees semi-height: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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-~~14 13~~:37:11 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-30 10:42:25 UTC</tt>.<br>

: The original revision id was <tt>~~345394770~~</tt>.<br>

: The original revision id was <tt>479870430</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>

<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. The set of JI intervals with kees height less than or equal to an odd integer q comprises the [[Odd limit|q odd limit]]

<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 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]].

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]]

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<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. 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 />

<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 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 />

<br />

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 />

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 />

<br />

<a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow">Kees tuning pages</a><br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-06-14 13:37:11 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-30 10:42:25 UTC</tt>.<br>
-: The original revision id was <tt>345394770</tt>.<br>
+: The original revision id was <tt>479870430</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>
 <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. The set of JI intervals with kees height less than or equal to an odd integer q comprises the [[Odd limit|q odd limit]]
+<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 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]].
+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]]
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 ||= 2/1 ||= 1 ||</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Kees Height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Given a ratio of positive integers p/q, the &lt;em&gt;kees height&lt;/em&gt; 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 &amp;quot;expressibility&amp;quot; is then the logarithm of the kees height. The set of JI intervals with kees height less than or equal to an odd integer q comprises the &lt;a class="wiki_link" href="/Odd%20limit"&gt;q odd limit&lt;/a&gt;&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Kees Height&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Given a ratio of positive integers p/q, the &lt;em&gt;Kees height&lt;/em&gt; 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 &amp;quot;expressibility&amp;quot; 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 &lt;a class="wiki_link" href="/Odd%20limit"&gt;q odd limit&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-The point of kees height is to serve as a metric/height on &lt;a class="wiki_link" href="/Pitch%20class"&gt;JI pitch classes&lt;/a&gt; corresponding to &lt;a class="wiki_link" href="/benedetti%20height"&gt;benedetti height&lt;/a&gt; on pitches. The measure was proposed by &lt;a class="wiki_link" href="/Kees%20van%20Prooijen"&gt;Kees van Prooijen&lt;/a&gt;.&lt;br /&gt;
+The point of kees height is to serve as a metric/height on &lt;a class="wiki_link" href="/Pitch%20class"&gt;JI pitch classes&lt;/a&gt; corresponding to &lt;a class="wiki_link" href="/Benedetti%20height"&gt;Benedetti height&lt;/a&gt; on pitches. The measure was proposed by &lt;a class="wiki_link" href="/Kees%20van%20Prooijen"&gt;Kees van Prooijen&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.kees.cc/tuning/perbl.html" rel="nofollow"&gt;Kees tuning pages&lt;/a&gt;&lt;br /&gt;