Interval size measure: 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:xenwolf|xenwolf]] and made on <tt>2011-06-13 09:11:15 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-13 09:17:32 UTC</tt>.<br>

: The original revision id was <tt>~~236214326~~</tt>.<br>

: The original revision id was <tt>236215506</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>

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Intervals can be measured also giving their [[http://en.wikipedia.org/wiki/Interval_ratio|(frequency) ratio]]. For instance the major third as [[5_4|5/4]] or the pure Fifth [[3_2|3/2]]. When combining sizes given in ratios, you have to multiply oder divide.

Another notation for ratios is a vector of prime ~~factors~~ exponents |-4 4 -1> (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors. </pre></div>

Another notation for ratios is a vector of prime factor exponents |-4 4 -1> (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors. </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"><html><head><title>Interval size measure</title></head><body><strong>Interval measure</strong> is the <em>distance</em> between pitches. Intervals can be measured logarithmically or by frequancy ratios.<br />

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Intervals can be measured also giving their <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_ratio" rel="nofollow">(frequency) ratio</a>. For instance the major third as <a class="wiki_link" href="/5_4">5/4</a> or the pure Fifth <a class="wiki_link" href="/3_2">3/2</a>. When combining sizes given in ratios, you have to multiply oder divide.<br />

<br />

Another notation for ratios is a vector of prime ~~factors~~ exponents |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors.</body></html></pre></div>

Another notation for ratios is a vector of prime factor exponents |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors.</body></html></pre></div>

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-06-13 09:11:15 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-13 09:17:32 UTC</tt>.<br>
-: The original revision id was <tt>236214326</tt>.<br>
+: The original revision id was <tt>236215506</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>
@@ Line 28: / Line 28: @@
 Intervals can be measured also giving their [[http://en.wikipedia.org/wiki/Interval_ratio|(frequency) ratio]]. For instance the major third as [[5_4|5/4]] or the pure Fifth [[3_2|3/2]]. When combining sizes given in ratios, you have to multiply oder divide.
-Another notation for ratios is a vector of prime factors exponents |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors. </pre></div>
+Another notation for ratios is a vector of prime factor exponents |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors. </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;Interval size measure&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Interval measure&lt;/strong&gt; is the &lt;em&gt;distance&lt;/em&gt; between pitches. Intervals can be measured logarithmically or by frequancy ratios.&lt;br /&gt;
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 Intervals can be measured also giving their &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_ratio" rel="nofollow"&gt;(frequency) ratio&lt;/a&gt;. For instance the major third as &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; or the pure Fifth &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;. When combining sizes given in ratios, you have to multiply oder divide.&lt;br /&gt;
 &lt;br /&gt;
-Another notation for ratios is a vector of prime factors exponents |-4 4 -1&amp;gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Another notation for ratios is a vector of prime factor exponents |-4 4 -1&amp;gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or substraction of their vectors.&lt;/body&gt;&lt;/html&gt;</pre></div>