Interval class: 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>2011-06-29 07:56:42 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:57:00 UTC</tt>.<br>

: The original revision id was <tt>~~239300673~~</tt>.<br>

: The original revision id was <tt>239300707</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">//Interval class// is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.

//Interval class// is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.

The second definition, used for example by Scala, defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps i apart belong. //see also [[interval size measure]], [[interval measure]]//

==Links==

* [[http://solomonsmusic.net/setheory.htm#Basic%20Definition]]

[[http://solomonsmusic.net/setheory.htm#Basic%20Definition]]

* [[http://en.wikipedia.org/wiki/Interval_class|Interval class]] </pre></div>

[[http://en.wikipedia.org/wiki/Interval_class|Interval class]] </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 class</title></head><body>~~<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>Interval class</title></head><body><em>Interval class</em> is used in two different ways. One, common in academic &quot;set theory&quot;, defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or &quot;ic&quot;--in <a class="wiki_link" href="/12edo">12edo</a>--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.<br />

<em>Interval class</em> is used in two different ways. One, common in academic &quot;set theory&quot;, defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or &quot;ic&quot;--in <a class="wiki_link" href="/12edo">12edo</a>--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.<br />

<br />

The second definition, used for example by Scala, defines the interval class as the &quot;generic interval&quot; to which the specific intervals at a certain number of scale steps i apart belong. <em>see also <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>, <a class="wiki_link" href="/interval%20measure">interval measure</a></em><br />

<br />

<h2 id="toc0"><a name="x-Links"></a>Links</h2>

<~~br /~~>

<ul><li><a class="wiki_link_ext" href="http://solomonsmusic.net/setheory.htm#Basic%20Definition" rel="nofollow">http://solomonsmusic.net/setheory.htm#Basic%20Definition</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_class" rel="nofollow">Interval class</a></li></ul></body></html></pre></div>

<a class="wiki_link_ext" href="http://solomonsmusic.net/setheory.htm#Basic%20Definition" rel="nofollow">http://solomonsmusic.net/setheory.htm#Basic%20Definition</a><br />

<~~br /~~>

<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_class" rel="nofollow">Interval class</a></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>2011-06-29 07:56:42 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:57:00 UTC</tt>.<br>
-: The original revision id was <tt>239300673</tt>.<br>
+: The original revision id was <tt>239300707</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">
+<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">//Interval class// is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.
-//Interval class// is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.
 The second definition, used for example by Scala, defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps i apart belong. //see also [[interval size measure]], [[interval measure]]//
 ==Links==
+* [[http://solomonsmusic.net/setheory.htm#Basic%20Definition]]
-[[http://solomonsmusic.net/setheory.htm#Basic%20Definition]]
+* [[http://en.wikipedia.org/wiki/Interval_class|Interval class]] </pre></div>
-[[http://en.wikipedia.org/wiki/Interval_class|Interval class]] </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 class&lt;/title&gt;&lt;/head&gt;&lt;body&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;Interval class&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Interval class&lt;/em&gt; is used in two different ways. One, common in academic &amp;quot;set theory&amp;quot;, defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or &amp;quot;ic&amp;quot;--in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.&lt;br /&gt;
-&lt;em&gt;Interval class&lt;/em&gt; is used in two different ways. One, common in academic &amp;quot;set theory&amp;quot;, defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or &amp;quot;ic&amp;quot;--in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.&lt;br /&gt;
 &lt;br /&gt;
 The second definition, used for example by Scala, defines the interval class as the &amp;quot;generic interval&amp;quot; to which the specific intervals at a certain number of scale steps i apart belong. &lt;em&gt;see also &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;, &lt;a class="wiki_link" href="/interval%20measure"&gt;interval measure&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Links&lt;/h2&gt;
-&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://solomonsmusic.net/setheory.htm#Basic%20Definition" rel="nofollow"&gt;http://solomonsmusic.net/setheory.htm#Basic%20Definition&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_class" rel="nofollow"&gt;Interval class&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
-&lt;a class="wiki_link_ext" href="http://solomonsmusic.net/setheory.htm#Basic%20Definition" rel="nofollow"&gt;http://solomonsmusic.net/setheory.htm#Basic%20Definition&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_class" rel="nofollow"&gt;Interval class&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>