Constant structure: 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:~~xenjacob~~|~~xenjacob~~]] and made on <tt>2016-06-~~06 08~~:20:35 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-06-07 04:23:18 UTC</tt>.<br>

: The original revision id was <tt>~~584867645~~</tt>.<br>

: The original revision id was <tt>584931949</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>moved definition to top</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">~~[[image:11toneconstantstructures.jpg width="800" height="875"]]~~

<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">A [[scale]] is said to have //constant structure// (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.

A [[scale]] is said to have //constant structure// (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.

The term "constant structure" was coined by [[Erv Wilson]]. In academic music theory, constant structure is called the partitioning property, but Erv got there first.

To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an [[interval matrix]] ([[Scala]] can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).

[[image:11toneconstantstructures.jpg width="800" height="875"]]

=Examples=

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[[media type="custom" key="26024358"]]</pre></div>

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<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>constant structure</title></head><body><img src="/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg" alt="11toneconstantstructures.jpg" title="11toneconstantstructures.jpg" style="height: 875px; width: 800px;" /><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>constant structure</title></head><body>A <a class="wiki_link" href="/scale">scale</a> is said to have <em>constant structure</em> (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.<br />

~~<br />~~

A <a class="wiki_link" href="/scale">scale</a> is said to have <em>constant structure</em> (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.<br />

<br />

The term &quot;constant structure&quot; was coined by <a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a>. In academic music theory, constant structure is called the partitioning property, but Erv got there first.<br />

<br />

To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an <a class="wiki_link" href="/interval%20matrix">interval matrix</a> (<a class="wiki_link" href="/Scala">Scala</a> can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).<br />

<br />

<img src="/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg" alt="11toneconstantstructures.jpg" title="11toneconstantstructures.jpg" style="height: 875px; width: 800px;" /><br />

<br />

<h1 id="toc0"><a name="Examples"></a>Examples</h1>

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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:xenjacob|xenjacob]] and made on <tt>2016-06-06 08:20:35 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-06-07 04:23:18 UTC</tt>.<br>
-: The original revision id was <tt>584867645</tt>.<br>
+: The original revision id was <tt>584931949</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>moved definition to top</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">[[image:11toneconstantstructures.jpg width="800" height="875"]]
+<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">A [[scale]] is said to have //constant structure// (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.
-A [[scale]] is said to have //constant structure// (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.
 The term "constant structure" was coined by [[Erv Wilson]]. In academic music theory, constant structure is called the partitioning property, but Erv got there first.
 To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an [[interval matrix]] ([[Scala]] can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).
+[[image:11toneconstantstructures.jpg width="800" height="875"]]
 =Examples=
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 [[media type="custom" key="26024358"]]</pre></div>
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-<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;constant structure&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextLocalImageRule:739:&amp;lt;img src=&amp;quot;/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 875px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg" alt="11toneconstantstructures.jpg" title="11toneconstantstructures.jpg" style="height: 875px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:739 --&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;constant structure&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;a class="wiki_link" href="/scale"&gt;scale&lt;/a&gt; is said to have &lt;em&gt;constant structure&lt;/em&gt; (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.&lt;br /&gt;
-&lt;br /&gt;
-A &lt;a class="wiki_link" href="/scale"&gt;scale&lt;/a&gt; is said to have &lt;em&gt;constant structure&lt;/em&gt; (CS) if its generic interval classes are distinct. That is, each interval occurs always subtended by the same number of steps. This means that you never get something like an interval being counted as a fourth one place, and a fifth another place.&lt;br /&gt;
 &lt;br /&gt;
 The term &amp;quot;constant structure&amp;quot; was coined by &lt;a class="wiki_link" href="/Erv%20Wilson"&gt;Erv Wilson&lt;/a&gt;. In academic music theory, constant structure is called the partitioning property, but Erv got there first.&lt;br /&gt;
 &lt;br /&gt;
 To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an &lt;a class="wiki_link" href="/interval%20matrix"&gt;interval matrix&lt;/a&gt; (&lt;a class="wiki_link" href="/Scala"&gt;Scala&lt;/a&gt; can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:739:&amp;lt;img src=&amp;quot;/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 875px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/11toneconstantstructures.jpg/584867501/800x875/11toneconstantstructures.jpg" alt="11toneconstantstructures.jpg" title="11toneconstantstructures.jpg" style="height: 875px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:739 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Examples&lt;/h1&gt;