Constant structure
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Original Wikitext content:
A [[scale]] is said to have //constant structure// 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. =Examples= This common pentatonic scale is a constant structure: 1/1 - 9/8 - 5/4 - 3/2 - 5/3 - 2/1 Here is the [[interval matrix]] of this scale: ||~ ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ (6) || ||~ 1/1 || 1/1 || 9/8 || 5/4 || 3/2 || 5/3 || 2/1 || ||~ 9/8 || 1/1 || 10/9 || 4/3 || 40/27 || 16/9 || 2/1 || ||~ 5/4 || 1/1 || 6/5 || 4/3 || 8/5 || 9/5 || 2/1 || ||~ 3/2 || 1/1 || 10/9 || 4/3 || 3/2 || 5/3 || 2/1 || ||~ 5/3 || 1/1 || 6/5 || 27/20 || 3/2 || 9/5 || 2/1 || Note that every interval always appears in the same position (column). For example, 3/2 is always the "fourth" of this scale. This pentatonic scale is not a constant structure: 1/1 - 25/24 - 6/5 - 3/2 - 5/3 - 2/1 Its interval matrix: ||~ ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ (6) || ||~ 1/1 || 1/1 || 25/24 || 6/5 || 3/2 || 5/3 || 2/1 || ||~ 25/24 || 1/1 || 144/125 || 36/25 || 8/5 || 48/25 || 2/1 || ||~ 6/5 || 1/1 || 5/4 || 25/18 || 5/3 || 125/72 || 2/1 || ||~ 3/2 || 1/1 || 10/9 || 4/3 || 25/18 || 8/5 || 2/1 || ||~ 5/3 || 1/1 || 6/5 || 5/4 || 36/25 || 9/5 || 2/1 || Note that 5/4 occurs as both the "second" and "third". [[media type="custom" key="26024358"]]
Original HTML content:
<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> 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 />
<!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:1 -->Examples</h1>
<br />
This common pentatonic scale is a constant structure: 1/1 - 9/8 - 5/4 - 3/2 - 5/3 - 2/1<br />
Here is the <a class="wiki_link" href="/interval%20matrix">interval matrix</a> of this scale:<br />
<table class="wiki_table">
<tr>
<th><br />
</th>
<th>1<br />
</th>
<th>2<br />
</th>
<th>3<br />
</th>
<th>4<br />
</th>
<th>5<br />
</th>
<th>(6)<br />
</th>
</tr>
<tr>
<th>1/1<br />
</th>
<td>1/1<br />
</td>
<td>9/8<br />
</td>
<td>5/4<br />
</td>
<td>3/2<br />
</td>
<td>5/3<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>9/8<br />
</th>
<td>1/1<br />
</td>
<td>10/9<br />
</td>
<td>4/3<br />
</td>
<td>40/27<br />
</td>
<td>16/9<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>5/4<br />
</th>
<td>1/1<br />
</td>
<td>6/5<br />
</td>
<td>4/3<br />
</td>
<td>8/5<br />
</td>
<td>9/5<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>3/2<br />
</th>
<td>1/1<br />
</td>
<td>10/9<br />
</td>
<td>4/3<br />
</td>
<td>3/2<br />
</td>
<td>5/3<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>5/3<br />
</th>
<td>1/1<br />
</td>
<td>6/5<br />
</td>
<td>27/20<br />
</td>
<td>3/2<br />
</td>
<td>9/5<br />
</td>
<td>2/1<br />
</td>
</tr>
</table>
Note that every interval always appears in the same position (column). For example, 3/2 is always the "fourth" of this scale.<br />
<br />
<br />
This pentatonic scale is not a constant structure: 1/1 - 25/24 - 6/5 - 3/2 - 5/3 - 2/1<br />
Its interval matrix:<br />
<table class="wiki_table">
<tr>
<th><br />
</th>
<th>1<br />
</th>
<th>2<br />
</th>
<th>3<br />
</th>
<th>4<br />
</th>
<th>5<br />
</th>
<th>(6)<br />
</th>
</tr>
<tr>
<th>1/1<br />
</th>
<td>1/1<br />
</td>
<td>25/24<br />
</td>
<td>6/5<br />
</td>
<td>3/2<br />
</td>
<td>5/3<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>25/24<br />
</th>
<td>1/1<br />
</td>
<td>144/125<br />
</td>
<td>36/25<br />
</td>
<td>8/5<br />
</td>
<td>48/25<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>6/5<br />
</th>
<td>1/1<br />
</td>
<td>5/4<br />
</td>
<td>25/18<br />
</td>
<td>5/3<br />
</td>
<td>125/72<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>3/2<br />
</th>
<td>1/1<br />
</td>
<td>10/9<br />
</td>
<td>4/3<br />
</td>
<td>25/18<br />
</td>
<td>8/5<br />
</td>
<td>2/1<br />
</td>
</tr>
<tr>
<th>5/3<br />
</th>
<td>1/1<br />
</td>
<td>6/5<br />
</td>
<td>5/4<br />
</td>
<td>36/25<br />
</td>
<td>9/5<br />
</td>
<td>2/1<br />
</td>
</tr>
</table>
Note that 5/4 occurs as both the "second" and "third".<br />
<br />
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