Constant structure: Difference between revisions
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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). | 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). | ||
<span style="font-size: 1.4em;">**Examples**</span> | |||
This common pentatonic scale is a constant structure: 1/1 - 9/8 - 5/4 - 3/2 - 5/3 - 2/1 | This common pentatonic scale is a constant structure: 1/1 - 9/8 - 5/4 - 3/2 - 5/3 - 2/1 | ||
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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 /> | 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 /> | ||
<span style="font-size: 1.4em;"><strong>Examples</strong></span><br /> | |||
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This common pentatonic scale is a constant structure: 1/1 - 9/8 - 5/4 - 3/2 - 5/3 - 2/1<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 interval matrix of this scale:<br /> | Here is the interval matrix of this scale:<br /> | ||
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F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. (However, a meantone tuning of this scale, in which F# and Gb are distinguished, would have constant structure.)<br /> | F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. (However, a meantone tuning of this scale, in which F# and Gb are distinguished, would have constant structure.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Density of CS Scales in EDO's"></a><!-- ws:end:WikiTextHeadingRule:1 -->Density of CS Scales in EDO's</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:3 -->See also</h1> | ||
<a class="wiki_link" href="/Gallery%20of%20CS%20Scales">Gallery of CS Scales</a><br /> | <a class="wiki_link" href="/Gallery%20of%20CS%20Scales">Gallery of CS Scales</a><br /> | ||
<a class="wiki_link" href="/Scale%20properties%20simplified">Scale properties simplified</a><br /> | <a class="wiki_link" href="/Scale%20properties%20simplified">Scale properties simplified</a><br /> | ||