Equal-step tuning: Difference between revisions

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<h4>Original Wikitext content:</h4>

**Equal: a tuning in which every single step is the same interval; an equal-step scale.** See also [[edo]].

[[edo anatomy]], [[macrotonal edos]], [[maximal evenness]], [[Toctave]], [[The Riemann Zeta Function and Tuning]]</pre></div>

<h4>Original HTML content:</h4>

&lt;strong&gt;Equal: a tuning in which every single step is the same interval; an equal-step scale.&lt;/strong&gt; See also &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;.&lt;br /&gt;

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&lt;strong&gt;As there are infinite intervals, there are infinite equal scales.&lt;/strong&gt; Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings &lt;a class="wiki_link" href="/ET%20surveys"&gt;sequentially&lt;/a&gt; or &lt;a class="wiki_link" href="/Polymicrotonality"&gt;simultaneously&lt;/a&gt;.&lt;br /&gt;

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  What do 12ed2, 19ed3, and 28ed5 all have in common? They're all approximately the same scale. This happens because 12ed2 is an accurate temperament (for its size) that contains relatively close approximations of 3/1 and 5/1. In contrast, 11ed2 does not correspond closely to any equal division of 3/1 or 5/1.&lt;br /&gt;

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The following plot shows equal divisions of 2/1, 3/1, 5/1, and 7/1, and points out some instances when three or more of them happen to be close together. Note that any equal division of 2/1 is automatically an equal division of 4/1; and if something is simultaneously a good equal division of both 2/1 and 3/1, then it's a good equal division of 6/1 as well.&lt;br /&gt;

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(Unlimited resolution version: &lt;a href="http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg');"&gt;equal.svg&lt;/a&gt;)&lt;br /&gt;

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  by far the most widespread ones&lt;br /&gt;

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  most famously the &lt;a class="wiki_link" href="/BP"&gt;BP&lt;/a&gt; scale, but lots of others, too&lt;br /&gt;

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  &lt;br /&gt;

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  most famously Carlos Alpha, Beta and Gamma, but lots of others, too&lt;br /&gt;

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  3 - &lt;a class="wiki_link" href="/Cube%20Root%20of%20P4"&gt;Cube Root of 4/3&lt;/a&gt;&lt;br /&gt;

9 - '&lt;a class="wiki_link" href="/Noleta"&gt;Noleta&lt;/a&gt;' Scale&lt;br /&gt;

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  &lt;a class="wiki_link" href="/Square%20root%20of%2013%20over%2010"&gt;Square root of 13 over 10&lt;/a&gt;&lt;br /&gt;

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  &lt;a class="wiki_link" href="/88cET"&gt;88-cET&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="/65cET"&gt;65cET&lt;/a&gt;&lt;br /&gt;

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  &lt;a class="wiki_link" href="/9%208ths%20equal%20temperament"&gt;9:8&lt;/a&gt;, &lt;a class="wiki_link" href="/10%209ths%20equal%20temperament"&gt;10:9&lt;/a&gt;, &lt;a class="wiki_link" href="/12%2011th%20equal%20temperament"&gt;12:11&lt;/a&gt;, &lt;a class="wiki_link" href="/13%2012ths%20equal%20temperament"&gt;13:12&lt;/a&gt;&lt;br /&gt;

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  &lt;a class="wiki_link" href="/edo%20anatomy"&gt;edo anatomy&lt;/a&gt;, &lt;a class="wiki_link" href="/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;, &lt;a class="wiki_link" href="/maximal%20evenness"&gt;maximal evenness&lt;/a&gt;, &lt;a class="wiki_link" href="/Toctave"&gt;Toctave&lt;/a&gt;, &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;The Riemann Zeta Function and Tuning&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>