58edo: Difference between revisions

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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;58edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;58 equal temperament&lt;/em&gt;, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the &lt;a class="wiki_link" href="/11-limit"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13&lt;/a&gt; and &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;s. It is the smallest &lt;a class="wiki_link" href="/edo"&gt;equal temperament&lt;/a&gt; which is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through the 17-limit, and is also the first et to map the entire 11-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; to distinct scale steps, and hence the first et which can define a version of the famous 43-note &lt;a class="wiki_link" href="/Harry%20Partch%20related%20scales"&gt;Genesis scale&lt;/a&gt; of &lt;a class="wiki_link" href="/Harry%20Partch"&gt;Harry Partch&lt;/a&gt;. It supports &lt;a class="wiki_link" href="/hemififths"&gt;hemififths&lt;/a&gt;, &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt;, &lt;a class="wiki_link" href="/diaschismic"&gt;diaschismic&lt;/a&gt;, &lt;a class="wiki_link" href="/harry"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20temperaments#Thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt;s, and supplies the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments &lt;a class="wiki_link" href="/Starling%20family#Thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20family#Thrush-Bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20family#Aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder-Jofur"&gt;jofur&lt;/a&gt;.&lt;br /&gt;

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