58edo: 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:~~phylingual~~|~~phylingual~~]] and made on <tt>2012-07-13 08:36:00 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-13 12:16:01 UTC</tt>.<br>

: The original revision id was <tt>~~352968254~~</tt>.<br>

: The original revision id was <tt>353000072</tt>.<br>

: The revision comment was: <tt></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">The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] 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 [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest [[edo|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[temperament]]s, and supplies the [[optimal patent val]] 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 [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].

<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">The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] 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 [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest [[edo|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] 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 [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].

While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].

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|| 57 || 1179.31 || || ||</pre></div>

<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>58edo</title></head><body>The <em>58 equal temperament</em>, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> 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 <a class="wiki_link" href="/11-limit">11</a>, <a class="wiki_link" href="/13-limit">13</a> and <a class="wiki_link" href="/17-limit">17-limit</a>s. It is the smallest <a class="wiki_link" href="/edo">equal temperament</a> which is <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit, and is also the first et to map the entire 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> to distinct scale steps, and hence the first et which can define a version of the famous 43-note <a class="wiki_link" href="/~~Genesis~~%~~20scale~~">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports <a class="wiki_link" href="/hemififths">hemififths</a>, <a class="wiki_link" href="/myna">myna</a>, <a class="wiki_link" href="/diaschismic">diaschismic</a>, <a class="wiki_link" href="/harry">harry</a>, <a class="wiki_link" href="/~~mystery~~">mystery</a>, <a class="wiki_link" href="/~~buzzard~~">buzzard</a> and <a class="wiki_link" href="/~~thuja~~">thuja</a> <a class="wiki_link" href="/~~temperament~~">temperament</a>s, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> 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 <a class="wiki_link" href="/thrush">thrush</a>, <a class="wiki_link" href="/bluebird">bluebird</a>, <a class="wiki_link" href="/aplonis">aplonis</a> and <a class="wiki_link" href="/jofur">jofur</a>.<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>58edo</title></head><body>The <em>58 equal temperament</em>, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> 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 <a class="wiki_link" href="/11-limit">11</a>, <a class="wiki_link" href="/13-limit">13</a> and <a class="wiki_link" href="/17-limit">17-limit</a>s. It is the smallest <a class="wiki_link" href="/edo">equal temperament</a> which is <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit, and is also the first et to map the entire 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> to distinct scale steps, and hence the first et which can define a version of the famous 43-note <a class="wiki_link" href="/Harry%20Partch%20related%20scales">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports <a class="wiki_link" href="/hemififths">hemififths</a>, <a class="wiki_link" href="/myna">myna</a>, <a class="wiki_link" href="/diaschismic">diaschismic</a>, <a class="wiki_link" href="/harry">harry</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Mystery">mystery</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard">buzzard</a> and <a class="wiki_link" href="/Starling%20temperaments#Thuja">thuja</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>s, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> 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 <a class="wiki_link" href="/thrush">thrush</a>, <a class="wiki_link" href="/bluebird">bluebird</a>, <a class="wiki_link" href="/aplonis">aplonis</a> and <a class="wiki_link" href="/jofur">jofur</a>.<br />

<br />

While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with <a class="wiki_link" href="/29edo">29edo</a>.<br />

@@ Line 1: / Line 1: @@
 <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:phylingual|phylingual]] and made on <tt>2012-07-13 08:36:00 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-13 12:16:01 UTC</tt>.<br>
-: The original revision id was <tt>352968254</tt>.<br>
+: The original revision id was <tt>353000072</tt>.<br>
 : The revision comment was: <tt></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">The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] 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 [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest [[edo|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[temperament]]s, and supplies the [[optimal patent val]] 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 [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].
+<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">The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] 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 [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest [[edo|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] 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 [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].
 While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].
@@ Line 76: / Line 76: @@
 || 57 || 1179.31 ||   ||   ||</pre></div>
 <h4>Original HTML 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;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="/Genesis%20scale"&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="/mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/temperament"&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="/thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/jofur"&gt;jofur&lt;/a&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;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="/thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/jofur"&gt;jofur&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;.&lt;br /&gt;