62edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 340003066 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 368789204 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-09-29 03:50:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>368789204</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">=<span style="color: #790080; font-family: | <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">=<span style="color: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span>= | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | ||
Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel. | Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel. | ||
===**62-EDO Intervals**=== | ===**62-EDO Intervals**=== | ||
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* **‡** = Semisharp (1/4-tone up) | * **‡** = Semisharp (1/4-tone up) | ||
* **b** = Flat (5/8-tone down) | * **b** = Flat (5/8-tone down) | ||
* **◊** = Node ( | * **◊** = Node (sharp/flat blindspot 1/2-tone) | ||
* **#** = Sharp (5/8-tone up) | * **#** = Sharp (5/8-tone up) | ||
* **v** = Semiflat (1/4-tone down) | * **v** = Semiflat (1/4-tone down) | ||
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|| 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | || 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | ||
<h4>Original HTML content:</h4> | <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>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #790080; font-family: | <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>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | ||
<br /> | <br /> | ||
Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel. <br /> | Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | ||
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<td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node ( | <td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node (sharp/flat blindspot 1/2-tone)</li><li><strong>#</strong> = Sharp (5/8-tone up)</li><li><strong>v</strong> = Semiflat (1/4-tone down)</li><li><strong>⌐</strong> = Thin (1/8-tone down)</li></ul></td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||