62edo: 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:~~JosephRuhf~~|~~JosephRuhf~~]] and made on <tt>2012-05-~~26 21~~:33:38 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-27 13:57:31 UTC</tt>.<br>

: The original revision id was <tt>~~339785034~~</tt>.<br>

: The original revision id was <tt>339876836</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">62 ~~edo, being two parallel tracks~~ of 31, is a 1/~~10-tone meantone system like 60~~, 64, ~~66b, 68b and 70b~~ and the ~~best of all the six since~~ 31 ~~is the "real" 1/5~~-~~tone~~ meantone ~~system (33 is nearly equivalent to fifths of 10/9 and 35 barely qualifies as fifths of a tone because its so~~-~~called wholetone is 11¢ flat of 10/9 and 30, 32 and 34 aren't even meantones)~~. It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7/31, which is a good generator for [[Orwell]]. This makes 8/62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</pre></div>

<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">62edo divides the octave into 62 equal parts of 19.355 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 temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone|hemimeantone]] temperaments.

It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for [[Orwell]]. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</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>62edo</title></head><body>62 ~~edo, being two parallel tracks~~ of 31, is a 1/~~10-tone meantone system like 60~~, 64, ~~66b, 68b and 70b~~ and the ~~best of all the six since~~ 31 ~~is the~~ &~~amp~~;~~quot~~;~~real~~&~~amp~~;~~quot~~; 1/5-~~tone meantone system (33 is nearly equivalent to fifths of 10~~/9 and ~~35 barely qualifies as fifths of~~ a ~~tone because its so~~-~~called wholetone is 11¢ flat of 10~~/~~9 and 30, 32 and 34 aren't even meantones)~~. It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a &quot;false&quot; quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7/31, which is a good generator for <a class="wiki_link" href="/Orwell">Orwell</a>. This makes 8/62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</body></html></pre></div>

<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>62edo divides the octave into 62 equal parts of 19.355 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 temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone">hemimeantone</a> temperaments.<br />

<br />

It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a &quot;false&quot; quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for <a class="wiki_link" href="/Orwell">Orwell</a>. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</body></html></pre></div>

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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:JosephRuhf|JosephRuhf]] and made on <tt>2012-05-26 21:33:38 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-27 13:57:31 UTC</tt>.<br>
-: The original revision id was <tt>339785034</tt>.<br>
+: The original revision id was <tt>339876836</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">62 edo, being two parallel tracks of 31, is a 1/10-tone meantone system like 60, 64, 66b, 68b and 70b and the best of all the six since 31 is the "real" 1/5-tone meantone system (33 is nearly equivalent to fifths of 10/9 and 35 barely qualifies as fifths of a tone because its so-called wholetone is 11¢ flat of 10/9 and 30, 32 and 34 aren't even meantones). It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7/31, which is a good generator for [[Orwell]]. This makes 8/62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</pre></div>
+<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">62edo divides the octave into 62 equal parts of 19.355 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 temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone|hemimeantone]] temperaments.
+It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for [[Orwell]]. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</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;62edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;62 edo, being two parallel tracks of 31, is a 1/10-tone meantone system like 60, 64, 66b, 68b and 70b and the best of all the six since 31 is the &amp;quot;real&amp;quot; 1/5-tone meantone system (33 is nearly equivalent to fifths of 10/9 and 35 barely qualifies as fifths of a tone because its so-called wholetone is 11¢ flat of 10/9 and 30, 32 and 34 aren't even meantones). It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a &amp;quot;false&amp;quot; quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7/31, which is a good generator for &lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt;. This makes 8/62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;62edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;62edo divides the octave into 62 equal parts of 19.355 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 &lt;a class="wiki_link" href="/31%20comma%20temperaments#Gallium"&gt;gallium&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-Semivalentine"&gt;semivalentine&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone"&gt;hemimeantone&lt;/a&gt; temperaments.&lt;br /&gt;
+&lt;br /&gt;
+It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a &amp;quot;false&amp;quot; quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for &lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt;. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.&lt;/body&gt;&lt;/html&gt;</pre></div>