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:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2012-05-~~27 20~~:34:06 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-28 02:28:38 UTC</tt>.<br>

: The original revision id was <tt>~~339937392~~</tt>.<br>

: The original revision id was <tt>340003066</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>

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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.

~~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~~.

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**===

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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 />

~~It is also strong as an 1/8-tone <a class="wiki_link" href="/Armodue-Hornbostel">Armodue-Hornbostel</a> 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 ~~&lt~~;~~a class="wiki_link" href="/Orwell"~~>~~Orwell&~~lt;~~/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~~.<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 />

<h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><strong>62-EDO Intervals</strong></h3>

@@ 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-05-27 20:34:06 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-28 02:28:38 UTC</tt>.<br>
-: The original revision id was <tt>339937392</tt>.<br>
+: The original revision id was <tt>340003066</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>
@@ Line 10: / Line 10: @@
 edo 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.
-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.
+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.
 ===**62-EDO Intervals**===
@@ Line 90: / Line 90: @@
 edo 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 &lt;a class="wiki_link" href="/31%20comma%20temperaments#Gallium"&gt;gallium&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine"&gt;semivalentine&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone"&gt;hemimeantone&lt;/a&gt; temperaments.&lt;br /&gt;
 &lt;br /&gt;
-It is also strong as an 1/8-tone &lt;a class="wiki_link" href="/Armodue-Hornbostel"&gt;Armodue-Hornbostel&lt;/a&gt; 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;br /&gt;
+Using the 35\62 generator, which leads to the &amp;lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &amp;lt;62 97 143 172| supports hornbostel. &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x62 tone equal temperament--62-EDO Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;strong&gt;62-EDO Intervals&lt;/strong&gt;&lt;/h3&gt;