65edo: 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:

: This revision was by author [[User:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>~~2014~~-03-~~14 09~~:20:13 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 11:01:08 UTC</tt>.

: The original revision id was <tt>~~495766552~~</tt>.

: The original revision id was <tt>601622206</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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">~~[[toc|flat]]~~

<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">----

----

=65 tone equal temperament=

**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]~~, 393216/390625~~. In the [[7-limit]], there are two different maps; the first is <65 103 151 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.

**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is <65 103 151/1 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.

65edo approximates the intervals [[3_2|3/2]], [[5_4|5/4]], [[11_8|11/8]] and [[19_16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]].

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|| 23 || 424.6154 ||

|| 23 || 424.6154/1 ||

|| 24 || 443.0769 ||

|| 24 || 443.0769/1 ||

|| 25 || 461.5385 ||

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|| 26 || 480 ||

|| 27 || 498.4615 ||

|| 27 || 498.4615/1 ||

|| 28 || 516.9231 ||

|| 28 || 516.9231/1 ||

|| 29 || 535.3846 ||

|| 29 || 535.3846/1 ||

|| 30 || 553.8462 ||

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|| 31 || 572.3077 ||

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|| 42 || 775.3846/1 ||

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|| 55 || 1015.3846 ||

|| 56 || 1033.8462 ||

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[[photia12]]</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>65edo</title></head><body><a href="#x65 tone equal temperament">65 tone equal temperament</a> | <a href="#Intervals">Intervals</a> | <a href="#Scales">Scales</a>

~~<!-- ws:end:WikiTextTocRule:10 --~~><hr />

<h1 id="toc0"><a name="x65 tone equal temperament"></a>65 tone equal temperament</h1>

65edo divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the <a class="wiki_link" href="/schisma">schisma</a>, 32805/32768, the <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a>, 78732/78125, and the <a class="wiki_link" href="/wuerschmidt%20comma">wuerschmidt comma</a>~~, 393216/390625~~. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is &lt;65 103 151 182|, <a class="wiki_link" href="/tempering%20out">tempering out</a> 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the <a class="wiki_link" href="/5-limit">5-limit</a> over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit <a class="wiki_link" href="/wuerschmidt%20temperament">wuerschmidt temperament</a> (wurschmidt and worschmidt) these two mappings provide.

65edo divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the <a class="wiki_link" href="/schisma">schisma</a>, 32805/32768, the <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a>, 78732/78125, and the <a class="wiki_link" href="/wuerschmidt%20comma">wuerschmidt comma</a>. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is &lt;65 103 151/1 182|, <a class="wiki_link" href="/tempering%20out">tempering out</a> 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the <a class="wiki_link" href="/5-limit">5-limit</a> over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit <a class="wiki_link" href="/wuerschmidt%20temperament">wuerschmidt temperament</a> (wurschmidt and worschmidt) these two mappings provide.

65edo approximates the intervals <a class="wiki_link" href="/3_2">3/2</a>, <a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_8">11/8</a> and <a class="wiki_link" href="/19_16">19/16</a> well, so that it does a good job representing the 2.3.5.11.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. To this one may want to add 13/8 and 17/16, giving the <a class="wiki_link" href="/19-limit">19-limit</a> no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*65 subgroup</a> 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as <a class="wiki_link" href="/130edo">130edo</a>.

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<td>350.7692

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<td>369.2308

<td>369.2308/1

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<td>387.6923

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<td>406.1538

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<td>424.6154

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<td>443.0769

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<td>461.5385

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<td>498.4615

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<td>516.9231

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<td>572.3077

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<td>609.2308

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<td>664.6154

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<td>683.0769

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<td>701.5385

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<td>738.4615

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<td>941.5385

<td>941.5385/1

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<td>978.4615

<td>978.4615/1

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@@ 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2014-03-14 09:20:13 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 11:01:08 UTC</tt>.<br>
-: The original revision id was <tt>495766552</tt>.<br>
+: The original revision id was <tt>601622206</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">[[toc|flat]]
+<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">----
-----
 =&lt;span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;65 tone equal temperament&lt;/span&gt;=
-**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]], 393216/390625. In the [[7-limit]], there are two different maps; the first is &lt;65 103 151 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.
+**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is &lt;65 103 151/1 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.
 edo approximates the intervals [[3_2|3/2]], [[5_4|5/4]], [[11_8|11/8]] and [[19_16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]].
@@ Line 25: / Line 24: @@
 || 4 || 73.8462 ||
 || 5 || 92.3077 ||
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-|| 9 || 166.1538 ||
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-|| 10 || 184.6154 ||
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-|| 11 || 203.0769 ||
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-|| 12 || 221.5385 ||
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 || 13 || 240 ||
-|| 14 || 258.4615 ||
+|| 14 || 258.4615/1 ||
-|| 15 || 276.9231 ||
+|| 15 || 276.9231/1 ||
-|| 16 || 295.3846 ||
+|| 16 || 295.3846/1 ||
-|| 17 || 313.8462 ||
+|| 17 || 313.8462/1 ||
-|| 18 || 332.3077 ||
+|| 18 || 332.3077/1 ||
-|| 19 || 350.7692 ||
+|| 19 || 350.7692/1 ||
-|| 20 || 369.2308 ||
+|| 20 || 369.2308/1 ||
-|| 21 || 387.6923 ||
+|| 21 || 387.6923/1 ||
-|| 22 || 406.1538 ||
+|| 22 || 406.1538/1 ||
-|| 23 || 424.6154 ||
+|| 23 || 424.6154/1 ||
-|| 24 || 443.0769 ||
+|| 24 || 443.0769/1 ||
-|| 25 || 461.5385 ||
+|| 25 || 461.5385/1 ||
 || 26 || 480 ||
-|| 27 || 498.4615 ||
+|| 27 || 498.4615/1 ||
-|| 28 || 516.9231 ||
+|| 28 || 516.9231/1 ||
-|| 29 || 535.3846 ||
+|| 29 || 535.3846/1 ||
-|| 30 || 553.8462 ||
+|| 30 || 553.8462/1 ||
-|| 31 || 572.3077 ||
+|| 31 || 572.3077/1 ||
-|| 32 || 590.7692 ||
+|| 32 || 590.7692/1 ||
-|| 33 || 609.2308 ||
+|| 33 || 609.2308/1 ||
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+|| 34 || 627.6923/1 ||
-|| 35 || 646.1538 ||
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-|| 36 || 664.6154 ||
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-|| 37 || 683.0769 ||
+|| 37 || 683.0769/1 ||
-|| 38 || 701.5385 ||
+|| 38 || 701.5385/1 ||
 || 39 || 720 ||
-|| 40 || 738.4615 ||
+|| 40 || 738.4615/1 ||
-|| 41 || 756.9231 ||
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-|| 42 || 775.3846 ||
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-|| 43 || 793.8462 ||
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-|| 44 || 812.3077 ||
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-|| 46 || 849.2308 ||
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-|| 47 || 867.6923 ||
+|| 47 || 867.6923/1 ||
-|| 48 || 886.1538 ||
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-|| 49 || 904.6154 ||
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-|| 50 || 923.0769 ||
+|| 50 || 923.0769/1 ||
-|| 51 || 941.5385 ||
+|| 51 || 941.5385/1 ||
 || 52 || 960 ||
-|| 53 || 978.4615 ||
+|| 53 || 978.4615/1 ||
-|| 54 || 996.9231 ||
+|| 54 || 996.9231/1 ||
 || 55 || 1015.3846 ||
 || 56 || 1033.8462 ||
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 [[photia12]]</pre></div>
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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;65edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#x65 tone equal temperament"&gt;65 tone equal temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Scales"&gt;Scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&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;65edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;hr /&gt;
-&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;hr /&gt;
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 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x65 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;65 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;strong&gt;&lt;em&gt;65edo&lt;/em&gt;&lt;/strong&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, the &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;, 78732/78125, and the &lt;a class="wiki_link" href="/wuerschmidt%20comma"&gt;wuerschmidt comma&lt;/a&gt;, 393216/390625. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, there are two different maps; the first is &amp;lt;65 103 151 182|, &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &amp;lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit &lt;a class="wiki_link" href="/wuerschmidt%20temperament"&gt;wuerschmidt temperament&lt;/a&gt; (wurschmidt and worschmidt) these two mappings provide.&lt;br /&gt;
+&lt;strong&gt;&lt;em&gt;65edo&lt;/em&gt;&lt;/strong&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, the &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;, 78732/78125, and the &lt;a class="wiki_link" href="/wuerschmidt%20comma"&gt;wuerschmidt comma&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, there are two different maps; the first is &amp;lt;65 103 151/1 182|, &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &amp;lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit &lt;a class="wiki_link" href="/wuerschmidt%20temperament"&gt;wuerschmidt temperament&lt;/a&gt; (wurschmidt and worschmidt) these two mappings provide.&lt;br /&gt;
 &lt;br /&gt;
 edo approximates the intervals &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/19_16"&gt;19/16&lt;/a&gt; well, so that it does a good job representing the 2.3.5.11.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. To this one may want to add 13/8 and 17/16, giving the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*65 subgroup&lt;/a&gt; 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;.&lt;br /&gt;
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