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:~~hstraub~~|~~hstraub~~]] and made on <tt>2011-06-~~22 07~~:08:59 UTC</tt>.

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-30 17:59:56 UTC</tt>.

: The original revision id was <tt>~~238143293~~</tt>.

: The original revision id was <tt>239563915</tt>.

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

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=65 tone equal temperament=

//65edo// divides the [[octave]] into 65 equal parts of 18.462 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 18.462 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 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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<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 18.462 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|, 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 <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 18.462 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 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>.

@@ 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:hstraub|hstraub]] and made on <tt>2011-06-22 07:08:59 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-30 17:59:56 UTC</tt>.<br>
-: The original revision id was <tt>238143293</tt>.<br>
+: The original revision id was <tt>239563915</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 11: / Line 11: @@
 =&lt;span style="color: #750063;"&gt;65 tone equal temperament&lt;/span&gt;=
-//65edo// divides the [[octave]] into 65 equal parts of 18.462 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 18.462 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.
 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 92: / Line 92: @@
 &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;"&gt;65 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;em&gt;65edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.462 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|, tempering out 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;em&gt;65edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.462 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;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;