65edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 232739088 - Original comment: links to some intervals added** |
Wikispaces>hstraub **Imported revision 238143293 - 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:hstraub|hstraub]] and made on <tt>2011-06-22 07:08:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238143293</tt>.<br> | ||
: The revision comment was: <tt> | : 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: #750063 | <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]] | ||
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=<span style="color: #750063;">65 tone equal temperament</span>= | |||
//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]]. | 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]]. | ||
=Intervals= | |||
|| Degrees of 65-EDO || Cents value || | || Degrees of 65-EDO || Cents value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
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|| 62 || 1144,6154 || | || 62 || 1144,6154 || | ||
|| 63 || 1163,0769 || | || 63 || 1163,0769 || | ||
|| 64 || 1181,5385 ||</pre></div> | || 64 || 1181,5385 || | ||
=Scales= | |||
[[photia7]] | |||
[[photia12]]</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>65edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x65 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #750063 | <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><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#x65 tone equal temperament">65 tone equal temperament</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
<em>65edo</em> 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.<br /> | <!-- ws:end:WikiTextTocRule:10 --><hr /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x65 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #750063;">65 tone equal temperament</span></h1> | |||
<br /> | |||
<em>65edo</em> 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.<br /> | |||
<br /> | <br /> | ||
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>.<br /> | 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>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1> | ||
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</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->Scales</h1> | |||
<a class="wiki_link" href="/photia7">photia7</a><br /> | |||
<a class="wiki_link" href="/photia12">photia12</a></body></html></pre></div> | |||