69edo: Difference between revisions

Wikispaces>kai.lugheidh
**Imported revision 629810669 - Original comment: **
Wikispaces>xenwolf
**Imported revision 629821099 - Original comment: added links to interval pages**
Line 1: Line 1:
<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:kai.lugheidh|kai.lugheidh]] and made on <tt>2018-05-15 17:21:24 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2018-05-16 04:31:05 UTC</tt>.<br>
: The original revision id was <tt>629810669</tt>.<br>
: The original revision id was <tt>629821099</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>added links to interval pages</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">The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called  "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.
<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">The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called  "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.


In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as 126/125 maps to one step. It also supports the 12&amp;69 temperament tempering out 3125/3087 along with 81/80. In the 11-limit it tempers out 99/98, and supports the 31&amp;69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.</pre></div>
In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as [[126_125|126/125]] maps to one step. It also supports the 12&amp;69 temperament tempering out 3125/3087 along with [[81_80|81/80]]. In the 11-limit it tempers out [[99_98|99/98]], and supports the 31&amp;69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;69edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called  &amp;quot;the love-child of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt; and &lt;a class="wiki_link" href="/quarter-comma%20meantone"&gt;quarter-comma meantone&lt;/a&gt;&amp;quot;. As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to &amp;quot;Synch-Meantone&amp;quot;, or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.&lt;br /&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;69edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called  &amp;quot;the love-child of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt; and &lt;a class="wiki_link" href="/quarter-comma%20meantone"&gt;quarter-comma meantone&lt;/a&gt;&amp;quot;. As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to &amp;quot;Synch-Meantone&amp;quot;, or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as 126/125 maps to one step. It also supports the 12&amp;amp;69 temperament tempering out 3125/3087 along with 81/80. In the 11-limit it tempers out 99/98, and supports the 31&amp;amp;69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.&lt;/body&gt;&lt;/html&gt;</pre></div>
In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as &lt;a class="wiki_link" href="/126_125"&gt;126/125&lt;/a&gt; maps to one step. It also supports the 12&amp;amp;69 temperament tempering out 3125/3087 along with &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;. In the 11-limit it tempers out &lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt;, and supports the 31&amp;amp;69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.&lt;/body&gt;&lt;/html&gt;</pre></div>