121edo: 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:genewardsmith|genewardsmith]] and made on <tt>2011-08-~~05 14~~:00:08 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-06 03:35:49 UTC</tt>.<br>

: The original revision id was <tt>~~244515527~~</tt>.<br>

: The original revision id was <tt>244584971</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">The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[optimal patent val]] for 13-limit [[Mirkwai clan|grendel temperament]].

<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 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[optimal patent val]] for 13-limit [[Mirkwai clan|grendel temperament]]. It is [[consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.

Because it tempers out 540/539 it allows [[swetismic chords]], because it tempers out 325/324 it allows [[marveltwin triad|marveltwin chords]], because it tempers out 640/637 it allows [[huntmic chords]], because it tempers out 352/351 it allows [[minthmic chords]], because it tempers out 364/363 it allows [[gentle chords]], because it tempers out 676/675 it allows [[island tetrad|island chords]] and because it tempers out 1575/1573 it allows the [[nicolic tetrad]]. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.</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>121edo</title></head><body>The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 13-limit <a class="wiki_link" href="/Mirkwai%20clan">grendel temperament</a>.<br />

<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>121edo</title></head><body>The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 13-limit <a class="wiki_link" href="/Mirkwai%20clan">grendel temperament</a>. It is <a class="wiki_link" href="/consistent">consistent</a> through to the 19 odd limit and uniquely consistent to the 15 odd limit.<br />

<br />

Because it tempers out 540/539 it allows <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>, because it tempers out 325/324 it allows <a class="wiki_link" href="/marveltwin%20triad">marveltwin chords</a>, because it tempers out 640/637 it allows <a class="wiki_link" href="/huntmic%20chords">huntmic chords</a>, because it tempers out 352/351 it allows <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>, because it tempers out 364/363 it allows <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, because it tempers out 676/675 it allows <a class="wiki_link" href="/island%20tetrad">island chords</a> and because it tempers out 1575/1573 it allows the <a class="wiki_link" href="/nicolic%20tetrad">nicolic tetrad</a>. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.</body></html></pre></div>

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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:genewardsmith|genewardsmith]] and made on <tt>2011-08-05 14:00:08 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-06 03:35:49 UTC</tt>.<br>
-: The original revision id was <tt>244515527</tt>.<br>
+: The original revision id was <tt>244584971</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">The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374  and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[optimal patent val]] for 13-limit [[Mirkwai clan|grendel temperament]].
+<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 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374  and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[optimal patent val]] for 13-limit [[Mirkwai clan|grendel temperament]]. It is [[consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.
 Because it tempers out 540/539 it allows [[swetismic chords]], because it tempers out 325/324 it allows [[marveltwin triad|marveltwin chords]], because it tempers out 640/637 it allows [[huntmic chords]], because it tempers out 352/351 it allows [[minthmic chords]], because it tempers out 364/363 it allows [[gentle chords]], because it tempers out 676/675 it allows [[island tetrad|island chords]] and because it tempers out 1575/1573 it allows the [[nicolic tetrad]]. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;121edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374  and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 13-limit &lt;a class="wiki_link" href="/Mirkwai%20clan"&gt;grendel temperament&lt;/a&gt;.&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;121edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374  and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 13-limit &lt;a class="wiki_link" href="/Mirkwai%20clan"&gt;grendel temperament&lt;/a&gt;. It is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through to the 19 odd limit and uniquely consistent to the 15 odd limit.&lt;br /&gt;
 &lt;br /&gt;
 Because it tempers out 540/539 it allows &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;, because it tempers out 325/324 it allows &lt;a class="wiki_link" href="/marveltwin%20triad"&gt;marveltwin chords&lt;/a&gt;, because it tempers out 640/637 it allows &lt;a class="wiki_link" href="/huntmic%20chords"&gt;huntmic chords&lt;/a&gt;, because it tempers out 352/351 it allows &lt;a class="wiki_link" href="/minthmic%20chords"&gt;minthmic chords&lt;/a&gt;, because it tempers out 364/363 it allows &lt;a class="wiki_link" href="/gentle%20chords"&gt;gentle chords&lt;/a&gt;, because it tempers out 676/675 it allows &lt;a class="wiki_link" href="/island%20tetrad"&gt;island chords&lt;/a&gt; and because it tempers out 1575/1573 it allows the &lt;a class="wiki_link" href="/nicolic%20tetrad"&gt;nicolic tetrad&lt;/a&gt;. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.&lt;/body&gt;&lt;/html&gt;</pre></div>