1200edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 342578710 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 342579934 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-06-04 17: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-04 17:14:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>342579934</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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;white-space: pre-wrap ! important" class="old-revision-html">The //1200 division// divides the octave in 1200 equal parts of exactly 1 [[cent]] each. It is notable mostly because it is the equal division corresponding to cents. | <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 //1200 division// divides the octave in 1200 equal parts of exactly 1 [[cent]] each. It is notable mostly because it is the equal division corresponding to cents. | ||
1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit[[tonality diamond| tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val <1200 1902 2786 3369 4141|. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]]. In the 7-limit, it provides a val, 1200cd, | 1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit[[tonality diamond| tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val <1200 1902 2786 3369 4141|. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]]. In the 7-limit, it provides a val, 1200cd, which is extremely closely close to the 7-limit POTE tuning of [[Kleismic family#Quadritikleismic|quadritikleismic temperament]]: <1200 1902 2785 3368|. It also provides the optimal patent val for the 224&752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.</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>1200edo</title></head><body>The <em>1200 division</em> divides the octave in 1200 equal parts of exactly 1 <a class="wiki_link" href="/cent">cent</a> each. It is notable mostly because it is the equal division corresponding to cents.<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>1200edo</title></head><body>The <em>1200 division</em> divides the octave in 1200 equal parts of exactly 1 <a class="wiki_link" href="/cent">cent</a> each. It is notable mostly because it is the equal division corresponding to cents.<br /> | ||
<br /> | <br /> | ||
1200edo is uniquely <a class="wiki_link" href="/consistent">consistent</a> through the <a class="wiki_link" href="/11-limit">11-limit</a>, which means the intervals of the 11-limit<a class="wiki_link" href="/tonality%20diamond"> tonality diamond</a>, and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val &lt;1200 1902 2786 3369 4141|. It is <a class="wiki_link" href="/contorted">contorted</a> in the <a class="wiki_link" href="/5-limit">5-limit</a>, having the same mapping as 600edo. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by <a class="wiki_link" href="/171edo">171edo</a>. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by <a class="wiki_link" href="/494edo">494edo</a>. In the 7-limit, it provides a val, 1200cd, | 1200edo is uniquely <a class="wiki_link" href="/consistent">consistent</a> through the <a class="wiki_link" href="/11-limit">11-limit</a>, which means the intervals of the 11-limit<a class="wiki_link" href="/tonality%20diamond"> tonality diamond</a>, and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val &lt;1200 1902 2786 3369 4141|. It is <a class="wiki_link" href="/contorted">contorted</a> in the <a class="wiki_link" href="/5-limit">5-limit</a>, having the same mapping as 600edo. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by <a class="wiki_link" href="/171edo">171edo</a>. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by <a class="wiki_link" href="/494edo">494edo</a>. In the 7-limit, it provides a val, 1200cd, which is extremely closely close to the 7-limit POTE tuning of <a class="wiki_link" href="/Kleismic%20family#Quadritikleismic">quadritikleismic temperament</a>: &lt;1200 1902 2785 3368|. It also provides the optimal patent val for the 224&amp;752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.</body></html></pre></div> | ||