441edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 340729764 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 346000418 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-17 16:47:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>346000418</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> | ||
<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">**441edo** is the [[equal division of the octave]] into 441 parts of 2.721 [[cent]]s each. It is a very strong [[7-limit]] system; strong enough to qualify as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]]. In the [[5-limit]] It [[tempering out|tempers out]] the hemithirds [[comma]], |38 -2 -15>, the ennealimma, |1 -27 18>, whoosh, |37 25 -33>, and egads, |-36 -52 51>. In the 7-limit it tempers out 2401/2400, 4375/4374, 420175/419904 and 250047/250000, so that it supports [[Ragismic microtemperaments#Ennealimmal|ennealimmal temperament]]. In the [[11-limit]] it tempers out 4000/3993, and in the 13-limit, 1575/1573, 2080/2079 and 4225/4224. It provides the [[optimal patent val]] for 11- and [[13-limit]] [[Ragismic microtemperaments#Ennealimmal|semiennealimmal temperament]], and the 7-limit 41&359 temperament. Since it tempers out 1575/1573, the nicola, it allows the [[nicolic tetrad]]. | <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">**441edo** is the [[equal division of the octave]] into 441 parts of 2.721 [[cent]]s each. It is a very strong [[7-limit]] system; strong enough to qualify as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]]. In the [[5-limit]] It [[tempering out|tempers out]] the hemithirds [[comma]], |38 -2 -15>, the ennealimma, |1 -27 18>, whoosh, |37 25 -33>, and egads, |-36 -52 51>. In the 7-limit it tempers out 2401/2400, 4375/4374, 420175/419904 and 250047/250000, so that it supports [[Ragismic microtemperaments#Ennealimmal|ennealimmal temperament]]. In the [[11-limit]] it tempers out 4000/3993, and in the 13-limit, 1575/1573, 2080/2079 and 4225/4224. It provides the [[optimal patent val]] for 11- and [[13-limit]] [[Ragismic microtemperaments#Ennealimmal|semiennealimmal temperament]], and the 7-limit 41&359 temperament. Since it tempers out 1575/1573, the nicola, it allows the [[nicolic tetrad]]. | ||
The steps of 441 are only 1/30 of a cent sharp of 1/8 syntonic comma. Lowering the fifth, which is only 1/12 of a cent sharp, by two steps gives a generator, 256\441, close to 1/4 comma meantone. Like [[205edo]] but even more accurately, 441 can be used as a basis for a Vicentino style "adaptive JI" system. | |||
441 factors into primes as [[3edo|3]]<span style="vertical-align: super;">2</span> · [[7edo|7]]<span style="vertical-align: super;">2</span>, and has divisors 3, 7, [[9edo|9]], [[21edo|21]], [[49edo|49]], 63 and 147.</pre></div> | 441 factors into primes as [[3edo|3]]<span style="vertical-align: super;">2</span> · [[7edo|7]]<span style="vertical-align: super;">2</span>, and has divisors 3, 7, [[9edo|9]], [[21edo|21]], [[49edo|49]], 63 and 147.</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>441edo</title></head><body><strong>441edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 441 parts of 2.721 <a class="wiki_link" href="/cent">cent</a>s each. It is a very strong <a class="wiki_link" href="/7-limit">7-limit</a> system; strong enough to qualify as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a>. In the <a class="wiki_link" href="/5-limit">5-limit</a> It <a class="wiki_link" href="/tempering%20out">tempers out</a> the hemithirds <a class="wiki_link" href="/comma">comma</a>, |38 -2 -15&gt;, the ennealimma, |1 -27 18&gt;, whoosh, |37 25 -33&gt;, and egads, |-36 -52 51&gt;. In the 7-limit it tempers out 2401/2400, 4375/4374, 420175/419904 and 250047/250000, so that it supports <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">ennealimmal temperament</a>. In the <a class="wiki_link" href="/11-limit">11-limit</a> it tempers out 4000/3993, and in the 13-limit, 1575/1573, 2080/2079 and 4225/4224. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11- and <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">semiennealimmal temperament</a>, and the 7-limit 41&amp;359 temperament. Since it tempers out 1575/1573, the nicola, it allows the <a class="wiki_link" href="/nicolic%20tetrad">nicolic tetrad</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>441edo</title></head><body><strong>441edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 441 parts of 2.721 <a class="wiki_link" href="/cent">cent</a>s each. It is a very strong <a class="wiki_link" href="/7-limit">7-limit</a> system; strong enough to qualify as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a>. In the <a class="wiki_link" href="/5-limit">5-limit</a> It <a class="wiki_link" href="/tempering%20out">tempers out</a> the hemithirds <a class="wiki_link" href="/comma">comma</a>, |38 -2 -15&gt;, the ennealimma, |1 -27 18&gt;, whoosh, |37 25 -33&gt;, and egads, |-36 -52 51&gt;. In the 7-limit it tempers out 2401/2400, 4375/4374, 420175/419904 and 250047/250000, so that it supports <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">ennealimmal temperament</a>. In the <a class="wiki_link" href="/11-limit">11-limit</a> it tempers out 4000/3993, and in the 13-limit, 1575/1573, 2080/2079 and 4225/4224. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11- and <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">semiennealimmal temperament</a>, and the 7-limit 41&amp;359 temperament. Since it tempers out 1575/1573, the nicola, it allows the <a class="wiki_link" href="/nicolic%20tetrad">nicolic tetrad</a>.<br /> | ||
<br /> | |||
The steps of 441 are only 1/30 of a cent sharp of 1/8 syntonic comma. Lowering the fifth, which is only 1/12 of a cent sharp, by two steps gives a generator, 256\441, close to 1/4 comma meantone. Like <a class="wiki_link" href="/205edo">205edo</a> but even more accurately, 441 can be used as a basis for a Vicentino style &quot;adaptive JI&quot; system.<br /> | |||
<br /> | <br /> | ||
441 factors into primes as <a class="wiki_link" href="/3edo">3</a><span style="vertical-align: super;">2</span> · <a class="wiki_link" href="/7edo">7</a><span style="vertical-align: super;">2</span>, and has divisors 3, 7, <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/49edo">49</a>, 63 and 147.</body></html></pre></div> | 441 factors into primes as <a class="wiki_link" href="/3edo">3</a><span style="vertical-align: super;">2</span> · <a class="wiki_link" href="/7edo">7</a><span style="vertical-align: super;">2</span>, and has divisors 3, 7, <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/49edo">49</a>, 63 and 147.</body></html></pre></div> | ||