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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''441edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 441 parts of 2.721 [[cent|cent]]s each. It is a very strong [[7-limit|7-limit]] system; strong enough to qualify as a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]]. It is also very strong simply considered as a 5-limit system; it is the first division past 118 with a lower [[5-limit|5-limit]] [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. In the 5-limit It [[tempering_out|tempers out]] the hemithirds [[Comma|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|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|optimal patent val]] for 11- and [[13-limit|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|nicolic tetrad]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-16 10:26:41 UTC</tt>.<br>
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| : The original revision id was <tt>556757355</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">**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]]. It is also very strong simply considered as a 5-limit system; it is the first division past 118 with a lower [[5-limit]] [[Tenney-Euclidean temperament measures#TE simple badness|relative error]]. 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]].
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| 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. | | 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|205edo]] but even more accurately, 441 can be used as a basis for a Vicentino style "adaptive JI" system. |
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| 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. |
| <h4>Original HTML content:</h4>
| | [[Category:441edo]] |
| <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>. It is also very strong simply considered as a 5-limit system; it is the first division past 118 with a lower <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a>. In the 5-limit 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 />
| | [[Category:edo]] |
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| | [[Category:ennealimmal]] |
| 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 />
| | [[Category:hemithirds]] |
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| | [[Category:nicola]] |
| 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>
| | [[Category:semienealimmal]] |
| | [[Category:zeta]] |
441edo is the equal division of the octave into 441 parts of 2.721 cents each. It is a very strong 7-limit system; strong enough to qualify as a zeta peak edo. It is also very strong simply considered as a 5-limit system; it is the first division past 118 with a lower 5-limit relative error. In the 5-limit It 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 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 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 32 · 72, and has divisors 3, 7, 9, 21, 49, 63 and 147.