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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-06 03:30:05 UTC</tt>.<br>
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| : The original revision id was <tt>244584749</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">**147edo** is the [[equal division of the octave]] into 147 parts of 8.1633 [[cent]]s each. It [[tempering out|tempers out]] 32805/32768 in the [[5-limit]]; 225/224 and 3125/3087 in the [[7-limit]]; 243/242 in the [[11-limit]]; 364/363 in the [[13-limit]]; 442/441 and 595/594 in the [[17-limit]]. It is the [[optimal patent val]] for the 11-limit 41&106 temperament, and is the smallest division which is uniquely [[consistent]] through the 17-limit.
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| 147 = [[3edo|3]] * [[7edo|7]]<span style="vertical-align: super;">2</span>, with divisors 3, 7, [[21edo|21]] and [[49edo|49]].
| | == Theory == |
| | 147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits. |
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| =Scales=
| | One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo. Additionally, it equates a stack of three [[256/243|pythagorean limmas]] with [[299/256]] and a stack of four with [[16/13]], tempering out 4294967296/4290323193 and the [[tridecapyth comma]]. |
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| [[baldy6]]
| | === Prime harmonics === |
| [[baldy11]]
| | {{Harmonics in equal|147}} |
| [[baldy17]]</pre></div>
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| <h4>Original HTML content:</h4>
| | === Subsets and supersets === |
| <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>147edo</title></head><body><strong>147edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 147 parts of 8.1633 <a class="wiki_link" href="/cent">cent</a>s each. It <a class="wiki_link" href="/tempering%20out">tempers out</a> 32805/32768 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 225/224 and 3125/3087 in the <a class="wiki_link" href="/7-limit">7-limit</a>; 243/242 in the <a class="wiki_link" href="/11-limit">11-limit</a>; 364/363 in the <a class="wiki_link" href="/13-limit">13-limit</a>; 442/441 and 595/594 in the <a class="wiki_link" href="/17-limit">17-limit</a>. It is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the 11-limit 41&amp;106 temperament, and is the smallest division which is uniquely <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit.<br />
| | Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}. |
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| 147 = <a class="wiki_link" href="/3edo">3</a> * <a class="wiki_link" href="/7edo">7</a><span style="vertical-align: super;">2</span>, with divisors 3, 7, <a class="wiki_link" href="/21edo">21</a> and <a class="wiki_link" href="/49edo">49</a>.<br /> | | [[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system. |
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>
| | == Scales == |
| <br />
| | * [[Baldy6]] |
| <a class="wiki_link" href="/baldy6">baldy6</a><br />
| | * [[Baldy11]] |
| <a class="wiki_link" href="/baldy11">baldy11</a><br />
| | * [[Baldy17]] |
| <a class="wiki_link" href="/baldy17">baldy17</a></body></html></pre></div>
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| | [[Category:Baldy]] |