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147edo: Difference between revisions

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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>2011-03-26 00:41:56 UTC</tt>.<br>
: The original revision id was <tt>214141676</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 //147 equal division// divides the octave into 147 equal parts of 8.163 cents each. It 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&amp;106 temperament.


147 = 3 * 49, with divisors 3, 7, 21 and 49.</pre></div>
== Theory ==
<h4>Original HTML content:</h4>
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 &amp; 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.
<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;147edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;147 equal division&lt;/em&gt; divides the octave into 147 equal parts of 8.163 cents each. It 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 &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the 11-limit 41&amp;amp;106 temperament.&lt;br /&gt;
 
&lt;br /&gt;
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]].
147 = 3 * 49, with divisors 3, 7, 21 and 49.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Prime harmonics ===
{{Harmonics in equal|147}}
 
=== Subsets and supersets ===
Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}.
 
[[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system.
 
== Scales ==
* [[Baldy6]]
* [[Baldy11]]
* [[Baldy17]]
 
[[Category:Baldy]]
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