166edo: Difference between revisions

Revision as of 02:03, 11 February 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2012-02-11 02:03:34 UTC.

The original revision id was 300719332.

The revision comment was:

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Original Wikitext content:

The 166 equal temperament (in short 166-[[EDO]]) divides the [[octave]] into 166 equal steps of size 7.229 [[cent]]s each. Its principle interest lies in the usefulness of its approximations; it tempers out 1600000/1594323, 225/224, 385/384, 540/539, 4000/3993, 325/324 and 729/728. It is an excellent tuning for the rank three temperament [[marvel]], in both the [[11-limit]] and in the 13-limit extension [[Marvel family#Hecate|hecate]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[optimal patent val]] for all of these. In the [[13-limit]] it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and  tempering out both gives [[Marvel temperaments|gizzard]], the 72&94 temperament, for which 166 is an excellent tuning through the [[19-limit|19 limit]].

Its prime factorization is 166 = [[2edo|2]] * [[83edo|83]].

166edo (as 83edo) contains a very good approximation of the [[7_4|harmonic 7th]]. It's 0.15121 [[cent]] flat of the just interval 7:4.

== Scales ==
* [[prisun]]

Original HTML content:

<html><head><title>166edo</title></head><body>The 166 equal temperament (in short 166-<a class="wiki_link" href="/EDO">EDO</a>) divides the <a class="wiki_link" href="/octave">octave</a> into 166 equal steps of size 7.229 <a class="wiki_link" href="/cent">cent</a>s each. Its principle interest lies in the usefulness of its approximations; it tempers out 1600000/1594323, 225/224, 385/384, 540/539, 4000/3993, 325/324 and 729/728. It is an excellent tuning for the rank three temperament <a class="wiki_link" href="/marvel">marvel</a>, in both the <a class="wiki_link" href="/11-limit">11-limit</a> and in the 13-limit extension <a class="wiki_link" href="/Marvel%20family#Hecate">hecate</a>, and the rank two temperament wizard, which also tempers out 4000/3993, giving the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for all of these. In the <a class="wiki_link" href="/13-limit">13-limit</a> it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and  tempering out both gives <a class="wiki_link" href="/Marvel%20temperaments">gizzard</a>, the 72&amp;94 temperament, for which 166 is an excellent tuning through the <a class="wiki_link" href="/19-limit">19 limit</a>.<br />
<br />
Its prime factorization is 166 = <a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/83edo">83</a>.<br />
<br />
166edo (as 83edo) contains a very good approximation of the <a class="wiki_link" href="/7_4">harmonic 7th</a>. It's 0.15121 <a class="wiki_link" href="/cent">cent</a> flat of the just interval 7:4.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Scales"></a><!-- ws:end:WikiTextHeadingRule:0 --> Scales </h2>
<ul><li><a class="wiki_link" href="/prisun">prisun</a></li></ul></body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-10-28 20:45:28 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-11 02:03:34 UTC</tt>.<br>
-: The original revision id was <tt>269750516</tt>.<br>
+: The original revision id was <tt>300719332</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>
@@ Line 10: / Line 10: @@
 Its prime factorization is 166 = [[2edo|2]] * [[83edo|83]].
-edo (as 83edo) contains a very good approximation of the [[7_4|harmonic 7th]]. It's 0.15121 [[cent]] close to the just interval 7:4.
+edo (as 83edo) contains a very good approximation of the [[7_4|harmonic 7th]]. It's 0.15121 [[cent]] flat of the just interval 7:4.
 == Scales ==
@@ Line 19: / Line 19: @@
 Its prime factorization is 166 = &lt;a class="wiki_link" href="/2edo"&gt;2&lt;/a&gt; * &lt;a class="wiki_link" href="/83edo"&gt;83&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-edo (as 83edo) contains a very good approximation of the &lt;a class="wiki_link" href="/7_4"&gt;harmonic 7th&lt;/a&gt;. It's 0.15121 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt; close to the just interval 7:4.&lt;br /&gt;
+edo (as 83edo) contains a very good approximation of the &lt;a class="wiki_link" href="/7_4"&gt;harmonic 7th&lt;/a&gt;. It's 0.15121 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt; flat of the just interval 7:4.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; Scales &lt;/h2&gt;
 &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/prisun"&gt;prisun&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

166edo: Difference between revisions

Revision as of 02:03, 11 February 2012

IMPORTED REVISION FROM WIKISPACES

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