166edo: Difference between revisions

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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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-06-~~29 07~~:44:37 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 20:40:37 UTC</tt>.<br>

: The original revision id was <tt>~~239299647~~</tt>.<br>

: The original revision id was <tt>269749942</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 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 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament [[marvel]], in both the [[11-limit]] and the [[13-limit]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[optimal patent val]] for both of these. In the [[13-limit]] it tempers out 325/324, leading to ~~13-limit marvel~~, and 1573/1568, leading to marvell. Tempering out both gives [[Marvel temperaments|gizzard]], the 72&94 temperament, for which 166 is an excellent tuning through the [[19-limit|19 limit]].

<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 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 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament [[marvel]], in both the [[11-limit]] and the [[13-limit]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[optimal patent val]] for both of these. In the [[13-limit]] it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell. 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]].

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* [[prisun]]</pre></div>

<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>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 225/224, 385/384, 540/539 and 4000/3993. 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 the <a class="wiki_link" href="/13-limit">13-limit</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 both of these. In the <a class="wiki_link" href="/13-limit">13-limit</a> it tempers out 325/324, leading to ~~13-limit marvel~~, and 1573/1568, leading to marvell. 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 />

<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>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 225/224, 385/384, 540/539 and 4000/3993. 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 the <a class="wiki_link" href="/13-limit">13-limit</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 both 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. 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 />

@@ Line 1: / Line 1: @@
 <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:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:44:37 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 20:40:37 UTC</tt>.<br>
-: The original revision id was <tt>239299647</tt>.<br>
+: The original revision id was <tt>269749942</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 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 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament [[marvel]], in both the [[11-limit]] and the [[13-limit]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[optimal patent val]] for both of these. In the [[13-limit]] it tempers out 325/324, leading to 13-limit marvel, and 1573/1568, leading to marvell. Tempering out both gives [[Marvel temperaments|gizzard]], the 72&amp;94 temperament, for which 166 is an excellent tuning through the [[19-limit|19 limit]].
+<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 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 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament [[marvel]], in both the [[11-limit]] and the [[13-limit]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[optimal patent val]] for both of these. In the [[13-limit]] it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell. Tempering out both gives [[Marvel temperaments|gizzard]], the 72&amp;94 temperament, for which 166 is an excellent tuning through the [[19-limit|19 limit]].
 Its prime factorization is 166 = [[2edo|2]] * [[83edo|83]].
@@ Line 15: / Line 15: @@
 * [[prisun]]</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;166edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 166 equal temperament (in short 166-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;) divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 166 equal steps of size 7.229 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. Its principle interest lies in the usefulness of its approximations; it tempers out 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament &lt;a class="wiki_link" href="/marvel"&gt;marvel&lt;/a&gt;, in both the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, and the rank two temperament wizard, which also tempers out 4000/3993, giving the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for both of these. In the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; it tempers out 325/324, leading to 13-limit marvel, and 1573/1568, leading to marvell. Tempering out both gives &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;gizzard&lt;/a&gt;, the 72&amp;amp;94 temperament, for which 166 is an excellent tuning through the &lt;a class="wiki_link" href="/19-limit"&gt;19 limit&lt;/a&gt;.&lt;br /&gt;
+<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;166edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 166 equal temperament (in short 166-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;) divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 166 equal steps of size 7.229 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. Its principle interest lies in the usefulness of its approximations; it tempers out 225/224, 385/384, 540/539 and 4000/3993. It is an excellent tuning for the rank three temperament &lt;a class="wiki_link" href="/marvel"&gt;marvel&lt;/a&gt;, in both the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, and the rank two temperament wizard, which also tempers out 4000/3993, giving the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for both of these. In the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell. Tempering out both gives &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;gizzard&lt;/a&gt;, the 72&amp;amp;94 temperament, for which 166 is an excellent tuning through the &lt;a class="wiki_link" href="/19-limit"&gt;19 limit&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 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;