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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The 166 equal temperament (in short 166-[[EDO|EDO]]) divides the [[Octave|octave]] into 166 equal steps of size 7.229 [[cent|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|marvel]], in both the [[11-limit|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|optimal patent val]] for all of these. In the [[13-limit|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]]. |
| 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>2012-02-11 02:03:34 UTC</tt>.<br>
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| : The original revision id was <tt>300719332</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">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]].
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| Its prime factorization is 166 = [[2edo|2]] * [[83edo|83]]. | | Its prime factorization is 166 = [[2edo|2]] * [[83edo|83]]. |
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| 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. | | 166edo (as 83edo) contains a very good approximation of the [[7/4|harmonic 7th]]. It's 0.15121 [[cent|cent]] flat of the just interval 7:4. |
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| == Scales == | | == Scales == |
| * [[prisun]]</pre></div>
| | <ul><li>[[prisun|prisun]]</li></ul> [[Category:166edo]] |
| <h4>Original HTML content:</h4>
| | [[Category:edo]] |
| <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 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 />
| | [[Category:gizzard]] |
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| | [[Category:marvel]] |
| Its prime factorization is 166 = <a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/83edo">83</a>.<br />
| | [[Category:theory]] |
| <br />
| | [[Category:wizard]] |
| 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 />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Scales"></a><!-- ws:end:WikiTextHeadingRule:0 --> Scales </h2>
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| <ul><li><a class="wiki_link" href="/prisun">prisun</a></li></ul></body></html></pre></div>
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The 166 equal temperament (in short 166-EDO) divides the octave into 166 equal steps of size 7.229 cents 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 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 gizzard, the 72&94 temperament, for which 166 is an excellent tuning through the 19 limit.
Its prime factorization is 166 = 2 * 83.
166edo (as 83edo) contains a very good approximation of the harmonic 7th. It's 0.15121 cent flat of the just interval 7:4.
Scales