166edo
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.
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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&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:<h2> --><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>