166edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 239297553 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 239299647 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:44:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239299647</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 8: | Line 8: | ||
<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 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]]. | ||
Its | 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]] close to the just interval 7:4. | |||
== Scales == | == Scales == | ||
| Line 17: | Line 17: | ||
<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 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 /> | ||
<br /> | <br /> | ||
Its | Its prime factorization is 166 = <a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/83edo">83</a>.<br /> | ||
<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> close to the just interval 7:4.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Scales"></a><!-- ws:end:WikiTextHeadingRule:0 --> Scales </h2> | <!-- 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></pre></div> | <ul><li><a class="wiki_link" href="/prisun">prisun</a></li></ul></body></html></pre></div> | ||