32edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 219942206 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 219952490 - Original comment: ** |
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<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:genewardsmith|genewardsmith]] and made on <tt>2011-04-13 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-13 13:32:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>219952490</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> | ||
<h4>Original Wikitext content:</h4> | <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 //32 equal division// divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Parízek]]'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. | <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 //32 equal division// divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Parízek]]'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Parízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents, so 32edo does sixix about as well as sixix can be done. | ||
It also tempers out 2048/2025 in the 5-limit, and 50/49 with 64/63 in the 7-limit, which means it supports [[Diaschismic family|pajara temperament]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]. | |||
=Z function= | |||
Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with flattened octaves. This will ameliorate the fifth somewhat, at the expense of the third. | |||
[[image:plot32.png]] | |||
=Music= | =Music= | ||
[[http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg|Sixix] by Petr Parízek</pre></div> | [[http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg|Sixix]] by Petr Parízek</pre></div> | ||
<h4>Original HTML content:</h4> | <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>32edo</title></head><body>The <em>32 equal division</em> divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for <a class="wiki_link" href="/Petr%20Par%C3%ADzek">Petr Parízek</a>'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents.<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>32edo</title></head><body>The <em>32 equal division</em> divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for <a class="wiki_link" href="/Petr%20Par%C3%ADzek">Petr Parízek</a>'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Parízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents, so 32edo does sixix about as well as sixix can be done.<br /> | ||
<br /> | |||
It also tempers out 2048/2025 in the 5-limit, and 50/49 with 64/63 in the 7-limit, which means it supports <a class="wiki_link" href="/Diaschismic%20family">pajara temperament</a>, with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of <a class="wiki_link" href="/27edo">27edo</a>.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:0 -->Z function</h1> | |||
Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with flattened octaves. This will ameliorate the fifth somewhat, at the expense of the third.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:4:&lt;img src=&quot;/file/view/plot32.png/219952208/plot32.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot32.png/219952208/plot32.png" alt="plot32.png" title="plot32.png" /><!-- ws:end:WikiTextLocalImageRule:4 --><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg" rel="nofollow">Sixix</a> by Petr Parízek</body></html></pre></div> | |||
Revision as of 13:32, 13 April 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-04-13 13:32:02 UTC.
- The original revision id was 219952490.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The //32 equal division// divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Parízek]]'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Parízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents, so 32edo does sixix about as well as sixix can be done. It also tempers out 2048/2025 in the 5-limit, and 50/49 with 64/63 in the 7-limit, which means it supports [[Diaschismic family|pajara temperament]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]. =Z function= Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with flattened octaves. This will ameliorate the fifth somewhat, at the expense of the third. [[image:plot32.png]] =Music= [[http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg|Sixix]] by Petr Parízek
Original HTML content:
<html><head><title>32edo</title></head><body>The <em>32 equal division</em> divides the octave into 32 equal parts of precisely 37.5 cents each. While even advocates of less-common edos can struggle to find something about it worth noting, it does provide an excellent tuning for <a class="wiki_link" href="/Petr%20Par%C3%ADzek">Petr Parízek</a>'s sixix temperament, which tempers out the 5-limit sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Parízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents, so 32edo does sixix about as well as sixix can be done.<br /> <br /> It also tempers out 2048/2025 in the 5-limit, and 50/49 with 64/63 in the 7-limit, which means it supports <a class="wiki_link" href="/Diaschismic%20family">pajara temperament</a>, with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of <a class="wiki_link" href="/27edo">27edo</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:0 -->Z function</h1> Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with flattened octaves. This will ameliorate the fifth somewhat, at the expense of the third.<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:4:<img src="/file/view/plot32.png/219952208/plot32.png" alt="" title="" /> --><img src="/file/view/plot32.png/219952208/plot32.png" alt="plot32.png" title="plot32.png" /><!-- ws:end:WikiTextLocalImageRule:4 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h1> <a class="wiki_link_ext" href="http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg" rel="nofollow">Sixix</a> by Petr Parízek</body></html>