32edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 219952490 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 220050658 - 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 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-13 18:09:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>220050658</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. 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. | <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 and which gives equal error to fifths and major thirds, 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]]. | 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= | =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 | Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1189.617 cents. This will improve the fifth, at the expense of the third. | ||
[[image:plot32.png]] | [[image:plot32.png]] | ||
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[[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. 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 /> | <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 and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done.<br /> | ||
<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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:0 -->Z function</h1> | <!-- 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 | Below is a plot of the Z function, showing how its peak value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1189.617 cents. This will improve the fifth, 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 /> | <!-- 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 /> | ||
Revision as of 18:09, 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 18:09:32 UTC.
- The original revision id was 220050658.
- 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 and which gives equal error to fifths and major thirds, 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 octaves flattened to 1189.617 cents. This will improve the fifth, 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 and which gives equal error to fifths and major thirds, 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 octaves flattened to 1189.617 cents. This will improve the fifth, 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>