53edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>2011-10-02 16:36:57 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:01:59 UTC</tt>.<br>

: The original revision id was <tt>~~260681240~~</tt>.<br>

: The original revision id was <tt>288887019</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>

<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">[[toc|flat]]

=Theory=

The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel family|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]].

The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel family|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] and the 16th [[prime numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].

53EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]] .

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<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>53edo</title></head><body><a href="#Theory">Theory</a> | <a href="#Just Approximation">Just Approximation</a> | <a href="#Intervals">Intervals</a> | <a href="#Compositions">Compositions</a>

~~<br />~~

<h1 id="toc0"><a name="Theory"></a>Theory</h1>

<h1 id="toc0"><a name="Theory"></a>Theory</h1>

The famous <em>53 equal division</em> divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a <a class="wiki_link" href="/5-limit">5-limit</a> system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Nuwell%20family">Big Brother</a> temperament, which tempers out both, as well as 11-limit <a class="wiki_link" href="/Semicomma%20family">orwell temperament</a>, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for <a class="wiki_link" href="/Marvel%20family">athene temperament</a>. It is the eighth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> and the 16th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/47edo">47edo</a> and coming before <a class="wiki_link" href="/59edo">59edo</a>.<br />

The famous <em>53 equal division</em> divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a <a class="wiki_link" href="/5-limit">5-limit</a> system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Nuwell%20family">Big Brother</a> temperament, which tempers out both, as well as 11-limit <a class="wiki_link" href="/Semicomma%20family">orwell temperament</a>, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for <a class="wiki_link" href="/Marvel%20family">athene temperament</a>. It is the eighth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>.<br />

<br />

53EDO has also found a certain dissemination as an EDO tuning for <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic/Turkish/Persian music</a> .<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-02 16:36:57 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:01:59 UTC</tt>.<br>
-: The original revision id was <tt>260681240</tt>.<br>
+: The original revision id was <tt>288887019</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>
 <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">[[toc|flat]]
 =Theory=
-The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel family|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]].
+The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel family|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] and the 16th [[prime numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].
 EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]] .
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 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;53edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt; | &lt;a href="#Just Approximation"&gt;Just Approximation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Theory&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Theory&lt;/h1&gt;
+  The famous &lt;em&gt;53 equal division&lt;/em&gt; divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/Nuwell%20family"&gt;Big Brother&lt;/a&gt; temperament, which tempers out both, as well as 11-limit &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell temperament&lt;/a&gt;, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for &lt;a class="wiki_link" href="/Marvel%20family"&gt;athene temperament&lt;/a&gt;. It is the eighth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; and the 16th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/59edo"&gt;59edo&lt;/a&gt;.&lt;br /&gt;
-  The famous &lt;em&gt;53 equal division&lt;/em&gt; divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/Nuwell%20family"&gt;Big Brother&lt;/a&gt; temperament, which tempers out both, as well as 11-limit &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell temperament&lt;/a&gt;, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for &lt;a class="wiki_link" href="/Marvel%20family"&gt;athene temperament&lt;/a&gt;. It is the eighth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 EDO has also found a certain dissemination as an EDO tuning for &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic/Turkish/Persian music&lt;/a&gt; .&lt;br /&gt;