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:

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>2011-07-~~07 04~~:28:11 UTC</tt>.

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

: The original revision id was <tt>~~240327195~~</tt>.

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

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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 ~~EDO lists~~|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]].

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

Line 32:

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|| 0 || 0.00 || ||

|| 1 || 22.64 || ||

|| 2 || 45.28 || ||

|| 2 || 45.28 || [[Quartonic]] ||

|| 3 || 67.92 || ||

|| 4 || 90.57 || ||

|| 5 || 113.21 || ||

|| 6 || 135.85 || ||

|| 7 || 158.49 || ||

|| 7 || 158.49 || [[Hemikleismic]] ||

|| 8 || 181.13 || ||

|| 9 || 203.77 || ||

|| 10 || 226.42 || ||

|| 11 || 249.06 || ||

|| 11 || 249.06 || [[Hemischis]] ||

|| 12 || 271.70 || Orwell ||

|| 12 || 271.70 || [[Orwell]] ||

|| 13 || 294.34 || ||

|| 14 || 316.98 || Hanson ||

|| 14 || 316.98 || [[Hanson]]/[[Catakleismic]] ||

|| 15 || 339.62 || Amity ||

|| 15 || 339.62 || [[Amity]]/[[Hitchcock]] ||

|| 16 || 362.26 || ||

|| 17 || 384.91 || ||

Line 51:

Line 50:

|| 19 || 430.19 || ||

|| 20 || 452.83 || ||

|| 21 || 475.47 || ||

|| 21 || 475.47 || [[Vulture]]/[[Buzzard]] ||

|| 22 || 498.11 || ||

|| 23 || 520.75 || ||

|| 24 || 543.40 || ||

|| 25 || 566.04 || ||

|| 25 || 566.04 || [[Tricot]] ||

|| 26 || 588.68 || ||

|| 27 || 611.32 || ||

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Line 60:

|| 29 || 656.60 || ||

|| 30 || 679.25 || ||

|| 31 || 701.89 || Helmholtz ||

|| 31 || 701.89 || [[Helmholtz]]/[[Garibaldi]] ||

|| 32 || 724.53 || ||

|| 33 || 747.17 || ||

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<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>

~~ ~~

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

The famous 53 equal division 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 ~~EDO lists~~">zeta integral edo</a>.

The famous 53 equal division 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>.

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> .

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<td>45.28

</td>

<td>

<td><a class="wiki_link" href="/Quartonic">Quartonic</a>

</td>

</tr>

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<td>158.49

</td>

<td>

<td><a class="wiki_link" href="/Hemikleismic">Hemikleismic</a>

</td>

</tr>

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<td>249.06

</td>

<td>

<td><a class="wiki_link" href="/Hemischis">Hemischis</a>

</td>

</tr>

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<td>271.70

</td>

<td>Orwell

<td><a class="wiki_link" href="/Orwell">Orwell</a>

</td>

</tr>

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<td>316.98

</td>

<td>Hanson

<td><a class="wiki_link" href="/Hanson">Hanson</a>/<a class="wiki_link" href="/Catakleismic">Catakleismic</a>

</td>

</tr>

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<td>339.62

</td>

<td>Amity

<td><a class="wiki_link" href="/Amity">Amity</a>/<a class="wiki_link" href="/Hitchcock">Hitchcock</a>

</td>

</tr>

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<td>475.47

</td>

<td>

<td><a class="wiki_link" href="/Vulture">Vulture</a>/<a class="wiki_link" href="/Buzzard">Buzzard</a>

</td>

</tr>

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<td>566.04

</td>

<td>

<td><a class="wiki_link" href="/Tricot">Tricot</a>

</td>

</tr>

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<td>701.89

</td>

<td>Helmholtz

<td><a class="wiki_link" href="/Helmholtz">Helmholtz</a>/<a class="wiki_link" href="/Garibaldi">Garibaldi</a>

</td>

</tr>

@@ 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:hstraub|hstraub]] and made on <tt>2011-07-07 04:28:11 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-02 16:36:57 UTC</tt>.<br>
-: The original revision id was <tt>240327195</tt>.<br>
+: The original revision id was <tt>260681240</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 EDO lists|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]].
 EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]] .
@@ Line 32: / Line 31: @@
 || 0 || 0.00 ||   ||
 || 1 || 22.64 ||   ||
-|| 2 || 45.28 ||   ||
+|| 2 || 45.28 || [[Quartonic]] ||
 || 3 || 67.92 ||   ||
 || 4 || 90.57 ||   ||
 || 5 || 113.21 ||   ||
 || 6 || 135.85 ||   ||
-|| 7 || 158.49 ||   ||
+|| 7 || 158.49 || [[Hemikleismic]] ||
 || 8 || 181.13 ||   ||
 || 9 || 203.77 ||   ||
 || 10 || 226.42 ||   ||
-|| 11 || 249.06 ||   ||
+|| 11 || 249.06 || [[Hemischis]] ||
-|| 12 || 271.70 || Orwell ||
+|| 12 || 271.70 || [[Orwell]] ||
 || 13 || 294.34 ||   ||
-|| 14 || 316.98 || Hanson ||
+|| 14 || 316.98 || [[Hanson]]/[[Catakleismic]] ||
-|| 15 || 339.62 || Amity ||
+|| 15 || 339.62 || [[Amity]]/[[Hitchcock]] ||
 || 16 || 362.26 ||   ||
 || 17 || 384.91 ||   ||
@@ Line 51: / Line 50: @@
 || 19 || 430.19 ||   ||
 || 20 || 452.83 ||   ||
-|| 21 || 475.47 ||   ||
+|| 21 || 475.47 || [[Vulture]]/[[Buzzard]] ||
 || 22 || 498.11 ||   ||
 || 23 || 520.75 ||   ||
 || 24 || 543.40 ||   ||
-|| 25 || 566.04 ||   ||
+|| 25 || 566.04 || [[Tricot]] ||
 || 26 || 588.68 ||   ||
 || 27 || 611.32 ||   ||
@@ Line 61: / Line 60: @@
 || 29 || 656.60 ||   ||
 || 30 || 679.25 ||   ||
-|| 31 || 701.89 || Helmholtz ||
+|| 31 || 701.89 || [[Helmholtz]]/[[Garibaldi]] ||
 || 32 || 724.53 ||   ||
 || 33 || 747.17 ||   ||
@@ Line 94: / Line 93: @@
 <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;br /&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 EDO lists"&gt;zeta integral edo&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;
@@ Line 201: / Line 199: @@
          &lt;td&gt;45.28&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Quartonic"&gt;Quartonic&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 241: / Line 239: @@
          &lt;td&gt;158.49&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Hemikleismic"&gt;Hemikleismic&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 273: / Line 271: @@
          &lt;td&gt;249.06&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Hemischis"&gt;Hemischis&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 281: / Line 279: @@
          &lt;td&gt;271.70&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Orwell&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 297: / Line 295: @@
          &lt;td&gt;316.98&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Hanson&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Hanson"&gt;Hanson&lt;/a&gt;/&lt;a class="wiki_link" href="/Catakleismic"&gt;Catakleismic&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 305: / Line 303: @@
          &lt;td&gt;339.62&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Amity&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Amity"&gt;Amity&lt;/a&gt;/&lt;a class="wiki_link" href="/Hitchcock"&gt;Hitchcock&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 353: / Line 351: @@
          &lt;td&gt;475.47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Vulture"&gt;Vulture&lt;/a&gt;/&lt;a class="wiki_link" href="/Buzzard"&gt;Buzzard&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 385: / Line 383: @@
          &lt;td&gt;566.04&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Tricot"&gt;Tricot&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 433: / Line 431: @@
          &lt;td&gt;701.89&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Helmholtz&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Helmholtz"&gt;Helmholtz&lt;/a&gt;/&lt;a class="wiki_link" href="/Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;