253edo: 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-05-~~19 17~~:27:47 UTC</tt>.<br>

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:29:20 UTC</tt>.<br>

: The original revision id was <tt>~~230140130~~</tt>.<br>

: The original revision id was <tt>240943537</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">=<span style="color: #630080; font-size: 113%;">253 tone equal temperament</span>=

<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">=<span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">253 tone equal temperament</span>=

//~~253edo~~// divides the octave into 253 steps of 4.743083 ~~cents~~. It approximates the fifth by **148\253**, which is 701.976285 Cents, a **0.004487 Cents sharp**. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic family|sesquiquartififths]] temperament.

**//253-EDO//** or **253-tET** divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by **148\253**, which is 701.976285 Cents, a **0.004487 Cents sharp**. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic family|sesquiquartififths]] temperament.

__**253 tone equal modes**__

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31 31 31 18 31 31 31 31 18: [[7L 2s]] MOS ([[Armodue-Mesotonic]] Tuning)

26 26 15 26 26 26 15 26 26 26 15: [[8L 3s]] MOS ([[sensi11|Sensi-11]] [or Undecimal Triatonic])

20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s]] MOS [[[WITNOTS]] Tuning (Tetradecimal Triatonic scale)]</pre></div>

20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s]] MOS [[[WITNOTS]] Tuning (Tetradecimal Triatonic scale)]

**PRIME FACTORIZATION:**

253 = [[11edo|11]] * [[23edo|23]]</pre></div>

<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>253edo</title></head><body><h1 id="toc0"><a name="x253 tone equal temperament"></a><span style="color: #630080; font-size: 113%;">253 tone equal temperament</span></h1>

<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>253edo</title></head><body><h1 id="toc0"><a name="x253 tone equal temperament"></a><span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">253 tone equal temperament</span></h1>

<br />

<em>~~253edo~~</em> divides the octave into 253 steps of 4.743083 ~~cents~~. It approximates the fifth by <strong>148\253</strong>, which is 701.976285 Cents, a <strong>0.004487 Cents sharp</strong>. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit <a class="wiki_link" href="/Schismatic%20family">sesquiquartififths</a> temperament.<br />

<strong><em>253-EDO</em></strong> or <strong>253-tET</strong> divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by <strong>148\253</strong>, which is 701.976285 Cents, a <strong>0.004487 Cents sharp</strong>. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit <a class="wiki_link" href="/Schismatic%20family">sesquiquartififths</a> temperament.<br />

<br />

<u><strong>253 tone equal modes</strong></u><br />

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31 31 31 18 31 31 31 31 18: <a class="wiki_link" href="/7L%202s">7L 2s</a> MOS (<a class="wiki_link" href="/Armodue-Mesotonic">Armodue-Mesotonic</a> Tuning)<br />

26 26 15 26 26 26 15 26 26 26 15: <a class="wiki_link" href="/8L%203s">8L 3s</a> MOS (<a class="wiki_link" href="/sensi11">Sensi-11</a> [or Undecimal Triatonic])<br />

20 20 20 11 20 20 20 20 11 20 20 20 20 11: <a class="wiki_link" href="/11L%203s">11L 3s</a> MOS [<a class="wiki_link" href="/WITNOTS">WITNOTS</a> Tuning (Tetradecimal Triatonic scale)]</body></html></pre></div>

20 20 20 11 20 20 20 20 11 20 20 20 20 11: <a class="wiki_link" href="/11L%203s">11L 3s</a> MOS [<a class="wiki_link" href="/WITNOTS">WITNOTS</a> Tuning (Tetradecimal Triatonic scale)]<br />

<br />

<strong>PRIME FACTORIZATION:</strong><br />

253 = <a class="wiki_link" href="/11edo">11</a> * <a class="wiki_link" href="/23edo">23</a></body></html></pre></div>

@@ 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-05-19 17:27:47 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:29:20 UTC</tt>.<br>
-: The original revision id was <tt>230140130</tt>.<br>
+: The original revision id was <tt>240943537</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">=&lt;span style="color: #630080; font-size: 113%;"&gt;253 tone equal temperament&lt;/span&gt;=
+<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">=&lt;span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;253 tone equal temperament&lt;/span&gt;=
-//253edo// divides the octave into 253 steps of 4.743083 cents. It approximates the fifth by **148\253**, which is 701.976285 Cents, a **0.004487 Cents sharp**. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic family|sesquiquartififths]] temperament.
+**//253-EDO//** or **253-tET** divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by **148\253**, which is 701.976285 Cents, a **0.004487 Cents sharp**. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic family|sesquiquartififths]] temperament.
 __**253 tone equal modes**__
@@ Line 18: / Line 18: @@
 31 31 18 31 31 31 31 18: [[7L 2s]] MOS ([[Armodue-Mesotonic]] Tuning)
 26 15 26 26 26 15 26 26 26 15: [[8L 3s]] MOS ([[sensi11|Sensi-11]] [or Undecimal Triatonic])
-20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s]] MOS [[[WITNOTS]] Tuning (Tetradecimal Triatonic scale)]</pre></div>
+20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s]] MOS [[[WITNOTS]] Tuning (Tetradecimal Triatonic scale)]
+**PRIME FACTORIZATION:**
+= [[11edo|11]] * [[23edo|23]]</pre></div>
 <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;253edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x253 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #630080; font-size: 113%;"&gt;253 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
+<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;253edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x253 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;253 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;em&gt;253edo&lt;/em&gt; divides the octave into 253 steps of 4.743083 cents. It approximates the fifth by &lt;strong&gt;148\253&lt;/strong&gt;, which is 701.976285 Cents, a &lt;strong&gt;0.004487 Cents sharp&lt;/strong&gt;. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit &lt;a class="wiki_link" href="/Schismatic%20family"&gt;sesquiquartififths&lt;/a&gt; temperament.&lt;br /&gt;
+&lt;strong&gt;&lt;em&gt;253-EDO&lt;/em&gt;&lt;/strong&gt; or &lt;strong&gt;253-tET&lt;/strong&gt; divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by &lt;strong&gt;148\253&lt;/strong&gt;, which is 701.976285 Cents, a &lt;strong&gt;0.004487 Cents sharp&lt;/strong&gt;. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit &lt;a class="wiki_link" href="/Schismatic%20family"&gt;sesquiquartififths&lt;/a&gt; temperament.&lt;br /&gt;
 &lt;br /&gt;
 &lt;u&gt;&lt;strong&gt;253 tone equal modes&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
@@ Line 32: / Line 35: @@
 31 31 18 31 31 31 31 18: &lt;a class="wiki_link" href="/7L%202s"&gt;7L 2s&lt;/a&gt; MOS (&lt;a class="wiki_link" href="/Armodue-Mesotonic"&gt;Armodue-Mesotonic&lt;/a&gt; Tuning)&lt;br /&gt;
 26 15 26 26 26 15 26 26 26 15: &lt;a class="wiki_link" href="/8L%203s"&gt;8L 3s&lt;/a&gt; MOS (&lt;a class="wiki_link" href="/sensi11"&gt;Sensi-11&lt;/a&gt; [or Undecimal Triatonic])&lt;br /&gt;
-20 20 11 20 20 20 20 11 20 20 20 20 11: &lt;a class="wiki_link" href="/11L%203s"&gt;11L 3s&lt;/a&gt; MOS [&lt;a class="wiki_link" href="/WITNOTS"&gt;WITNOTS&lt;/a&gt; Tuning (Tetradecimal Triatonic scale)]&lt;/body&gt;&lt;/html&gt;</pre></div>
+20 20 11 20 20 20 20 11 20 20 20 20 11: &lt;a class="wiki_link" href="/11L%203s"&gt;11L 3s&lt;/a&gt; MOS [&lt;a class="wiki_link" href="/WITNOTS"&gt;WITNOTS&lt;/a&gt; Tuning (Tetradecimal Triatonic scale)]&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;PRIME FACTORIZATION:&lt;/strong&gt;&lt;br /&gt;
+= &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt; * &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>