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50edo: Difference between revisions

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**Imported revision 342313156 - Original comment: **
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**Imported revision 342313400 - 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:jdfreivald|jdfreivald]] and made on <tt>2012-06-03 23:24:52 UTC</tt>.<br>
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-06-03 23:26:27 UTC</tt>.<br>
: The original revision id was <tt>342313156</tt>.<br>
: The original revision id was <tt>342313400</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>
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==Commas==  
==Commas==  
50 EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.)
50 EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not exclusive, and is based on the interval table from Scala version 2.2.
||~ ===In bra format=== ||~ ===In cents=== ||~ ===Ratio=== ||~ ===Name 1=== ||~ ===Name2=== ||
||~ ===In bra format=== ||~ ===In cents=== ||~ ===Ratio=== ||~ ===Name 1=== ||~ ===Name2=== ||
|| | -4 4 -1 &gt; ||&gt; 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||
|| | -4 4 -1 &gt; ||&gt; 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||
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[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]]
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &gt; 21.51 81/80 syntonic comma, Didymus comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;
| -8 8 -2 &gt; 43.01 6561/6400 Mathieu superdiesis
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -8 8 -2 &gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;
| 23 6 -14 &gt; 3.34 1212717/1210381 Vishnu comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 23 6 -14 &gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;
| 1 2 -3 1 &gt; 13.79 126/125 small septimal comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 1 2 -3 1 &gt; 13.79 126/125 small septimal comma&lt;/span&gt;
| -5 2 2 -1 &gt; 7.71 225/224 septimal kleisma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -5 2 2 -1 &gt; 7.71 225/224 septimal kleisma&lt;/span&gt;
| 6 0 -5 2 &gt; 6.08 3136/3125 middle second comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 6 0 -5 2 &gt; 6.08 3136/3125 middle second comma&lt;/span&gt;
| -6 -8 2 5 &gt; 1.12 420175/419904
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -6 -8 2 5 &gt; 1.12 420175/419904&lt;/span&gt;
|-11 2 7 -3 &gt; 1.63 703125/702464
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; |-11 2 7 -3 &gt; 1.63 703125/702464&lt;/span&gt;
| 11 -10 -10 10 &gt; 5.57 6772805/6751042
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 11 -10 -10 10 &gt; 5.57 6772805/6751042&lt;/span&gt;
|-13 10 0 -1 &gt; 50.72 59049/57344 Harrison's comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; |-13 10 0 -1 &gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;
| 2 3 1 -2 -1 &gt; 3.21 540/539 Swets' comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 3 1 -2 -1 &gt; 3.21 540/539 Swets' comma&lt;/span&gt;
| -3 4 -2 -2 2 &gt; 0.18 9801/9800 kalisma, Gauss' comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -3 4 -2 -2 2 &gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;
| 5 -1 3 0 -3 &gt; 3.03 4000/3993 undecimal schisma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 5 -1 3 0 -3 &gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;
| -7 -1 1 1 1 &gt; 4.50 385/384 undecimal kleisma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -7 -1 1 1 1 &gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;
| 2 -1 0 1 -2 1 &gt; 4.76 364/363
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 -1 0 1 -2 1 &gt; 4.76 364/363&lt;/span&gt;
| 2 3 0 -1 1 -2 &gt; 7.30 1188/1183 Kestrel Comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 3 0 -1 1 -2 &gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;
| 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;
| -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;
| 3 -2 0 1 -1 -1 0 0 1 &gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;</pre></div>
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 3 -2 0 1 -1 -1 0 0 1 &gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;50edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;50edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 50 equal parts of precisely 24 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out 81/80, making it a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; system, and in that capacity has historically has drawn some notice. In &amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the &lt;a class="wiki_link" href="/Target%20tunings"&gt;least squares&lt;/a&gt; tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; extends meantone with a &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; which is nearly pure, 50 has a flat 7/4 but both &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; are nearly pure.&lt;br /&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;50edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;50edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 50 equal parts of precisely 24 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out 81/80, making it a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; system, and in that capacity has historically has drawn some notice. In &amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the &lt;a class="wiki_link" href="/Target%20tunings"&gt;least squares&lt;/a&gt; tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; extends meantone with a &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; which is nearly pure, 50 has a flat 7/4 but both &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; are nearly pure.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Commas&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Commas&lt;/h2&gt;
  50 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.)&lt;br /&gt;
  50 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not exclusive, and is based on the interval table from Scala version 2.2.&lt;br /&gt;




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&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow"&gt;Twinkle canon – 50 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow"&gt;Twinkle canon – 50 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &amp;gt; 21.51 81/80 syntonic comma, Didymus comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &amp;gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;&lt;br /&gt;
| -8 8 -2 &amp;gt; 43.01 6561/6400 Mathieu superdiesis&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -8 8 -2 &amp;gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;&lt;br /&gt;
| 23 6 -14 &amp;gt; 3.34 1212717/1210381 Vishnu comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 23 6 -14 &amp;gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;&lt;br /&gt;
| 1 2 -3 1 &amp;gt; 13.79 126/125 small septimal comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 1 2 -3 1 &amp;gt; 13.79 126/125 small septimal comma&lt;/span&gt;&lt;br /&gt;
| -5 2 2 -1 &amp;gt; 7.71 225/224 septimal kleisma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -5 2 2 -1 &amp;gt; 7.71 225/224 septimal kleisma&lt;/span&gt;&lt;br /&gt;
| 6 0 -5 2 &amp;gt; 6.08 3136/3125 middle second comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 6 0 -5 2 &amp;gt; 6.08 3136/3125 middle second comma&lt;/span&gt;&lt;br /&gt;
| -6 -8 2 5 &amp;gt; 1.12 420175/419904&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -6 -8 2 5 &amp;gt; 1.12 420175/419904&lt;/span&gt;&lt;br /&gt;
|-11 2 7 -3 &amp;gt; 1.63 703125/702464&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; |-11 2 7 -3 &amp;gt; 1.63 703125/702464&lt;/span&gt;&lt;br /&gt;
| 11 -10 -10 10 &amp;gt; 5.57 6772805/6751042&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 11 -10 -10 10 &amp;gt; 5.57 6772805/6751042&lt;/span&gt;&lt;br /&gt;
|-13 10 0 -1 &amp;gt; 50.72 59049/57344 Harrison's comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; |-13 10 0 -1 &amp;gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;&lt;br /&gt;
| 2 3 1 -2 -1 &amp;gt; 3.21 540/539 Swets' comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 3 1 -2 -1 &amp;gt; 3.21 540/539 Swets' comma&lt;/span&gt;&lt;br /&gt;
| -3 4 -2 -2 2 &amp;gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -3 4 -2 -2 2 &amp;gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;&lt;br /&gt;
| 5 -1 3 0 -3 &amp;gt; 3.03 4000/3993 undecimal schisma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 5 -1 3 0 -3 &amp;gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;&lt;br /&gt;
| -7 -1 1 1 1 &amp;gt; 4.50 385/384 undecimal kleisma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -7 -1 1 1 1 &amp;gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;&lt;br /&gt;
| 2 -1 0 1 -2 1 &amp;gt; 4.76 364/363&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 -1 0 1 -2 1 &amp;gt; 4.76 364/363&lt;/span&gt;&lt;br /&gt;
| 2 3 0 -1 1 -2 &amp;gt; 7.30 1188/1183 Kestrel Comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 2 3 0 -1 1 -2 &amp;gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;&lt;br /&gt;
| 3 0 2 0 1 -3 &amp;gt; 2.36 2200/2197 Parizek comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 3 0 2 0 1 -3 &amp;gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;&lt;br /&gt;
| -3 1 1 1 0 -1 &amp;gt; 16.57 105/104 small tridecimal comma&lt;br /&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | -3 1 1 1 0 -1 &amp;gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;&lt;br /&gt;
| 3 -2 0 1 -1 -1 0 0 1 &amp;gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt; | 3 -2 0 1 -1 -1 0 0 1 &amp;gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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