55edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 164473677 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 211592224 - 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: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-03-17 19:19:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>211592224</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">//55edo// divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) [[http://en.wikipedia.org/wiki/Georg_Philipp_Telemann|Telemann]] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [[http://en.wikipedia.org/wiki/Leopold_Mozart|Leopold]] and [[http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart|Wolfgang Mozart]]. It can also be used for [[Meantone family|mohajira and liese]] temperaments. | <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: #008023; font-size: 103%;">55 tone equal temperament</span>= | ||
//55edo// divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) [[http://en.wikipedia.org/wiki/Georg_Philipp_Telemann|Telemann]] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [[http://en.wikipedia.org/wiki/Leopold_Mozart|Leopold]] and [[http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart|Wolfgang Mozart]]. It can also be used for [[Meantone family|mohajira and liese]] temperaments. | |||
5-limit commas: 81/80, <31 1 -14| | 5-limit commas: 81/80, <31 1 -14| | ||
| Line 12: | Line 13: | ||
7-limit commas: 81/80, 686/675, 6144/6125 | 7-limit commas: 81/80, 686/675, 6144/6125 | ||
11-limit commas: 81/80, 121/120, 176/175, 686/675</pre></div> | 11-limit commas: 81/80, 121/120, 176/175, 686/675 | ||
==Intervals== | |||
|| Degrees of 55-EDO || Cents value || | |||
|| 0 || 0 || | |||
|| 1 || 21,818 || | |||
|| 2 || 43,636 || | |||
|| 3 || 65,455 || | |||
|| 4 || 87,273 || | |||
|| 5 || 109,091 || | |||
|| 6 || 130,909 || | |||
|| 7 || 152,727 || | |||
|| 8 || 174,545 || | |||
|| 9 || 196,364 || | |||
|| 10 || 218,182 || | |||
|| 11 || 240 || | |||
|| 12 || 261,818 || | |||
|| 13 || 283,636 || | |||
|| 14 || 305,455 || | |||
|| 15 || 327,273 || | |||
|| 16 || 349,091 || | |||
|| 17 || 370,909 || | |||
|| 18 || 392,727 || | |||
|| 19 || 414,545 || | |||
|| 20 || 436,364 || | |||
|| 21 || 458,182 || | |||
|| 22 || 480 || | |||
|| 23 || 501,818 || | |||
|| 24 || 523,636 || | |||
|| 25 || 545,455 || | |||
|| 26 || 567,273 || | |||
|| 27 || 589,091 || | |||
|| 28 || 610,909 || | |||
|| 29 || 632,727 || | |||
|| 30 || 654,545 || | |||
|| 31 || 676,364 || | |||
|| 32 || 698,182 || | |||
|| 33 || 720 || | |||
|| 34 || 741,818 || | |||
|| 35 || 763,636 || | |||
|| 36 || 785,455 || | |||
|| 37 || 807,273 || | |||
|| 38 || 829,091 || | |||
|| 39 || 850,909 || | |||
|| 40 || 872,727 || | |||
|| 41 || 894,545 || | |||
|| 42 || 916,364 || | |||
|| 43 || 938,182 || | |||
|| 44 || 960 || | |||
|| 45 || 981,818 || | |||
|| 46 || 1003,636 || | |||
|| 47 || 1025,455 || | |||
|| 48 || 1047,273 || | |||
|| 49 || 1069,091 || | |||
|| 50 || 1090,909 || | |||
|| 51 || 1112,727 || | |||
|| 52 || 1134,545 || | |||
|| 53 || 1156,364 || | |||
|| 54 || 1178,182 ||</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>55edo</title></head><body><em>55edo</em> divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Philipp_Telemann" rel="nofollow">Telemann</a> suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Leopold_Mozart" rel="nofollow">Leopold</a> and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart" rel="nofollow">Wolfgang Mozart</a>. It can also be used for <a class="wiki_link" href="/Meantone%20family">mohajira and liese</a> temperaments.<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>55edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x55 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #008023; font-size: 103%;">55 tone equal temperament</span></h1> | ||
<em>55edo</em> divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Philipp_Telemann" rel="nofollow">Telemann</a> suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Leopold_Mozart" rel="nofollow">Leopold</a> and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart" rel="nofollow">Wolfgang Mozart</a>. It can also be used for <a class="wiki_link" href="/Meantone%20family">mohajira and liese</a> temperaments.<br /> | |||
<br /> | <br /> | ||
5-limit commas: 81/80, &lt;31 1 -14|<br /> | 5-limit commas: 81/80, &lt;31 1 -14|<br /> | ||
| Line 20: | Line 80: | ||
7-limit commas: 81/80, 686/675, 6144/6125<br /> | 7-limit commas: 81/80, 686/675, 6144/6125<br /> | ||
<br /> | <br /> | ||
11-limit commas: 81/80, 121/120, 176/175, 686/675</body></html></pre></div> | 11-limit commas: 81/80, 121/120, 176/175, 686/675<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x55 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Degrees of 55-EDO<br /> | |||
</td> | |||
<td>Cents value<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>21,818<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>43,636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>65,455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>87,273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>109,091<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>130,909<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>152,727<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>174,545<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>196,364<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>218,182<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>240<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>261,818<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>283,636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>305,455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>327,273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>349,091<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>370,909<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>392,727<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>414,545<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>436,364<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>458,182<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>480<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>501,818<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>523,636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>545,455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>567,273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>589,091<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>610,909<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>632,727<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>654,545<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31<br /> | |||
</td> | |||
<td>676,364<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32<br /> | |||
</td> | |||
<td>698,182<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33<br /> | |||
</td> | |||
<td>720<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>34<br /> | |||
</td> | |||
<td>741,818<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35<br /> | |||
</td> | |||
<td>763,636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36<br /> | |||
</td> | |||
<td>785,455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37<br /> | |||
</td> | |||
<td>807,273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38<br /> | |||
</td> | |||
<td>829,091<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>39<br /> | |||
</td> | |||
<td>850,909<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>40<br /> | |||
</td> | |||
<td>872,727<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41<br /> | |||
</td> | |||
<td>894,545<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>42<br /> | |||
</td> | |||
<td>916,364<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43<br /> | |||
</td> | |||
<td>938,182<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>44<br /> | |||
</td> | |||
<td>960<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>45<br /> | |||
</td> | |||
<td>981,818<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>46<br /> | |||
</td> | |||
<td>1003,636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>47<br /> | |||
</td> | |||
<td>1025,455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>48<br /> | |||
</td> | |||
<td>1047,273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>49<br /> | |||
</td> | |||
<td>1069,091<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>50<br /> | |||
</td> | |||
<td>1090,909<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>51<br /> | |||
</td> | |||
<td>1112,727<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>52<br /> | |||
</td> | |||
<td>1134,545<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>53<br /> | |||
</td> | |||
<td>1156,364<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>54<br /> | |||
</td> | |||
<td>1178,182<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||