43edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 189158617 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 210047522 - 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>2011-03-13 16:25:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>210047522</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">//43edo//, which divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 or 11-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440. | <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: #027bac; font-size: 103%;">43 tone equal temperament</span>= | ||
= = | |||
//43edo//, which divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 or 11-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440. | |||
In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|.</pre></div> | In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|. | ||
==Intervals== | |||
|| Degrees of 43-EDO || Cents value || | |||
|| 0 || 0 || | |||
|| 1 || 27,907 || | |||
|| 2 || 55,814 || | |||
|| 3 || 83,721 || | |||
|| 4 || 111,628 || | |||
|| 5 || 139,535 || | |||
|| 6 || 167,442 || | |||
|| 7 || 195,349 || | |||
|| 8 || 223,256 || | |||
|| 9 || 251,163 || | |||
|| 10 || 279,07 || | |||
|| 11 || 306,977 || | |||
|| 12 || 334,884 || | |||
|| 13 || 362,791 || | |||
|| 14 || 390,698 || | |||
|| 15 || 418,605 || | |||
|| 16 || 446,512 || | |||
|| 17 || 474,419 || | |||
|| 18 || 502,326 || | |||
|| 19 || 530,233 || | |||
|| 20 || 558,139 || | |||
|| 21 || 586,046 || | |||
|| 22 || 613,953 || | |||
|| 23 || 641,86 || | |||
|| 24 || 669,767 || | |||
|| 25 || 697,674 || | |||
|| 26 || 725,581 || | |||
|| 27 || 753,488 || | |||
|| 28 || 781,395 || | |||
|| 29 || 809,302 || | |||
|| 30 || 837,209 || | |||
|| 31 || 865,116 || | |||
|| 32 || 893,023 || | |||
|| 33 || 920,93 || | |||
|| 34 || 948,837 || | |||
|| 35 || 976,744 || | |||
|| 36 || 1004,651 || | |||
|| 37 || 1032,558 || | |||
|| 38 || 1060,465 || | |||
|| 39 || 1088,372 || | |||
|| 40 || 1116,279 || | |||
|| 41 || 1144,186 || | |||
|| 42 || 1172,093 ||</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>43edo</title></head><body><em>43edo</em>, which divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 or 11-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440.<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>43edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1> | |||
<em>43edo</em>, which divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 or 11-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440.<br /> | |||
<br /> | |||
In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping &lt;0 1 4 10 18 27|, and the second &lt;0 1 4 10 18 -16|.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Degrees of 43-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>27,907<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>55,814<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>83,721<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>111,628<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>139,535<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>167,442<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>195,349<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>223,256<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>251,163<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>279,07<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>306,977<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>334,884<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>362,791<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>390,698<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>418,605<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>446,512<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>474,419<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>502,326<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>530,233<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>558,139<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>586,046<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>613,953<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>641,86<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>669,767<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>697,674<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>725,581<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>753,488<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>781,395<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>809,302<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>837,209<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31<br /> | |||
</td> | |||
<td>865,116<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32<br /> | |||
</td> | |||
<td>893,023<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33<br /> | |||
</td> | |||
<td>920,93<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>34<br /> | |||
</td> | |||
<td>948,837<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35<br /> | |||
</td> | |||
<td>976,744<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36<br /> | |||
</td> | |||
<td>1004,651<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37<br /> | |||
</td> | |||
<td>1032,558<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38<br /> | |||
</td> | |||
<td>1060,465<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>39<br /> | |||
</td> | |||
<td>1088,372<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>40<br /> | |||
</td> | |||
<td>1116,279<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41<br /> | |||
</td> | |||
<td>1144,186<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>42<br /> | |||
</td> | |||
<td>1172,093<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||