43edo
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- This revision was by author genewardsmith and made on 2011-09-02 13:04:43 UTC.
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Original Wikitext content:
=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>= = = //43edo// 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|. The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. ==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 ||
Original HTML content:
<html><head><title>43edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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:<h1> --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
<em>43edo</em> 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 <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|.<br />
<br />
The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><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>