65edo
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[[toc|flat]] ---- =<span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;">65 tone equal temperament</span>= **//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]], 393216/390625. In the [[7-limit]], there are two different maps; the first is <65 103 151 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide. 65edo approximates the intervals [[3_2|3/2]], [[5_4|5/4]], [[11_8|11/8]] and [[19_16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]]. 65edo contains [[13edo]] as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [[https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded|Rubble: a Xenuke Unfolded]]. =Intervals= || Degrees of 65-EDO || Cents value || || 0 || 0 || || 1 || 18.4615 || || 2 || 36.9231 || || 3 || 55.3846 || || 4 || 73.8462 || || 5 || 92.3077 || || 6 || 110.7692 || || 7 || 129.2308 || || 8 || 147.6923 || || 9 || 166.1538 || || 10 || 184.6154 || || 11 || 203.0769 || || 12 || 221.5385 || || 13 || 240 || || 14 || 258.4615 || || 15 || 276.9231 || || 16 || 295.3846 || || 17 || 313.8462 || || 18 || 332.3077 || || 19 || 350.7692 || || 20 || 369.2308 || || 21 || 387.6923 || || 22 || 406.1538 || || 23 || 424.6154 || || 24 || 443.0769 || || 25 || 461.5385 || || 26 || 480 || || 27 || 498.4615 || || 28 || 516.9231 || || 29 || 535.3846 || || 30 || 553.8462 || || 31 || 572.3077 || || 32 || 590.7692 || || 33 || 609.2308 || || 34 || 627.6923 || || 35 || 646.1538 || || 36 || 664.6154 || || 37 || 683.0769 || || 38 || 701.5385 || || 39 || 720 || || 40 || 738.4615 || || 41 || 756.9231 || || 42 || 775.3846 || || 43 || 793.8462 || || 44 || 812.3077 || || 45 || 830.7692 || || 46 || 849.2308 || || 47 || 867.6923 || || 48 || 886.1538 || || 49 || 904.6154 || || 50 || 923.0769 || || 51 || 941.5385 || || 52 || 960 || || 53 || 978.4615 || || 54 || 996.9231 || || 55 || 1015.3846 || || 56 || 1033.8462 || || 57 || 1052.3077 || || 58 || 1070.7692 || || 59 || 1089.2308 || || 60 || 1107.6923 || || 61 || 1126.1538 || || 62 || 1144.6154 || || 63 || 1163.0769 || || 64 || 1181.5385 || =Scales= [[photia7]] [[photia12]]
Original HTML content:
<html><head><title>65edo</title></head><body><!-- ws:start:WikiTextTocRule:6:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#x65 tone equal temperament">65 tone equal temperament</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
<!-- ws:end:WikiTextTocRule:10 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x65 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;">65 tone equal temperament</span></h1>
<br />
<strong><em>65edo</em></strong> divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the <a class="wiki_link" href="/schisma">schisma</a>, 32805/32768, the <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a>, 78732/78125, and the <a class="wiki_link" href="/wuerschmidt%20comma">wuerschmidt comma</a>, 393216/390625. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is <65 103 151 182|, <a class="wiki_link" href="/tempering%20out">tempering out</a> 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the <a class="wiki_link" href="/5-limit">5-limit</a> over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit <a class="wiki_link" href="/wuerschmidt%20temperament">wuerschmidt temperament</a> (wurschmidt and worschmidt) these two mappings provide.<br />
<br />
65edo approximates the intervals <a class="wiki_link" href="/3_2">3/2</a>, <a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_8">11/8</a> and <a class="wiki_link" href="/19_16">19/16</a> well, so that it does a good job representing the 2.3.5.11.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. To this one may want to add 13/8 and 17/16, giving the <a class="wiki_link" href="/19-limit">19-limit</a> no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*65 subgroup</a> 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as <a class="wiki_link" href="/130edo">130edo</a>.<br />
<br />
65edo contains <a class="wiki_link" href="/13edo">13edo</a> as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see <a class="wiki_link_ext" href="https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded" rel="nofollow">Rubble: a Xenuke Unfolded</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>Degrees of 65-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>18.4615<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>36.9231<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>55.3846<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>73.8462<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>92.3077<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>110.7692<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>129.2308<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>147.6923<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>166.1538<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>184.6154<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>203.0769<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>221.5385<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>240<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>258.4615<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>276.9231<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>295.3846<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>313.8462<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>332.3077<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>350.7692<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>369.2308<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>387.6923<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>406.1538<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>424.6154<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>443.0769<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>461.5385<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>480<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>498.4615<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>516.9231<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>535.3846<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>553.8462<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>572.3077<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>590.7692<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>609.2308<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>627.6923<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>646.1538<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>664.6154<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>683.0769<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>701.5385<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>720<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>738.4615<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>756.9231<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>775.3846<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>793.8462<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>812.3077<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>830.7692<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>849.2308<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>867.6923<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>886.1538<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>904.6154<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>923.0769<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>941.5385<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>960<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>978.4615<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>996.9231<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>1015.3846<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>1033.8462<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>1052.3077<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>1070.7692<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>1089.2308<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>1107.6923<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>1126.1538<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>1144.6154<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>1163.0769<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>1181.5385<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->Scales</h1>
<a class="wiki_link" href="/photia7">photia7</a><br />
<a class="wiki_link" href="/photia12">photia12</a></body></html>