65edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2011-03-18 04:00:00 UTC.
- The original revision id was 211673536.
- The revision comment was: some links added
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Original Wikitext content:
=<span style="color: #750063; font-size: 103%;">65 tone equal temperament</span>= //65edo// divides the [[octave]] into 65 equal parts of 18.462 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. ==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 ||
Original HTML content:
<html><head><title>65edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x65 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #750063; font-size: 103%;">65 tone equal temperament</span></h1>
<em>65edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.462 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|, 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 <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 />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x65 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
<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>
</body></html>