|
|
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =<span style="color: #ffa610; font-family: 'Times New Roman',Times,serif; font-size: 122%;">'''61 tone equal temperament'''</span>= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | ''61-EDO'' refers to the equal division of [[2/1|2/1]] ratio into 61 equal parts, of 19.6721 [[cent|cent]]s each. It is the 18th [[prime_numbers|prime]] EDO, after of [[59edo|59edo]] and before of [[67edo|67edo]]. It provides the optimal patent val for the 24&37 temperament in the 7-, 11- and 13-limit. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-27 16:30:03 UTC</tt>.<br>
| |
| : The original revision id was <tt>339897230</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>
| |
| <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">=<span style="color: #ffa610; font-family: 'Times New Roman',Times,serif; font-size: 122%;">**61 tone equal temperament**</span>=
| |
| //61-EDO// refers to the equal division of [[xenharmonic/2_1|2/1]] ratio into 61 equal parts, of 19.6721 [[xenharmonic/cent|cent]]s each. It is the 18th [[prime numbers|prime]] EDO, after of [[59edo]] and before of [[67edo]]. It provides the optimal patent val for the 24&37 temperament in the 7-, 11- and 13-limit.
| |
|
| |
|
| =Poem= | | =Poem= |
| These 61 equal divisions of the octave, | | These 61 equal divisions of the octave, |
| | |
| though rare are assuredly a ROCK-tave (har har), | | though rare are assuredly a ROCK-tave (har har), |
| | |
| while the 3rd and 5th harmonics are about six cents sharp, | | while the 3rd and 5th harmonics are about six cents sharp, |
| | |
| (and the flattish 15th poised differently on the harp), | | (and the flattish 15th poised differently on the harp), |
| | |
| the 7th and 11th err by less, around three, | | the 7th and 11th err by less, around three, |
| | |
| and thus mayhap, a good orgone tuning found to be; | | and thus mayhap, a good orgone tuning found to be; |
| | |
| slightly sharp as well, is the 13th harmonic's place, | | slightly sharp as well, is the 13th harmonic's place, |
| | |
| but the 9th and 17th lack near so much grace, | | but the 9th and 17th lack near so much grace, |
| | |
| interestingly the 19th is good but a couple cents flat, | | interestingly the 19th is good but a couple cents flat, |
| | |
| and the 21st and 23rd are but a cent or two sharp! | | and the 21st and 23rd are but a cent or two sharp! |
|
| |
|
| ==**61-EDO Intervals**== | | =='''61-EDO Intervals'''== |
| || **Degrees** || **Cent Value** ||
| |
| || 0 || 0 ||
| |
| || 1 || 19.6721 ||
| |
| || 2 || 39.3443 ||
| |
| || 3 || 59.0164 ||
| |
| || 4 || 78.6885 ||
| |
| || 5 || 98.3607 ||
| |
| || 6 || 118.0328 ||
| |
| || 7 || 137.7049 ||
| |
| || 8 || 157.377 ||
| |
| || 9 || 177.0492 ||
| |
| || 10 || 196.7213 ||
| |
| || 11 || 216.3934 ||
| |
| || 12 || 236.0656 ||
| |
| || 13 || 255.7377 ||
| |
| || 14 || 275.4098 ||
| |
| || 15 || 295.082 ||
| |
| || 16 || 314.7541 ||
| |
| || 17 || 334.4262 ||
| |
| || 18 || 354.0984 ||
| |
| || 19 || 373.7705 ||
| |
| || 20 || 393.4426 ||
| |
| || 21 || 413.1148 ||
| |
| || 22 || 432.7869 ||
| |
| || 23 || 452.459 ||
| |
| || 24 || 472.1311 ||
| |
| || 25 || 491.8033 ||
| |
| || 26 || 511.4754 ||
| |
| || 27 || 531.1475 ||
| |
| || 28 || 550.8197 ||
| |
| || 29 || 570.4918 ||
| |
| || 30 || 590.1639 ||
| |
| || 31 || 609.8361 ||
| |
| || 32 || 629.5082 ||
| |
| || 33 || 649.1803 ||
| |
| || 34 || 668.8525 ||
| |
| || 35 || 688.5246 ||
| |
| || 36 || 708.1967 ||
| |
| || 37 || 727.8689 ||
| |
| || 38 || 747.541 ||
| |
| || 39 || 767.2131 ||
| |
| || 40 || 786.8852 ||
| |
| || 41 || 806.5574 ||
| |
| || 42 || 826.2295 ||
| |
| || 43 || 845.9016 ||
| |
| || 44 || 865.5738 ||
| |
| || 45 || 885.2459 ||
| |
| || 46 || 904.918 ||
| |
| || 47 || 924.5902 ||
| |
| || 48 || 944.2623 ||
| |
| || 49 || 963.9344 ||
| |
| || 50 || 983.6066 ||
| |
| || 51 || 1003.2787 ||
| |
| || 52 || 1022.9508 ||
| |
| || 53 || 1042.623 ||
| |
| || 54 || 1062.2951 ||
| |
| || 55 || 1081.9672 ||
| |
| || 56 || 1101.6393 ||
| |
| || 57 || 1121.3115 ||
| |
| || 58 || 1140.9836 ||
| |
| || 59 || 1160.6557 ||
| |
| || 60 || 1180.3279 ||</pre></div>
| |
| <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>61edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x61 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ffa610; font-family: 'Times New Roman',Times,serif; font-size: 122%;"><strong>61 tone equal temperament</strong></span></h1>
| |
| <em>61-EDO</em> refers to the equal division of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/2_1">2/1</a> ratio into 61 equal parts, of 19.6721 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s each. It is the 18th <a class="wiki_link" href="/prime%20numbers">prime</a> EDO, after of <a class="wiki_link" href="/59edo">59edo</a> and before of <a class="wiki_link" href="/67edo">67edo</a>. It provides the optimal patent val for the 24&amp;37 temperament in the 7-, 11- and 13-limit.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Poem"></a><!-- ws:end:WikiTextHeadingRule:2 -->Poem</h1>
| |
| These 61 equal divisions of the octave,<br />
| |
| though rare are assuredly a ROCK-tave (har har),<br />
| |
| while the 3rd and 5th harmonics are about six cents sharp,<br />
| |
| (and the flattish 15th poised differently on the harp),<br />
| |
| the 7th and 11th err by less, around three,<br />
| |
| and thus mayhap, a good orgone tuning found to be;<br />
| |
| slightly sharp as well, is the 13th harmonic's place,<br />
| |
| but the 9th and 17th lack near so much grace,<br />
| |
| interestingly the 19th is good but a couple cents flat,<br />
| |
| and the 21st and 23rd are but a cent or two sharp!<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Poem-61-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>61-EDO Intervals</strong></h2>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td><strong>Degrees</strong><br />
| |
| </td>
| |
| <td><strong>Cent Value</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>19.6721<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>39.3443<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>59.0164<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>78.6885<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>98.3607<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>118.0328<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>137.7049<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>157.377<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>177.0492<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>196.7213<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>216.3934<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>236.0656<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>255.7377<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>275.4098<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>295.082<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>314.7541<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>334.4262<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>354.0984<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>373.7705<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>393.4426<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>413.1148<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>432.7869<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>452.459<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>472.1311<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>491.8033<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>511.4754<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>531.1475<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>550.8197<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>570.4918<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>590.1639<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>609.8361<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>629.5082<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>649.1803<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>668.8525<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td>688.5246<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>708.1967<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>727.8689<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td>747.541<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>767.2131<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>786.8852<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>806.5574<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>826.2295<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>845.9016<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>865.5738<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>885.2459<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>904.918<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>924.5902<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>944.2623<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>963.9344<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>983.6066<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td>1003.2787<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>1022.9508<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>1042.623<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>1062.2951<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>1081.9672<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>1101.6393<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>1121.3115<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58<br />
| |
| </td>
| |
| <td>1140.9836<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>59<br />
| |
| </td>
| |
| <td>1160.6557<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>60<br />
| |
| </td>
| |
| <td>1180.3279<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | {| class="wikitable" |
| | |- |
| | | | '''Degrees''' |
| | | | '''Cent Value''' |
| | |- |
| | | | 0 |
| | | | 0 |
| | |- |
| | | | 1 |
| | | | 19.6721 |
| | |- |
| | | | 2 |
| | | | 39.3443 |
| | |- |
| | | | 3 |
| | | | 59.0164 |
| | |- |
| | | | 4 |
| | | | 78.6885 |
| | |- |
| | | | 5 |
| | | | 98.3607 |
| | |- |
| | | | 6 |
| | | | 118.0328 |
| | |- |
| | | | 7 |
| | | | 137.7049 |
| | |- |
| | | | 8 |
| | | | 157.377 |
| | |- |
| | | | 9 |
| | | | 177.0492 |
| | |- |
| | | | 10 |
| | | | 196.7213 |
| | |- |
| | | | 11 |
| | | | 216.3934 |
| | |- |
| | | | 12 |
| | | | 236.0656 |
| | |- |
| | | | 13 |
| | | | 255.7377 |
| | |- |
| | | | 14 |
| | | | 275.4098 |
| | |- |
| | | | 15 |
| | | | 295.082 |
| | |- |
| | | | 16 |
| | | | 314.7541 |
| | |- |
| | | | 17 |
| | | | 334.4262 |
| | |- |
| | | | 18 |
| | | | 354.0984 |
| | |- |
| | | | 19 |
| | | | 373.7705 |
| | |- |
| | | | 20 |
| | | | 393.4426 |
| | |- |
| | | | 21 |
| | | | 413.1148 |
| | |- |
| | | | 22 |
| | | | 432.7869 |
| | |- |
| | | | 23 |
| | | | 452.459 |
| | |- |
| | | | 24 |
| | | | 472.1311 |
| | |- |
| | | | 25 |
| | | | 491.8033 |
| | |- |
| | | | 26 |
| | | | 511.4754 |
| | |- |
| | | | 27 |
| | | | 531.1475 |
| | |- |
| | | | 28 |
| | | | 550.8197 |
| | |- |
| | | | 29 |
| | | | 570.4918 |
| | |- |
| | | | 30 |
| | | | 590.1639 |
| | |- |
| | | | 31 |
| | | | 609.8361 |
| | |- |
| | | | 32 |
| | | | 629.5082 |
| | |- |
| | | | 33 |
| | | | 649.1803 |
| | |- |
| | | | 34 |
| | | | 668.8525 |
| | |- |
| | | | 35 |
| | | | 688.5246 |
| | |- |
| | | | 36 |
| | | | 708.1967 |
| | |- |
| | | | 37 |
| | | | 727.8689 |
| | |- |
| | | | 38 |
| | | | 747.541 |
| | |- |
| | | | 39 |
| | | | 767.2131 |
| | |- |
| | | | 40 |
| | | | 786.8852 |
| | |- |
| | | | 41 |
| | | | 806.5574 |
| | |- |
| | | | 42 |
| | | | 826.2295 |
| | |- |
| | | | 43 |
| | | | 845.9016 |
| | |- |
| | | | 44 |
| | | | 865.5738 |
| | |- |
| | | | 45 |
| | | | 885.2459 |
| | |- |
| | | | 46 |
| | | | 904.918 |
| | |- |
| | | | 47 |
| | | | 924.5902 |
| | |- |
| | | | 48 |
| | | | 944.2623 |
| | |- |
| | | | 49 |
| | | | 963.9344 |
| | |- |
| | | | 50 |
| | | | 983.6066 |
| | |- |
| | | | 51 |
| | | | 1003.2787 |
| | |- |
| | | | 52 |
| | | | 1022.9508 |
| | |- |
| | | | 53 |
| | | | 1042.623 |
| | |- |
| | | | 54 |
| | | | 1062.2951 |
| | |- |
| | | | 55 |
| | | | 1081.9672 |
| | |- |
| | | | 56 |
| | | | 1101.6393 |
| | |- |
| | | | 57 |
| | | | 1121.3115 |
| | |- |
| | | | 58 |
| | | | 1140.9836 |
| | |- |
| | | | 59 |
| | | | 1160.6557 |
| | |- |
| | | | 60 |
| | | | 1180.3279 |
| | |} |