65edo: Difference between revisions

Revision as of 02:00, 29 May 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2011-05-29 02:00:36 UTC.

The original revision id was 232660568.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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=<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.

65edo approximates the intervals 3/2, 5/4, 11/8 and 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]].

==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:&lt;h1&gt; --><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 &lt;65 103 151 182|, tempering out 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;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 3/2, 5/4, 11/8 and 19/16 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 />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-03 13:28:36 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-29 02:00:36 UTC</tt>.<br>
-: The original revision id was <tt>216620528</tt>.<br>
+: The original revision id was <tt>232660568</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>
@@ Line 9: / Line 9: @@
 //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 &lt;65 103 151 182|, tempering out 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;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.
-edo approximates the intervals 3/2, 5/4, 11/8 and 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 subgroup 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]].
+edo approximates the intervals 3/2, 5/4, 11/8 and 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]].
 ==Intervals==
@@ Line 82: / Line 82: @@
   &lt;em&gt;65edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.462 cents each. It can be characterized as the temperament which tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, the &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;, 78732/78125, and the &lt;a class="wiki_link" href="/wuerschmidt%20comma"&gt;wuerschmidt comma&lt;/a&gt;, 393216/390625. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, there are two different maps; the first is &amp;lt;65 103 151 182|, tempering out 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &amp;lt;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 &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; 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 &lt;a class="wiki_link" href="/wuerschmidt%20temperament"&gt;wuerschmidt temperament&lt;/a&gt; (wurschmidt and worschmidt) these two mappings provide.&lt;br /&gt;
 &lt;br /&gt;
-edo approximates the intervals 3/2, 5/4, 11/8 and 19/16 well, so that it does a good job representing the 2.3.5.11.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. To this one may want to add 13/8 and 17/16, giving the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the subgroup 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;.&lt;br /&gt;
+edo approximates the intervals 3/2, 5/4, 11/8 and 19/16 well, so that it does a good job representing the 2.3.5.11.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. To this one may want to add 13/8 and 17/16, giving the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*65 subgroup&lt;/a&gt; 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x65 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h2&gt;

65edo: Difference between revisions

Revision as of 02:00, 29 May 2011

IMPORTED REVISION FROM WIKISPACES

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