Xenharmonic Wiki

65edo

Revision as of 11:01, 7 December 2016 by Wikispaces>JosephRuhf (**Imported revision 601622206 - Original comment: **)

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----

=<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]]. In the [[7-limit]], there are two different maps; the first is <65 103 151/1 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151/1 183|, 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 || 110.7692/1 ||
|| 7 || 129.2308/1 ||
|| 8 || 147.6923/1 ||
|| 9 || 166.1538/1 ||
|| 10 || 184.6154/1 ||
|| 11 || 203.0769/1 ||
|| 12 || 221.5385/1 ||
|| 13 || 240 ||
|| 14 || 258.4615/1 ||
|| 15 || 276.9231/1 ||
|| 16 || 295.3846/1 ||
|| 17 || 313.8462/1 ||
|| 18 || 332.3077/1 ||
|| 19 || 350.7692/1 ||
|| 20 || 369.2308/1 ||
|| 21 || 387.6923/1 ||
|| 22 || 406.1538/1 ||
|| 23 || 424.6154/1 ||
|| 24 || 443.0769/1 ||
|| 25 || 461.5385/1 ||
|| 26 || 480 ||
|| 27 || 498.4615/1 ||
|| 28 || 516.9231/1 ||
|| 29 || 535.3846/1 ||
|| 30 || 553.8462/1 ||
|| 31 || 572.3077/1 ||
|| 32 || 590.7692/1 ||
|| 33 || 609.2308/1 ||
|| 34 || 627.6923/1 ||
|| 35 || 646.1538/1 ||
|| 36 || 664.6154/1 ||
|| 37 || 683.0769/1 ||
|| 38 || 701.5385/1 ||
|| 39 || 720 ||
|| 40 || 738.4615/1 ||
|| 41 || 756.9231/1 ||
|| 42 || 775.3846/1 ||
|| 43 || 793.8462/1 ||
|| 44 || 812.3077/1 ||
|| 45 || 830.7692/1 ||
|| 46 || 849.2308/1 ||
|| 47 || 867.6923/1 ||
|| 48 || 886.1538/1 ||
|| 49 || 904.6154/1 ||
|| 50 || 923.0769/1 ||
|| 51 || 941.5385/1 ||
|| 52 || 960 ||
|| 53 || 978.4615/1 ||
|| 54 || 996.9231/1 ||
|| 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><hr />
<br />
<!-- 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-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>. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is &lt;65 103 151/1 182|, <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 &lt;65 103 151/1 183|, 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:&lt;h1&gt; --><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>110.7692/1<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>129.2308/1<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>147.6923/1<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>166.1538/1<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>184.6154/1<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>203.0769/1<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>221.5385/1<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>240<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>258.4615/1<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>276.9231/1<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>295.3846/1<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>313.8462/1<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>332.3077/1<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>350.7692/1<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>369.2308/1<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>387.6923/1<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>406.1538/1<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>424.6154/1<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>443.0769/1<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>461.5385/1<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>480<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>498.4615/1<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>516.9231/1<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>535.3846/1<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>553.8462/1<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>572.3077/1<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>590.7692/1<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>609.2308/1<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>627.6923/1<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>646.1538/1<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>664.6154/1<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>683.0769/1<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>701.5385/1<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>720<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>738.4615/1<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>756.9231/1<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>775.3846/1<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>793.8462/1<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>812.3077/1<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>830.7692/1<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>849.2308/1<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>867.6923/1<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>886.1538/1<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>904.6154/1<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>923.0769/1<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>941.5385/1<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>960<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>978.4615/1<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>996.9231/1<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:&lt;h1&gt; --><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>
Retrieved from "https://en.xen.wiki/index.php?title=65edo&oldid=9830"