59edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Andrew_Heathwaite and made on 2012-05-21 01:17:25 UTC.
- The original revision id was 337742820.
- The revision comment was:
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Original Wikitext content:
The //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its [[major third]] is nearly pure. It is a good [[Porcupine family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out 250/243 in the [[5-limit]], 64/63 and 16875/16807 in the [[7-limit]], and 55/54, 100/99 and 176/175 in the [[11-limit]]. 59edo is an excelent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting temperament. Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to [[Schismatic family|garibaldi temperament]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. 59edo is the 17th [[prime numbers|prime]] edo. || Degrees || Interval || || 1 || 20.339 || || 2 || 40.678 || || 3 || 61.017 || || 4 || 81.356 || || 5 || 101.695 || || 6 || 122.034 || || 7 || 142.373 || || 8 || 162.712 || || 9 || 183.051 || || 10 || 203.39 || || 11 || 223.729 || || 12 || 244.068 || || 13 || 264.407 || || 14 || 284.746 || || 15 || 305.085 || || 16 || 325.424 || || 17 || 345.763 || || 18 || 366.102 || || 19 || 386.441 || || 20 || 406.78 || || 21 || 427.119 || || 22 || 447.458 || || 23 || 467.797 || || 24 || 488.136 || || 25 || 508.475 || || 26 || 528.814 || || 27 || 549.153 || || 28 || 569.492 || || 29 || 589.831 || || 30 || 610.169 || || 31 || 630.508 || || 32 || 650.847 || || 33 || 671.186 || || 34 || 691.525 || || 35 || 691.525 || || 36 || 732.203 || || 37 || 752.542 || || 38 || 772.881 || || 39 || 793.22 || || 40 || 813.559 || || 41 || 833.898 || || 42 || 854.237 || || 43 || 874.576 || || 44 || 894.915 || || 45 || 915.254 || || 46 || 935.593 || || 47 || 955.932 || || 48 || 976.271 || || 49 || 996.61 || || 50 || 1016.949 || || 51 || 1037.288 || || 52 || 1057.627 || || 53 || 1077.966 || || 54 || 1098.305 || || 55 || 1118.644 || || 56 || 1138.983 || || 57 || 1159.322 || || 58 || 1179.661 ||
Original HTML content:
<html><head><title>59edo</title></head><body>The <em>59 equal division</em> divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its <a class="wiki_link" href="/major%20third">major third</a> is nearly pure. It is a good <a class="wiki_link" href="/Porcupine%20family">porcupine</a> tuning, giving in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/11-limit">11-limit</a> porcupine. This patent val tempers out 250/243 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 64/63 and 16875/16807 in the <a class="wiki_link" href="/7-limit">7-limit</a>, and 55/54, 100/99 and 176/175 in the <a class="wiki_link" href="/11-limit">11-limit</a>. 59edo is an excelent tuning for the 2.9.5.21.11 11-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*59 subgroup</a>, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting temperament.<br />
<br />
Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to <a class="wiki_link" href="/Schismatic%20family">garibaldi temperament</a> with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.<br />
<br />
59edo is the 17th <a class="wiki_link" href="/prime%20numbers">prime</a> edo.<br />
<br />
<table class="wiki_table">
<tr>
<td>Degrees<br />
</td>
<td>Interval<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>20.339<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>40.678<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>61.017<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>81.356<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>101.695<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>122.034<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>142.373<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>162.712<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>183.051<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>203.39<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>223.729<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>244.068<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>264.407<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>284.746<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>305.085<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>325.424<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>345.763<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>366.102<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>386.441<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>406.78<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>427.119<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>447.458<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>467.797<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>488.136<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>508.475<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>528.814<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>549.153<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>569.492<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>589.831<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>610.169<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>630.508<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>650.847<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>671.186<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>691.525<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>691.525<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>732.203<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>752.542<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>772.881<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>793.22<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>813.559<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>833.898<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>854.237<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>874.576<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>894.915<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>915.254<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>935.593<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>955.932<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>976.271<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>996.61<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>1016.949<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>1037.288<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>1057.627<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>1077.966<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>1098.305<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>1118.644<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>1138.983<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>1159.322<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>1179.661<br />
</td>
</tr>
</table>
</body></html>