59edo: Difference between revisions

Revision as of 01:17, 21 May 2012

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.

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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&amp;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&amp;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>

59edo: Difference between revisions

Revision as of 01:17, 21 May 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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