Wikispaces>Andrew_Heathwaite |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-05-21 02:08:28 UTC</tt>.<br>
| |
| : The original revision id was <tt>337752484</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
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| 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">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.
| | == Theory == |
| | 59edo's best [[3/2|fifth]] is stretched about 9.91 cents from the just interval, and yet its [[5/4]] is nearly pure (stretched only 0.127{{c}}), as the denominator of a convergent to log<sub>2</sub>5. It is a good [[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 the 17th [[prime numbers|prime]] edo.
| | Using the flat fifth instead of the sharp one allows for the {{nowrap|12 & 35}} temperament, which is a kind of bizarre cousin to [[garibaldi]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths. |
|
| |
|
| || Degrees || Cents Value ||
| | As every other step of [[118edo]], 59edo is an excellent 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. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the [[50edo|50]] & 59 temperament with a subminor third generator provides an interesting temperament. |
| || 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 || 203.390 ||
| |
| || 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 || 406.780 ||
| |
| || 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 || 711.864 ||
| |
| || 36 || 732.203 ||
| |
| || 37 || 752.542 ||
| |
| || 38 || 772.881 ||
| |
| || 39 || 793.220 ||
| |
| || 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 || 996.610 ||
| |
| || 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 ||</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>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 />
| |
|
| |
|
| | === Odd harmonics === |
| | {{Harmonics in equal|59|columns=13}} |
|
| |
|
| <table class="wiki_table">
| | === Subsets and supersets === |
| <tr>
| | 59edo is the 17th [[prime edo]], following [[53edo]] and before [[61edo]]. As noted above, 118edo is a superset that yields most of the same tuning properties, but it also adds a near-just third harmonic to enable strong full 11-limit tuning. |
| <td>Degrees<br />
| |
| </td>
| |
| <td>Cents Value<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>203.390<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>406.780<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>711.864<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>793.220<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>996.610<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></pre></div>
| | == Intervals == |
| | {| class="wikitable center-1 right-2" |
| | |- |
| | ! Steps |
| | ! Cents |
| | ! Approximate ratios<br>(2.9.5.21.11.39.17-subgroup) |
| | ! Ratios of 3, 7, 13<br>(tending sharp) |
| | ! Ratios of 3, 7, 13<br>(tending flat) |
| | |- |
| | | 0 |
| | | 0.0 |
| | | [[1/1]] |
| | | |
| | | |
| | |- |
| | | 1 |
| | | 20.3 |
| | | [[81/80]] |
| | | |
| | | |
| | |- |
| | | 2 |
| | | 40.7 |
| | | [[40/39]], [[45/44]] |
| | | |
| | | |
| | |- |
| | | 3 |
| | | 61.0 |
| | | [[27/26]], [[28/27]] |
| | | |
| | | |
| | |- |
| | | 4 |
| | | 81.4 |
| | | [[21/20]], [[22/21]] |
| | | |
| | | |
| | |- |
| | | 5 |
| | | 101.7 |
| | | [[17/16]], [[18/17]], [[35/33]] |
| | | |
| | | |
| | |- |
| | | 6 |
| | | 122.0 |
| | | [[15/14]], [[14/13]] |
| | | |
| | | |
| | |- |
| | | 7 |
| | | 142.4 |
| | | [[13/12]] |
| | | |
| | | |
| | |- |
| | | 8 |
| | | 162.7 |
| | | [[11/10]] |
| | | |
| | | |
| | |- |
| | | 9 |
| | | 183.1 |
| | | [[10/9]] |
| | | |
| | | |
| | |- |
| | | 10 |
| | | 203.4 |
| | | [[9/8]], [[44/39]] |
| | | |
| | | |
| | |- |
| | | 11 |
| | | 223.7 |
| | | [[25/22]] |
| | | [[8/7]] |
| | | |
| | |- |
| | | 12 |
| | | 244.1 |
| | | [[15/13]], [[39/34]] |
| | | |
| | | [[8/7]] |
| | |- |
| | | 13 |
| | | 264.4 |
| | | [[7/6]], [[64/55]] |
| | | |
| | | |
| | |- |
| | | 14 |
| | | 284.7 |
| | | [[20/17]], [[33/28]] |
| | | |
| | | |
| | |- |
| | | 15 |
| | | 305.1 |
| | | [[25/21]] |
| | | |
| | | |
| | |- |
| | | 16 |
| | | 325.4 |
| | | |
| | | |
| | | |
| | |- |
| | | 17 |
| | | 345.8 |
| | | [[11/9]], [[39/32]], [[128/105]] |
| | | [[16/13]] |
| | | |
| | |- |
| | | 18 |
| | | 366.1 |
| | | [[21/17]] |
| | | |
| | | [[16/13]] |
| | |- |
| | | 19 |
| | | 386.4 |
| | | [[5/4]] |
| | | |
| | | |
| | |- |
| | | 20 |
| | | 406.8 |
| | | [[81/64]] |
| | | |
| | | |
| | |- |
| | | 21 |
| | | 427.1 |
| | | [[32/25]], [[50/39]] |
| | | |
| | | |
| | |- |
| | | 22 |
| | | 447.5 |
| | | [[22/17]], [[35/27]], [[128/99]] |
| | | |
| | | |
| | |- |
| | | 23 |
| | | 467.8 |
| | | [[21/16]], [[64/49]] |
| | | |
| | | |
| | |- |
| | | 24 |
| | | 488.1 |
| | | [[45/34]], [[85/64]] |
| | | [[4/3]] |
| | | |
| | |- |
| | | 25 |
| | | 508.5 |
| | | [[35/26]] |
| | | |
| | | [[4/3]] |
| | |- |
| | | 26 |
| | | 528.8 |
| | | [[34/25]] |
| | | |
| | | |
| | |- |
| | | 27 |
| | | 549.2 |
| | | [[11/8]], [[48/35]] |
| | | |
| | | |
| | |- |
| | | 28 |
| | | 569.5 |
| | | [[25/18]] |
| | | |
| | | |
| | |- |
| | | 29 |
| | | 589.8 |
| | | [[45/32]], [[128/91]] |
| | | |
| | | |
| | |- |
| | | 30 |
| | | 610.2 |
| | | [[64/45]], [[91/64]] |
| | | |
| | | |
| | |- |
| | | 31 |
| | | 630.5 |
| | | [[36/25]] |
| | | |
| | | |
| | |- |
| | | 32 |
| | | 650.8 |
| | | [[16/11]], [[35/24]] |
| | | |
| | | |
| | |- |
| | | 33 |
| | | 671.2 |
| | | [[25/17]] |
| | | |
| | | |
| | |- |
| | | 34 |
| | | 691.5 |
| | | [[52/35]] |
| | | |
| | | [[3/2]] |
| | |- |
| | | 35 |
| | | 711.9 |
| | | [[68/45]], [[128/85]] |
| | | [[3/2]] |
| | | |
| | |- |
| | | 36 |
| | | 732.2 |
| | | [[32/21]], [[49/32]] |
| | | |
| | | |
| | |- |
| | | 37 |
| | | 752.5 |
| | | [[17/11]], [[54/35]], [[99/64]] |
| | | |
| | | |
| | |- |
| | | 38 |
| | | 772.9 |
| | | [[25/16]], [[39/25]] |
| | | |
| | | |
| | |- |
| | | 39 |
| | | 793.2 |
| | | [[128/81]] |
| | | |
| | | |
| | |- |
| | | 40 |
| | | 813.6 |
| | | [[8/5]] |
| | | |
| | | |
| | |- |
| | | 41 |
| | | 833.9 |
| | | [[34/21]] |
| | | |
| | | [[13/8]] |
| | |- |
| | | 42 |
| | | 854.2 |
| | | [[18/11]], [[64/39]], [[105/64]] |
| | | [[13/8]] |
| | | |
| | |- |
| | | 43 |
| | | 874.6 |
| | | |
| | | |
| | | |
| | |- |
| | | 44 |
| | | 894.9 |
| | | [[42/25]] |
| | | |
| | | |
| | |- |
| | | 45 |
| | | 915.3 |
| | | [[17/10]], [[56/33]] |
| | | |
| | | |
| | |- |
| | | 46 |
| | | 935.6 |
| | | [[12/7]], [[55/32]] |
| | | |
| | | |
| | |- |
| | | 47 |
| | | 955.9 |
| | | [[26/15]], [[68/39]] |
| | | |
| | | [[7/4]] |
| | |- |
| | | 48 |
| | | 976.3 |
| | | [[44/25]] |
| | | [[7/4]] |
| | | |
| | |- |
| | | 49 |
| | | 996.6 |
| | | [[16/9]], [[39/22]] |
| | | |
| | | |
| | |- |
| | | 50 |
| | | 1016.9 |
| | | [[9/5]] |
| | | |
| | | |
| | |- |
| | | 51 |
| | | 1037.3 |
| | | [[20/11]] |
| | | |
| | | |
| | |- |
| | | 52 |
| | | 1057.6 |
| | | [[24/13]] |
| | | |
| | | |
| | |- |
| | | 53 |
| | | 1078.0 |
| | | [[13/7]], [[28/15]] |
| | | |
| | | |
| | |- |
| | | 54 |
| | | 1098.3 |
| | | [[17/9]], [[32/17]], [[66/35]] |
| | | |
| | | |
| | |- |
| | | 55 |
| | | 1118.6 |
| | | [[21/11]], [[40/21]] |
| | | |
| | | |
| | |- |
| | | 56 |
| | | 1139.0 |
| | | [[27/14]], [[52/27]] |
| | | |
| | | |
| | |- |
| | | 57 |
| | | 1159.3 |
| | | [[39/20]], [[88/45]] |
| | | |
| | | |
| | |- |
| | | 58 |
| | | 1179.7 |
| | | [[160/81]] |
| | | |
| | | |
| | |- |
| | | 59 |
| | | 1200.0 |
| | | [[2/1]] |
| | | |
| | | |
| | |}{{Todo|inline=1|complete table}} |
| | |
| | == Notation == |
| | |
| | === Sagittal notation === |
| | ==== Best fifth notation ==== |
| | This notation uses the same sagittal sequence as [[66edo#Sagittal notation|66-EDO]]. |
| | |
| | ===== Evo flavor ===== |
| | <imagemap> |
| | File:59-EDO_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 743 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 190 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | rect 190 80 320 106 [[144/143]] |
| | rect 320 80 430 106 [[81/80]] |
| | rect 430 80 570 106 [[1053/1024]] |
| | default [[File:59-EDO_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ===== Revo flavor ===== |
| | <imagemap> |
| | File:59-EDO_Revo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 743 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 190 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | rect 190 80 320 106 [[144/143]] |
| | rect 320 80 430 106 [[81/80]] |
| | rect 430 80 570 106 [[1053/1024]] |
| | default [[File:59-EDO_Revo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. |
| | |
| | ==== Second-best fifth notation ==== |
| | This notation uses the same sagittal sequence as EDOs [[45edo#Sagittal notation|45]] and [[52edo#Sagittal notation|52]]. |
| | |
| | ===== Evo flavor ===== |
| | <imagemap> |
| | File:59b_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[36/35]] |
| | default [[File:59b_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ===== Revo flavor ===== |
| | <imagemap> |
| | File:59b_Revo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 695 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[36/35]] |
| | default [[File:59b_Revo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ===== Evo-SZ flavor ===== |
| | <imagemap> |
| | File:59b_Evo-SZ_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[36/35]] |
| | default [[File:59b_Evo-SZ_Sagittal.svg]] |
| | </imagemap> |
| | |
| | Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein–Zimmerman notation. |
| | |
| | == Octave stretch or compression == |
| | 59edo’s approximations of 3/1, 7/1 and 11/1 are improved by [[93edt]], a [[Octave stretch|stretched-octave]] version of 59edo. The trade-off is a slightly worse 2/1 and 5/1. |
| | |
| | [[ed12|211ed12]] is also a solid stretched-octave option, which improves 59edo's 3/1, doing a little, but not much, damage to most other primes. |
| | |
| | If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[ed6|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1. |
| | |
| | == Scales == |
| | ; [[Porcupine]] scales |
| | * Porcupine[7]: 8 8 8 11 8 8 8 |
| | * Porcupine[15]: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 |
| | * Porcupine[22]: 3 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 2 3 |
| | * [[User:BudjarnLambeth/Antechinus|Antechinus]] (''nonoctave period'') |
| | |
| | == Instruments == |
| | ; Lumatone |
| | |
| | See [[Lumatone mapping for 59edo]]. |
| | |
| | == Music == |
| | ; [[Bryan Deister]] |
| | * [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025) |
| | * [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025) |
| | * [https://www.youtube.com/shorts/XYr4j6Abwlw ''Le Ciel - Malice Mizer (microtonal cover in 59edo)''] (2026) |
| | |
| | ; [[Francium]] |
| | * "too powerful if i had social skills" from ''Melancholie'' (2023) – [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] | [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] | [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube] |
| | * "Stay Away From The Fog" from ''Void'' (2025) – [https://open.spotify.com/track/6swFGV70cPYwruPrnu3iHX Spotify] | [https://francium223.bandcamp.com/track/stay-away-from-the-fog Bandcamp] | [https://www.youtube.com/watch?v=zVsjM-LRjNo YouTube] |
| | |
| | ; [[Budjarn Lambeth]] |
| | * [https://youtu.be/YDbqf3g88BE ''The Odd Effects of Breathing the Fairy Dust''] (2026) |
| | |
| | ; [[Ray Perlner]] |
| | * [https://www.youtube.com/watch?v=JJ4B47S1TUI ''Chinchillian Fugue''] – first mode of the Porcupine[7] scale in 59edo |
| | |
| | [[Category:Porcupine]] |
| | [[Category:Listen]] |
| | [[Category:Todo:add rank 2 temperaments table]] |