58edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~guest~~|~~guest~~]] and made on <tt>2012-02-~~26 23~~:53:52 UTC</tt>.

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-13 08:36:00 UTC</tt>.

: The original revision id was <tt>~~305358568~~</tt>.

: The original revision id was <tt>352968254</tt>.

: The revision comment was: <tt></tt>

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

Line 16:

==Intervals==

|| degree of 58edo || cents value || associated temperament ||

|| degree of 58edo || cents value || ratios || associated temperament ||

|| 0 || 0.00 || ||

|| 0 || 0.00 || 1/1 || ||

|| 1 || 20.69 || ||

|| 1 || 20.69 || 56/55, 64/63, 81/80, 128/125 || ||

|| 2 || 41.38 || ||

|| 2 || 41.38 || 36/35, 49/48, 50/49, 55/54 || ||

|| 3 || 62.07 || ||

|| 3 || 62.07 || 25/24, 26/25, 27/26, 28/27, 33/32 || ||

|| 4 || 82.76 || ||

|| 4 || 82.76 || 21/20, 22/21 || ||

|| 5 || 103.45 || ||

|| 5 || 103.45 || 16/15, 17/16, 18/17 || ||

|| 6 || 124.14 || ||

|| 6 || 124.14 || 14/13, 15/14, 27/25 || ||

|| 7 || 144.83 || ||

|| 7 || 144.83 || 12/11, 13/12 || ||

|| 8 || 165.52 || ||

|| 8 || 165.52 || 11/10 || ||

|| 9 || 186.21 || ||

|| 9 || 186.21 || 10/9 || ||

|| 10 || 206.9 || ||

|| 10 || 206.9 || 9/8, 17/15 || ||

|| 11 || 227.59 || ||

|| 11 || 227.59 || 8/7 || ||

|| 12 || 248.28 || ||

|| 12 || 248.28 || 15/13 || ||

|| 13 || 268.97 || ||

|| 13 || 268.97 || 7/6 || ||

|| 14 || 289.66 || ||

|| 14 || 289.66 || 13/11, 20/17 || ||

|| 15 || 310.34 || ||

|| 15 || 310.34 || 6/5 || Myna ||

|| 16 || 331.03 || ||

|| 16 || 331.03 || 17/14 || ||

|| 17 || 351.72 || ||

|| 17 || 351.72 || 11/9, 16/13 || ||

|| 18 || 372.41 || ||

|| 18 || 372.41 || 21/17 || ||

|| 19 || 393.1 || ||

|| 19 || 393.1 || 5/4 || ||

|| 20 || 413.79 || ||

|| 20 || 413.79 || 14/11 || ||

|| 21 || 434.48 || ||

|| 21 || 434.48 || 9/7 || ||

|| 22 || 455.17 || ||

|| 22 || 455.17 || 13/10, 17/13, 22/17 || ||

|| 23 || 475.86 || ||

|| 23 || 475.86 || 21/16 || ||

|| 24 || 496.55 || ||

|| 24 || 496.55 || 4/3 || ||

|| 25 || 517.24 || ||

|| 25 || 517.24 || 27/20 || ||

|| 26 || 537.93 || ||

|| 26 || 537.93 || 15/11 || ||

|| 27 || 558.62 || ||

|| 27 || 558.62 || 11/8, 18/13 || ||

|| 28 || 579.31 || ||

|| 28 || 579.31 || 7/5 || ||

|| 29 || 600 || ||

|| 29 || 600 || 17/12, 24/17 || ||

|| 30 || 620.69 || ||

|| 30 || 620.69 || 10/7 || ||

|| 31 || 641.38 || ||

|| 31 || 641.38 || 13/9, 16/11 || ||

|| 32 || 662.07 || ||

|| 32 || 662.07 || 22/15 || ||

|| 33 || 682.76 || ||

|| 33 || 682.76 || 40/27 || ||

|| 34 || 703.45 || ||

|| 34 || 703.45 || 3/2 || ||

|| 35 || 724.14 || ||

|| 35 || 724.14 || 32/21 || ||

|| 36 || 744.83 || ||

|| 36 || 744.83 || 20/13, 26/17, 17/11 || ||

|| 37 || 765.52 || ||

|| 37 || 765.52 || 14/9 || ||

|| 38 || 786.21 || ||

|| 38 || 786.21 || 11/7 || ||

|| 39 || 806.9 || ||

|| 39 || 806.9 || 8/5 || ||

|| 40 || 827.59 || ||

|| 40 || 827.59 || || ||

|| 41 || 848.28 || ||

|| 41 || 848.28 || 13/8, 18/11 || ||

|| 42 || 868.97 || ||

|| 42 || 868.97 || || ||

|| 43 || 889.66 || ||

|| 43 || 889.66 || || ||

|| 44 || 910.34 || ||

|| 44 || 910.34 || || ||

|| 45 || 931.03 || ||

|| 45 || 931.03 || || ||

|| 46 || 951.72 || ||

|| 46 || 951.72 || || ||

|| 47 || 972.41 || ||

|| 47 || 972.41 || 7/4 || ||

|| 48 || 993.1 || ||

|| 48 || 993.1 || 16/9 || ||

|| 49 || 1013.79 || ||

|| 49 || 1013.79 || 9/5 || ||

|| 50 || 1034.48 || ||

|| 50 || 1034.48 || || ||

|| 51 || 1055.17 || ||

|| 51 || 1055.17 || || ||

|| 52 || 1075.86 || ||

|| 52 || 1075.86 || || ||

|| 53 || 1096.55 || ||

|| 53 || 1096.55 || || ||

|| 54 || 1117.24 || ||

|| 54 || 1117.24 || || ||

|| 55 || 1137.93 || ||

|| 55 || 1137.93 || || ||

|| 56 || 1158.62 || ||

|| 56 || 1158.62 || || ||

|| 57 || 1179.31 || ||</pre></div>

|| 57 || 1179.31 || || ||</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>58edo</title></head><body>The 58 equal temperament, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the <a class="wiki_link" href="/11-limit">11</a>, <a class="wiki_link" href="/13-limit">13</a> and <a class="wiki_link" href="/17-limit">17-limit</a>s. It is the smallest <a class="wiki_link" href="/edo">equal temperament</a> which is <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit, and is also the first et to map the entire 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> to distinct scale steps, and hence the first et which can define a version of the famous 43-note <a class="wiki_link" href="/Genesis%20scale">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports <a class="wiki_link" href="/hemififths">hemififths</a>, <a class="wiki_link" href="/myna">myna</a>, <a class="wiki_link" href="/diaschismic">diaschismic</a>, <a class="wiki_link" href="/harry">harry</a>, <a class="wiki_link" href="/mystery">mystery</a>, <a class="wiki_link" href="/buzzard">buzzard</a> and <a class="wiki_link" href="/thuja">thuja</a> <a class="wiki_link" href="/temperament">temperament</a>s, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments <a class="wiki_link" href="/thrush">thrush</a>, <a class="wiki_link" href="/bluebird">bluebird</a>, <a class="wiki_link" href="/aplonis">aplonis</a> and <a class="wiki_link" href="/jofur">jofur</a>.

Line 93:

</td>

<td>cents value

</td>

<td>ratios

</td>

<td>associated temperament

Line 101:

Line 103:

</td>

<td>0.00

</td>

<td>1/1

</td>

<td>

Line 109:

Line 113:

</td>

<td>20.69

</td>

<td>56/55, 64/63, 81/80, 128/125

</td>

<td>

Line 117:

Line 123:

</td>

<td>41.38

</td>

<td>36/35, 49/48, 50/49, 55/54

</td>

<td>

Line 125:

Line 133:

</td>

<td>62.07

</td>

<td>25/24, 26/25, 27/26, 28/27, 33/32

</td>

<td>

Line 133:

Line 143:

</td>

<td>82.76

</td>

<td>21/20, 22/21

</td>

<td>

Line 141:

Line 153:

</td>

<td>103.45

</td>

<td>16/15, 17/16, 18/17

</td>

<td>

Line 149:

Line 163:

</td>

<td>124.14

</td>

<td>14/13, 15/14, 27/25

</td>

<td>

Line 157:

Line 173:

</td>

<td>144.83

</td>

<td>12/11, 13/12

</td>

<td>

Line 165:

Line 183:

</td>

<td>165.52

</td>

<td>11/10

</td>

<td>

Line 173:

Line 193:

</td>

<td>186.21

</td>

<td>10/9

</td>

<td>

Line 181:

Line 203:

</td>

<td>206.9

</td>

<td>9/8, 17/15

</td>

<td>

Line 189:

Line 213:

</td>

<td>227.59

</td>

<td>8/7

</td>

<td>

Line 197:

Line 223:

</td>

<td>248.28

</td>

<td>15/13

</td>

<td>

Line 205:

Line 233:

</td>

<td>268.97

</td>

<td>7/6

</td>

<td>

Line 213:

Line 243:

</td>

<td>289.66

</td>

<td>13/11, 20/17

</td>

<td>

Line 222:

Line 254:

<td>310.34

</td>

<td>

<td>6/5

</td>

<td>Myna

</td>

</tr>

Line 229:

Line 263:

</td>

<td>331.03

</td>

<td>17/14

</td>

<td>

Line 237:

Line 273:

</td>

<td>351.72

</td>

<td>11/9, 16/13

</td>

<td>

Line 245:

Line 283:

</td>

<td>372.41

</td>

<td>21/17

</td>

<td>

Line 253:

Line 293:

</td>

<td>393.1

</td>

<td>5/4

</td>

<td>

Line 261:

Line 303:

</td>

<td>413.79

</td>

<td>14/11

</td>

<td>

Line 269:

Line 313:

</td>

<td>434.48

</td>

<td>9/7

</td>

<td>

Line 277:

Line 323:

</td>

<td>455.17

</td>

<td>13/10, 17/13, 22/17

</td>

<td>

Line 285:

Line 333:

</td>

<td>475.86

</td>

<td>21/16

</td>

<td>

Line 293:

Line 343:

</td>

<td>496.55

</td>

<td>4/3

</td>

<td>

Line 301:

Line 353:

</td>

<td>517.24

</td>

<td>27/20

</td>

<td>

Line 309:

Line 363:

</td>

<td>537.93

</td>

<td>15/11

</td>

<td>

Line 317:

Line 373:

</td>

<td>558.62

</td>

<td>11/8, 18/13

</td>

<td>

Line 325:

Line 383:

</td>

<td>579.31

</td>

<td>7/5

</td>

<td>

Line 333:

Line 393:

</td>

<td>600

</td>

<td>17/12, 24/17

</td>

<td>

Line 341:

Line 403:

</td>

<td>620.69

</td>

<td>10/7

</td>

<td>

Line 349:

Line 413:

</td>

<td>641.38

</td>

<td>13/9, 16/11

</td>

<td>

Line 357:

Line 423:

</td>

<td>662.07

</td>

<td>22/15

</td>

<td>

Line 365:

Line 433:

</td>

<td>682.76

</td>

<td>40/27

</td>

<td>

Line 373:

Line 443:

</td>

<td>703.45

</td>

<td>3/2

</td>

<td>

Line 381:

Line 453:

</td>

<td>724.14

</td>

<td>32/21

</td>

<td>

Line 389:

Line 463:

</td>

<td>744.83

</td>

<td>20/13, 26/17, 17/11

</td>

<td>

Line 397:

Line 473:

</td>

<td>765.52

</td>

<td>14/9

</td>

<td>

Line 405:

Line 483:

</td>

<td>786.21

</td>

<td>11/7

</td>

<td>

Line 413:

Line 493:

</td>

<td>806.9

</td>

<td>8/5

</td>

<td>

Line 421:

Line 503:

</td>

<td>827.59

</td>

<td>

</td>

<td>

Line 429:

Line 513:

</td>

<td>848.28

</td>

<td>13/8, 18/11

</td>

<td>

Line 437:

Line 523:

</td>

<td>868.97

</td>

<td>

</td>

<td>

Line 445:

Line 533:

</td>

<td>889.66

</td>

<td>

</td>

<td>

Line 453:

Line 543:

</td>

<td>910.34

</td>

<td>

</td>

<td>

Line 461:

Line 553:

</td>

<td>931.03

</td>

<td>

</td>

<td>

Line 469:

Line 563:

</td>

<td>951.72

</td>

<td>

</td>

<td>

Line 477:

Line 573:

</td>

<td>972.41

</td>

<td>7/4

</td>

<td>

Line 485:

Line 583:

</td>

<td>993.1

</td>

<td>16/9

</td>

<td>

Line 493:

Line 593:

</td>

<td>1013.79

</td>

<td>9/5

</td>

<td>

Line 501:

Line 603:

</td>

<td>1034.48

</td>

<td>

</td>

<td>

Line 509:

Line 613:

</td>

<td>1055.17

</td>

<td>

</td>

<td>

Line 517:

Line 623:

</td>

<td>1075.86

</td>

<td>

</td>

<td>

Line 525:

Line 633:

</td>

<td>1096.55

</td>

<td>

</td>

<td>

Line 533:

Line 643:

</td>

<td>1117.24

</td>

<td>

</td>

<td>

Line 541:

Line 653:

</td>

<td>1137.93

</td>

<td>

</td>

<td>

Line 549:

Line 663:

</td>

<td>1158.62

</td>

<td>

</td>

<td>

Line 557:

Line 673:

</td>

<td>1179.31

</td>

<td>

</td>

<td>

@@ 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:guest|guest]] and made on <tt>2012-02-26 23:53:52 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-13 08:36:00 UTC</tt>.<br>
-: The original revision id was <tt>305358568</tt>.<br>
+: The original revision id was <tt>352968254</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 16: / Line 16: @@
 ==Intervals==
-|| degree of 58edo || cents value || associated temperament ||
+|| degree of 58edo || cents value || ratios || associated temperament ||
-|| 0 || 0.00 ||   ||
+|| 0 || 0.00 || 1/1 ||   ||
-|| 1 || 20.69 ||   ||
+|| 1 || 20.69 || 56/55, 64/63, 81/80, 128/125 ||   ||
-|| 2 || 41.38 ||   ||
+|| 2 || 41.38 || 36/35, 49/48, 50/49, 55/54 ||   ||
-|| 3 || 62.07 ||   ||
+|| 3 || 62.07 || 25/24, 26/25, 27/26, 28/27, 33/32 ||   ||
-|| 4 || 82.76 ||   ||
+|| 4 || 82.76 || 21/20, 22/21 ||   ||
-|| 5 || 103.45 ||   ||
+|| 5 || 103.45 || 16/15, 17/16, 18/17 ||   ||
-|| 6 || 124.14 ||   ||
+|| 6 || 124.14 || 14/13, 15/14, 27/25 ||   ||
-|| 7 || 144.83 ||   ||
+|| 7 || 144.83 || 12/11, 13/12 ||   ||
-|| 8 || 165.52 ||   ||
+|| 8 || 165.52 || 11/10 ||   ||
-|| 9 || 186.21 ||   ||
+|| 9 || 186.21 || 10/9 ||   ||
-|| 10 || 206.9 ||   ||
+|| 10 || 206.9 || 9/8, 17/15 ||   ||
-|| 11 || 227.59 ||   ||
+|| 11 || 227.59 || 8/7 ||   ||
-|| 12 || 248.28 ||   ||
+|| 12 || 248.28 || 15/13 ||   ||
-|| 13 || 268.97 ||   ||
+|| 13 || 268.97 || 7/6 ||   ||
-|| 14 || 289.66 ||   ||
+|| 14 || 289.66 || 13/11, 20/17 ||   ||
-|| 15 || 310.34 ||   ||
+|| 15 || 310.34 || 6/5 || Myna ||
-|| 16 || 331.03 ||   ||
+|| 16 || 331.03 || 17/14 ||   ||
-|| 17 || 351.72 ||   ||
+|| 17 || 351.72 || 11/9, 16/13 ||   ||
-|| 18 || 372.41 ||   ||
+|| 18 || 372.41 || 21/17 ||   ||
-|| 19 || 393.1 ||   ||
+|| 19 || 393.1 || 5/4 ||   ||
-|| 20 || 413.79 ||   ||
+|| 20 || 413.79 || 14/11 ||   ||
-|| 21 || 434.48 ||   ||
+|| 21 || 434.48 || 9/7 ||   ||
-|| 22 || 455.17 ||   ||
+|| 22 || 455.17 || 13/10, 17/13, 22/17 ||   ||
-|| 23 || 475.86 ||   ||
+|| 23 || 475.86 || 21/16 ||   ||
-|| 24 || 496.55 ||   ||
+|| 24 || 496.55 || 4/3 ||   ||
-|| 25 || 517.24 ||   ||
+|| 25 || 517.24 || 27/20 ||   ||
-|| 26 || 537.93 ||   ||
+|| 26 || 537.93 || 15/11 ||   ||
-|| 27 || 558.62 ||   ||
+|| 27 || 558.62 || 11/8, 18/13 ||   ||
-|| 28 || 579.31 ||   ||
+|| 28 || 579.31 || 7/5 ||   ||
-|| 29 || 600 ||   ||
+|| 29 || 600 || 17/12, 24/17 ||   ||
-|| 30 || 620.69 ||   ||
+|| 30 || 620.69 || 10/7 ||   ||
-|| 31 || 641.38 ||   ||
+|| 31 || 641.38 || 13/9, 16/11 ||   ||
-|| 32 || 662.07 ||   ||
+|| 32 || 662.07 || 22/15 ||   ||
-|| 33 || 682.76 ||   ||
+|| 33 || 682.76 || 40/27 ||   ||
-|| 34 || 703.45 ||   ||
+|| 34 || 703.45 || 3/2 ||   ||
-|| 35 || 724.14 ||   ||
+|| 35 || 724.14 || 32/21 ||   ||
-|| 36 || 744.83 ||   ||
+|| 36 || 744.83 || 20/13, 26/17, 17/11 ||   ||
-|| 37 || 765.52 ||   ||
+|| 37 || 765.52 || 14/9 ||   ||
-|| 38 || 786.21 ||   ||
+|| 38 || 786.21 || 11/7 ||   ||
-|| 39 || 806.9 ||   ||
+|| 39 || 806.9 || 8/5 ||   ||
-|| 40 || 827.59 ||   ||
+|| 40 || 827.59 ||   ||   ||
-|| 41 || 848.28 ||   ||
+|| 41 || 848.28 || 13/8, 18/11 ||   ||
-|| 42 || 868.97 ||   ||
+|| 42 || 868.97 ||   ||   ||
-|| 43 || 889.66 ||   ||
+|| 43 || 889.66 ||   ||   ||
-|| 44 || 910.34 ||   ||
+|| 44 || 910.34 ||   ||   ||
-|| 45 || 931.03 ||   ||
+|| 45 || 931.03 ||   ||   ||
-|| 46 || 951.72 ||   ||
+|| 46 || 951.72 ||   ||   ||
-|| 47 || 972.41 ||   ||
+|| 47 || 972.41 || 7/4 ||   ||
-|| 48 || 993.1 ||   ||
+|| 48 || 993.1 || 16/9 ||   ||
-|| 49 || 1013.79 ||   ||
+|| 49 || 1013.79 || 9/5 ||   ||
-|| 50 || 1034.48 ||   ||
+|| 50 || 1034.48 ||   ||   ||
-|| 51 || 1055.17 ||   ||
+|| 51 || 1055.17 ||   ||   ||
-|| 52 || 1075.86 ||   ||
+|| 52 || 1075.86 ||   ||   ||
-|| 53 || 1096.55 ||   ||
+|| 53 || 1096.55 ||   ||   ||
-|| 54 || 1117.24 ||   ||
+|| 54 || 1117.24 ||   ||   ||
-|| 55 || 1137.93 ||   ||
+|| 55 || 1137.93 ||   ||   ||
-|| 56 || 1158.62 ||   ||
+|| 56 || 1158.62 ||   ||   ||
-|| 57 || 1179.31 ||   ||</pre></div>
+|| 57 || 1179.31 ||   ||   ||</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;58edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;58 equal temperament&lt;/em&gt;, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the &lt;a class="wiki_link" href="/11-limit"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13&lt;/a&gt; and &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;s. It is the smallest &lt;a class="wiki_link" href="/edo"&gt;equal temperament&lt;/a&gt; which is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through the 17-limit, and is also the first et to map the entire 11-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; to distinct scale steps, and hence the first et which can define a version of the famous 43-note &lt;a class="wiki_link" href="/Genesis%20scale"&gt;Genesis scale&lt;/a&gt; of &lt;a class="wiki_link" href="/Harry%20Partch"&gt;Harry Partch&lt;/a&gt;. It supports &lt;a class="wiki_link" href="/hemififths"&gt;hemififths&lt;/a&gt;, &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt;, &lt;a class="wiki_link" href="/diaschismic"&gt;diaschismic&lt;/a&gt;, &lt;a class="wiki_link" href="/harry"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/temperament"&gt;temperament&lt;/a&gt;s, and supplies the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments &lt;a class="wiki_link" href="/thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/jofur"&gt;jofur&lt;/a&gt;.&lt;br /&gt;
@@ Line 93: / Line 93: @@
 &lt;/td&gt;
          &lt;td&gt;cents value&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ratios&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;associated temperament&lt;br /&gt;
@@ Line 101: / Line 103: @@
 &lt;/td&gt;
          &lt;td&gt;0.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 109: / Line 113: @@
 &lt;/td&gt;
          &lt;td&gt;20.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;56/55, 64/63, 81/80, 128/125&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 117: / Line 123: @@
 &lt;/td&gt;
          &lt;td&gt;41.38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;36/35, 49/48, 50/49, 55/54&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 125: / Line 133: @@
 &lt;/td&gt;
          &lt;td&gt;62.07&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25/24, 26/25, 27/26, 28/27, 33/32&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 133: / Line 143: @@
 &lt;/td&gt;
          &lt;td&gt;82.76&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/20, 22/21&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 141: / Line 153: @@
 &lt;/td&gt;
          &lt;td&gt;103.45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/15, 17/16, 18/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 149: / Line 163: @@
 &lt;/td&gt;
          &lt;td&gt;124.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/13, 15/14, 27/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 157: / Line 173: @@
 &lt;/td&gt;
          &lt;td&gt;144.83&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12/11, 13/12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 165: / Line 183: @@
 &lt;/td&gt;
          &lt;td&gt;165.52&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 173: / Line 193: @@
 &lt;/td&gt;
          &lt;td&gt;186.21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 181: / Line 203: @@
 &lt;/td&gt;
          &lt;td&gt;206.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/8, 17/15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 189: / Line 213: @@
 &lt;/td&gt;
          &lt;td&gt;227.59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 197: / Line 223: @@
 &lt;/td&gt;
          &lt;td&gt;248.28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 205: / Line 233: @@
 &lt;/td&gt;
          &lt;td&gt;268.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 213: / Line 243: @@
 &lt;/td&gt;
          &lt;td&gt;289.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/11, 20/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 222: / Line 254: @@
          &lt;td&gt;310.34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;6/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Myna&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 229: / Line 263: @@
 &lt;/td&gt;
          &lt;td&gt;331.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/14&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 237: / Line 273: @@
 &lt;/td&gt;
          &lt;td&gt;351.72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/9, 16/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 245: / Line 283: @@
 &lt;/td&gt;
          &lt;td&gt;372.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 253: / Line 293: @@
 &lt;/td&gt;
          &lt;td&gt;393.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 261: / Line 303: @@
 &lt;/td&gt;
          &lt;td&gt;413.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 269: / Line 313: @@
 &lt;/td&gt;
          &lt;td&gt;434.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 277: / Line 323: @@
 &lt;/td&gt;
          &lt;td&gt;455.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/10, 17/13, 22/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 285: / Line 333: @@
 &lt;/td&gt;
          &lt;td&gt;475.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/16&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 293: / Line 343: @@
 &lt;/td&gt;
          &lt;td&gt;496.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 301: / Line 353: @@
 &lt;/td&gt;
          &lt;td&gt;517.24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27/20&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 309: / Line 363: @@
 &lt;/td&gt;
          &lt;td&gt;537.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 317: / Line 373: @@
 &lt;/td&gt;
          &lt;td&gt;558.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/8, 18/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 325: / Line 383: @@
 &lt;/td&gt;
          &lt;td&gt;579.31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 333: / Line 393: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/12, 24/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 341: / Line 403: @@
 &lt;/td&gt;
          &lt;td&gt;620.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 349: / Line 413: @@
 &lt;/td&gt;
          &lt;td&gt;641.38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/9, 16/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 357: / Line 423: @@
 &lt;/td&gt;
          &lt;td&gt;662.07&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22/15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 365: / Line 433: @@
 &lt;/td&gt;
          &lt;td&gt;682.76&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;40/27&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 373: / Line 443: @@
 &lt;/td&gt;
          &lt;td&gt;703.45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 381: / Line 453: @@
 &lt;/td&gt;
          &lt;td&gt;724.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32/21&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 389: / Line 463: @@
 &lt;/td&gt;
          &lt;td&gt;744.83&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20/13, 26/17, 17/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 397: / Line 473: @@
 &lt;/td&gt;
          &lt;td&gt;765.52&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 405: / Line 483: @@
 &lt;/td&gt;
          &lt;td&gt;786.21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 413: / Line 493: @@
 &lt;/td&gt;
          &lt;td&gt;806.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 421: / Line 503: @@
 &lt;/td&gt;
          &lt;td&gt;827.59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 429: / Line 513: @@
 &lt;/td&gt;
          &lt;td&gt;848.28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/8, 18/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 437: / Line 523: @@
 &lt;/td&gt;
          &lt;td&gt;868.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 445: / Line 533: @@
 &lt;/td&gt;
          &lt;td&gt;889.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 453: / Line 543: @@
 &lt;/td&gt;
          &lt;td&gt;910.34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 461: / Line 553: @@
 &lt;/td&gt;
          &lt;td&gt;931.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 469: / Line 563: @@
 &lt;/td&gt;
          &lt;td&gt;951.72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 477: / Line 573: @@
 &lt;/td&gt;
          &lt;td&gt;972.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 485: / Line 583: @@
 &lt;/td&gt;
          &lt;td&gt;993.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 493: / Line 593: @@
 &lt;/td&gt;
          &lt;td&gt;1013.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 501: / Line 603: @@
 &lt;/td&gt;
          &lt;td&gt;1034.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 509: / Line 613: @@
 &lt;/td&gt;
          &lt;td&gt;1055.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 517: / Line 623: @@
 &lt;/td&gt;
          &lt;td&gt;1075.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 525: / Line 633: @@
 &lt;/td&gt;
          &lt;td&gt;1096.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 533: / Line 643: @@
 &lt;/td&gt;
          &lt;td&gt;1117.24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 541: / Line 653: @@
 &lt;/td&gt;
          &lt;td&gt;1137.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 549: / Line 663: @@
 &lt;/td&gt;
          &lt;td&gt;1158.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 557: / Line 673: @@
 &lt;/td&gt;
          &lt;td&gt;1179.31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;