35edo: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>phylingual **Imported revision 329676148 - Original comment: ** |
Wikispaces>phylingual **Imported revision 330015248 - Original comment: ** |
||
Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05- | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-04 11:21:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>330015248</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
Line 63: | Line 63: | ||
|| 1 || 11\35 || [[xenharmonic/Magic|Magic]] || | || 1 || 11\35 || [[xenharmonic/Magic|Magic]] || | ||
|| 1 || 12\35 || || | || 1 || 12\35 || || | ||
|| 1 || 13\35 || [[Sensipent family|Sensipent]] || | || 1 || 13\35 || [[xenharmonic/Sensipent family|Sensipent]] || | ||
|| 1 || 16\35 || || | || 1 || 16\35 || || | ||
|| 1 || 17\35 || || | || 1 || 17\35 || || | ||
Line 70: | Line 70: | ||
|| || || || | || || || || | ||
|| 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || | || 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || | ||
|| 7 || 2\35 || [[Greenwoodmic temperaments#Greenwood|Greenwood]] || | || 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || | ||
==<span style="background-color: #ffffff;">Commas</span>== | ==<span style="background-color: #ffffff;">Commas</span>== | ||
35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.) | |||
== == | |||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | == == | ||
|| | ||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || | ||
|| | || 2187/2048 || | -11 7 > || 113.69 || Apotome || Whitewood comma || || | ||
|| | || 6561/6250 || | -1 8 -5 > || 84.07 || Ripple comma || || || | ||
|| | || 10077696/9765625 || | 9 9 -10 > || 54.46 || Mynic comma || || || | ||
|| | || 3125/3072 || | -10 -1 5 > || 29.61 || Small diesis || Magic comma || || | ||
|| | || 78732/78125 || | 2 9 -7 > || 13.40 || Medium semicomma || Sensipent comma || || | ||
|| | || 405/392 || | -3 4 1 -2 > || 56.48 || Greenwoodma || || || | ||
|| | || 16807/16384 || | -14 0 0 5 > || 44.13 || || || || | ||
|| | || 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || || || | ||
|| | || 126/125 || | 1 2 -3 1 > || 13.79 || Starling comma || Septimal semicomma || || | ||
|| | || 99/98 || | -1 2 0 -2 1 > || 17.58 || Mothwellsma || || || | ||
|| 66/65 || | 1 1 -1 0 1 -1 > || 26.43 || || || || | |||
== == | |||
== == </pre></div> | |||
<h4>Original HTML content:</h4> | <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>35edo</title></head><body>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br /> | <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>35edo</title></head><body>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br /> | ||
Line 609: | Line 614: | ||
<td>13\35<br /> | <td>13\35<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Sensipent%20family">Sensipent</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensipent%20family">Sensipent</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 665: | Line 670: | ||
<td>2\35<br /> | <td>2\35<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 671: | Line 676: | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2> | ||
35EDO tempers out the following commas. (Note: This assumes the val &lt;35 55 81 98 121 130|.)<br /> | |||
< | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h2> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th>Comma<br /> | <th><strong>Comma</strong><br /> | ||
</th> | </th> | ||
<th>Monzo<br /> | <th><strong>Monzo</strong><br /> | ||
</th> | </th> | ||
<th>Value (Cents)<br /> | <th><strong>Value (Cents)</strong><br /> | ||
</th> | </th> | ||
<th>Name 1<br /> | <th><strong>Name 1</strong><br /> | ||
</th> | </th> | ||
<th>Name 2<br /> | <th><strong>Name 2</strong><br /> | ||
</th> | </th> | ||
<th>Name 3<br /> | <th><strong>Name 3</strong><br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>2187/2048<br /> | ||
</td> | </td> | ||
<td | <td>| -11 7 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>113.69<br /> | ||
</td> | </td> | ||
<td | <td>Apotome<br /> | ||
</td> | </td> | ||
<td | <td>Whitewood comma<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>6561/6250<br /> | ||
</td> | </td> | ||
<td | <td>| -1 8 -5 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>84.07<br /> | ||
</td> | </td> | ||
<td | <td>Ripple comma<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 719: | Line 726: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>10077696/9765625<br /> | ||
</td> | </td> | ||
<td>| 9 9 -10 &gt;<br /> | <td>| 9 9 -10 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>54.46<br /> | ||
</td> | </td> | ||
<td | <td>Mynic comma<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 733: | Line 740: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>3125/3072<br /> | ||
</td> | </td> | ||
<td | <td>| -10 -1 5 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>29.61<br /> | ||
</td> | </td> | ||
<td | <td>Small diesis<br /> | ||
</td> | </td> | ||
<td | <td>Magic comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 747: | Line 754: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>78732/78125<br /> | ||
</td> | </td> | ||
<td>| 2 9 -7 &gt;<br /> | <td>| 2 9 -7 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>13.40<br /> | ||
</td> | </td> | ||
<td | <td>Medium semicomma<br /> | ||
</td> | </td> | ||
<td | <td>Sensipent comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 761: | Line 768: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>405/392<br /> | ||
</td> | </td> | ||
<td>| -3 4 1 -2 &gt;<br /> | <td>| -3 4 1 -2 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>56.48<br /> | ||
</td> | </td> | ||
<td | <td>Greenwoodma<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 775: | Line 782: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>16807/16384<br /> | ||
</td> | </td> | ||
<td | <td>| -14 0 0 5 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>44.13<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 789: | Line 796: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>525/512<br /> | ||
</td> | </td> | ||
<td>| -9 1 2 1 &gt;<br /> | <td>| -9 1 2 1 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>43.41<br /> | ||
</td> | </td> | ||
<td | <td>Avicennma<br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 803: | Line 810: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>126/125<br /> | ||
</td> | </td> | ||
<td | <td>| 1 2 -3 1 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>13.79<br /> | ||
</td> | </td> | ||
<td | <td>Starling comma<br /> | ||
</td> | </td> | ||
<td | <td>Septimal semicomma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 817: | Line 824: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>99/98<br /> | ||
</td> | </td> | ||
<td>| -1 2 0 -2 1 &gt;<br /> | <td>| -1 2 0 -2 1 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>17.58<br /> | ||
</td> | </td> | ||
<td>Mothwellsma<br /> | <td>Mothwellsma<br /> | ||
Line 831: | Line 838: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td>66/65<br /> | ||
</td> | </td> | ||
<td>| 1 1 -1 0 1 -1 &gt;<br /> | <td>| 1 1 -1 0 1 -1 &gt;<br /> | ||
</td> | </td> | ||
<td | <td>26.43<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 846: | Line 853: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | |||
</body></html></pre></div> | </body></html></pre></div> |
Revision as of 11:21, 4 May 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author phylingual and made on 2012-05-04 11:21:48 UTC.
- The original revision id was 330015248.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
35-tET or 35-[[xenharmonic/edo|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[xenharmonic/cent|34.29¢]] each. As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[xenharmonic/macrotonal edos|macrotonal edos]]: [[xenharmonic/5edo|5edo]] and [[xenharmonic/7edo|7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. 35edo can also represent the 2.3.5.7.11.17 [[xenharmonic/Just intonation subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9, and if you ignore [[xenharmonic/22edo|22edo]]'s consistent representation of both subgroups. 35edo has the optimal patent val for [[xenharmonic/Greenwoodmic temperaments|greenwood]] and [[xenharmonic/Greenwoodmic temperaments#Secund|secund]] temperaments. A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a [[xenharmonic/MOS|MOS]] of 3L2s: 9 4 9 9 4. =Intervals= || Degrees of 35-EDO || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with 9 || || 0 || 0 || 1/1 || || || || 1 || 34.29 || || || || || 2 || 68.57 || || || || || 3 || 102.86 || 17/16 || || 18/17 || || 4 || 137.14 || || 12/11 || || || 5 || 171.43 || 11/10 || || 10/9 || || 6 || 205.71 || || || 9/8 || || 7 || 240 || 8/7 || || || || 8 || 274.29 || 20/17 || 7/6 || || || 9 || 308.57 || || 6/5 || || || 10 || 342.86 || 17/14 || || 11/9 || || 11 || 377.14 || 5/4 || || || || 12 || 411.43 || 14/11 || || 14/11 || || 13 || 445.71 || 22/17 || || 9/7 || || 14 || 480 || || || || || 15 || 514.29 || || 4/3 || || || 16 || 548.57 || 11/8 || || || || 17 || 582.86 || 7/5 || 24/17 || || || 18 || 617.14 || 10/7 || 17/12 || || || 19 || 651.43 || 16/11 || || || || 20 || 685.71 || || 3/2 || || || 21 || 720 || || || || || 22 || 754.29 || 17/11 || || 14/9 || || 23 || 788.57 || 11/7 || || || || 24 || 822.86 || 8/5 || || || || 25 || 857.15 || || || 18/11 || || 26 || 891.43 || || 5/3 || || || 27 || 925.71 || 17/10 || 12/7 || || || 28 || 960 || 7/4 || || || || 29 || 994.29 || || || 16/9 || || 30 || 1028.57 || 20/11 || || 9/5 || || 31 || 1062.86 || || 11/6 || || || 32 || 1097.14 || 32/17 || || 17/9 || || 33 || 1131.43 || || || || || 34 || 1165.71 || || || || =Rank two temperaments= ||~ Periods per octave ||~ Generator ||~ Temperaments || || 1 || 3\35 || Ripple || || 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || || 1 || 6\35 || || || 1 || 8\35 || || || 1 || 9\35 || [[xenharmonic/Myna|Myna]] || || 1 || 11\35 || [[xenharmonic/Magic|Magic]] || || 1 || 12\35 || || || 1 || 13\35 || [[xenharmonic/Sensipent family|Sensipent]] || || 1 || 16\35 || || || 1 || 17\35 || || || || || || || 5 || 2\35 || || || || || || || 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || || 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || ==<span style="background-color: #ffffff;">Commas</span>== 35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.) == == == == ||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || || 2187/2048 || | -11 7 > || 113.69 || Apotome || Whitewood comma || || || 6561/6250 || | -1 8 -5 > || 84.07 || Ripple comma || || || || 10077696/9765625 || | 9 9 -10 > || 54.46 || Mynic comma || || || || 3125/3072 || | -10 -1 5 > || 29.61 || Small diesis || Magic comma || || || 78732/78125 || | 2 9 -7 > || 13.40 || Medium semicomma || Sensipent comma || || || 405/392 || | -3 4 1 -2 > || 56.48 || Greenwoodma || || || || 16807/16384 || | -14 0 0 5 > || 44.13 || || || || || 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || || || || 126/125 || | 1 2 -3 1 > || 13.79 || Starling comma || Septimal semicomma || || || 99/98 || | -1 2 0 -2 1 > || 17.58 || Mothwellsma || || || || 66/65 || | 1 1 -1 0 1 -1 > || 26.43 || || || || == == == ==
Original HTML content:
<html><head><title>35edo</title></head><body>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br /> <br /> As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a>. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. 35edo can also represent the 2.3.5.7.11.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups">subgroup</a> and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9, and if you ignore <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>'s consistent representation of both subgroups. 35edo has the optimal patent val for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments">greenwood</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">secund</a> temperaments.<br /> <br /> A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS">MOS</a> of 3L2s: 9 4 9 9 4.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1> <br /> <br /> <table class="wiki_table"> <tr> <td>Degrees of 35-EDO<br /> </td> <td>Cents value<br /> </td> <td>Ratios in 2.5.7.11.17 subgroup<br /> </td> <td>Ratios with flat 3<br /> </td> <td>Ratios with 9<br /> </td> </tr> <tr> <td>0<br /> </td> <td>0<br /> </td> <td>1/1<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>34.29<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>2<br /> </td> <td>68.57<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>3<br /> </td> <td>102.86<br /> </td> <td>17/16<br /> </td> <td><br /> </td> <td>18/17<br /> </td> </tr> <tr> <td>4<br /> </td> <td>137.14<br /> </td> <td><br /> </td> <td>12/11<br /> </td> <td><br /> </td> </tr> <tr> <td>5<br /> </td> <td>171.43<br /> </td> <td>11/10<br /> </td> <td><br /> </td> <td>10/9<br /> </td> </tr> <tr> <td>6<br /> </td> <td>205.71<br /> </td> <td><br /> </td> <td><br /> </td> <td>9/8<br /> </td> </tr> <tr> <td>7<br /> </td> <td>240<br /> </td> <td>8/7<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>8<br /> </td> <td>274.29<br /> </td> <td>20/17<br /> </td> <td>7/6<br /> </td> <td><br /> </td> </tr> <tr> <td>9<br /> </td> <td>308.57<br /> </td> <td><br /> </td> <td>6/5<br /> </td> <td><br /> </td> </tr> <tr> <td>10<br /> </td> <td>342.86<br /> </td> <td>17/14<br /> </td> <td><br /> </td> <td>11/9<br /> </td> </tr> <tr> <td>11<br /> </td> <td>377.14<br /> </td> <td>5/4<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>12<br /> </td> <td>411.43<br /> </td> <td>14/11<br /> </td> <td><br /> </td> <td>14/11<br /> </td> </tr> <tr> <td>13<br /> </td> <td>445.71<br /> </td> <td>22/17<br /> </td> <td><br /> </td> <td>9/7<br /> </td> </tr> <tr> <td>14<br /> </td> <td>480<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>15<br /> </td> <td>514.29<br /> </td> <td><br /> </td> <td>4/3<br /> </td> <td><br /> </td> </tr> <tr> <td>16<br /> </td> <td>548.57<br /> </td> <td>11/8<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>17<br /> </td> <td>582.86<br /> </td> <td>7/5<br /> </td> <td>24/17<br /> </td> <td><br /> </td> </tr> <tr> <td>18<br /> </td> <td>617.14<br /> </td> <td>10/7<br /> </td> <td>17/12<br /> </td> <td><br /> </td> </tr> <tr> <td>19<br /> </td> <td>651.43<br /> </td> <td>16/11<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>20<br /> </td> <td>685.71<br /> </td> <td><br /> </td> <td>3/2<br /> </td> <td><br /> </td> </tr> <tr> <td>21<br /> </td> <td>720<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>22<br /> </td> <td>754.29<br /> </td> <td>17/11<br /> </td> <td><br /> </td> <td>14/9<br /> </td> </tr> <tr> <td>23<br /> </td> <td>788.57<br /> </td> <td>11/7<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>24<br /> </td> <td>822.86<br /> </td> <td>8/5<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>25<br /> </td> <td>857.15<br /> </td> <td><br /> </td> <td><br /> </td> <td>18/11<br /> </td> </tr> <tr> <td>26<br /> </td> <td>891.43<br /> </td> <td><br /> </td> <td>5/3<br /> </td> <td><br /> </td> </tr> <tr> <td>27<br /> </td> <td>925.71<br /> </td> <td>17/10<br /> </td> <td>12/7<br /> </td> <td><br /> </td> </tr> <tr> <td>28<br /> </td> <td>960<br /> </td> <td>7/4<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>29<br /> </td> <td>994.29<br /> </td> <td><br /> </td> <td><br /> </td> <td>16/9<br /> </td> </tr> <tr> <td>30<br /> </td> <td>1028.57<br /> </td> <td>20/11<br /> </td> <td><br /> </td> <td>9/5<br /> </td> </tr> <tr> <td>31<br /> </td> <td>1062.86<br /> </td> <td><br /> </td> <td>11/6<br /> </td> <td><br /> </td> </tr> <tr> <td>32<br /> </td> <td>1097.14<br /> </td> <td>32/17<br /> </td> <td><br /> </td> <td>17/9<br /> </td> </tr> <tr> <td>33<br /> </td> <td>1131.43<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>34<br /> </td> <td>1165.71<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> </table> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two temperaments</h1> <br /> <br /> <table class="wiki_table"> <tr> <th>Periods<br /> per octave<br /> </th> <th>Generator<br /> </th> <th>Temperaments<br /> </th> </tr> <tr> <td>1<br /> </td> <td>3\35<br /> </td> <td>Ripple<br /> </td> </tr> <tr> <td>1<br /> </td> <td>4\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br /> </td> </tr> <tr> <td>1<br /> </td> <td>6\35<br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>8\35<br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>9\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br /> </td> </tr> <tr> <td>1<br /> </td> <td>11\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Magic">Magic</a><br /> </td> </tr> <tr> <td>1<br /> </td> <td>12\35<br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>13\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensipent%20family">Sensipent</a><br /> </td> </tr> <tr> <td>1<br /> </td> <td>16\35<br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>17\35<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>5<br /> </td> <td>2\35<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>7<br /> </td> <td>1\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family">Whitewood</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family#Redwood">Redwood</a><br /> </td> </tr> <tr> <td>7<br /> </td> <td>2\35<br /> </td> <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br /> </td> </tr> </table> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2> 35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.)<br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h2> <table class="wiki_table"> <tr> <th><strong>Comma</strong><br /> </th> <th><strong>Monzo</strong><br /> </th> <th><strong>Value (Cents)</strong><br /> </th> <th><strong>Name 1</strong><br /> </th> <th><strong>Name 2</strong><br /> </th> <th><strong>Name 3</strong><br /> </th> </tr> <tr> <td>2187/2048<br /> </td> <td>| -11 7 ><br /> </td> <td>113.69<br /> </td> <td>Apotome<br /> </td> <td>Whitewood comma<br /> </td> <td><br /> </td> </tr> <tr> <td>6561/6250<br /> </td> <td>| -1 8 -5 ><br /> </td> <td>84.07<br /> </td> <td>Ripple comma<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>10077696/9765625<br /> </td> <td>| 9 9 -10 ><br /> </td> <td>54.46<br /> </td> <td>Mynic comma<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>3125/3072<br /> </td> <td>| -10 -1 5 ><br /> </td> <td>29.61<br /> </td> <td>Small diesis<br /> </td> <td>Magic comma<br /> </td> <td><br /> </td> </tr> <tr> <td>78732/78125<br /> </td> <td>| 2 9 -7 ><br /> </td> <td>13.40<br /> </td> <td>Medium semicomma<br /> </td> <td>Sensipent comma<br /> </td> <td><br /> </td> </tr> <tr> <td>405/392<br /> </td> <td>| -3 4 1 -2 ><br /> </td> <td>56.48<br /> </td> <td>Greenwoodma<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>16807/16384<br /> </td> <td>| -14 0 0 5 ><br /> </td> <td>44.13<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>525/512<br /> </td> <td>| -9 1 2 1 ><br /> </td> <td>43.41<br /> </td> <td>Avicennma<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>126/125<br /> </td> <td>| 1 2 -3 1 ><br /> </td> <td>13.79<br /> </td> <td>Starling comma<br /> </td> <td>Septimal semicomma<br /> </td> <td><br /> </td> </tr> <tr> <td>99/98<br /> </td> <td>| -1 2 0 -2 1 ><br /> </td> <td>17.58<br /> </td> <td>Mothwellsma<br /> </td> <td><br /> </td> <td><br /> </td> </tr> <tr> <td>66/65<br /> </td> <td>| 1 1 -1 0 1 -1 ><br /> </td> <td>26.43<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> </tr> </table> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> </body></html>