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Wikispaces>jdfreivald **Imported revision 233346970 - Original comment: Added comma table.** |
Wikispaces>jdfreivald **Imported revision 233347464 - Original comment: ** |
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<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:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:15:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233347464</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 49: | Line 49: | ||
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | 25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
|| 256/243 || | 8 -5 > || 90.22 || Limma || Pythagorean Minor 2nd || || | ||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||= || | ||
|| 3125/3072 || | -10 -1 5 > || 29.61 || Small Diesis || Magic Comma || || | ||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || | ||
|| 6719816/6714445 || | 38 -2 -15 > || 1.38 || Hemithirds Comma || || || | ||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.38 ||= Hemithirds Comma ||= ||= || | ||
|| 49/48 || | -4 -1 0 2 > || 35.70 || Slendro Diesis || || || | ||= 16807/16384 || | -14 0 0 5 > ||> 44.13 || || || || | ||
|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma || | ||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= || | ||
|| 3125/3087 || | 0 -2 5 -3 > || 21.18 || Gariboh || || || | ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||
|| 50421/50000 || | -4 1 -5 5 > || 14.52 || Trimyna || || || | ||= 3125/3087 ||< | 0 -2 5 -3 > ||> 21.18 ||= Gariboh ||= ||= || | ||
|| 1029/1024 || | -10 1 0 3 > || 8.43 || Gamelisma || || || | ||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||= ||= || | ||
|| 3136/3125 || | 6 0 -5 2 > || 6.08 || Hemimean || || || | ||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= || | ||
|| 65625/65536 || | -16 1 5 1 > || 2.35 || Horwell || || || | ||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean ||= ||= || | ||
|| 100/99 || | 2 -2 2 0 -1 > || 17.40 || Ptolemisma || || || | ||= 65625/65536 ||< | -16 1 5 1 > ||> 2.35 ||= Horwell ||= ||= || | ||
|| 176/175 || | 4 0 -2 -1 1 > || 9.86 || Valinorsma || || || | ||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||= ||= || | ||
|| | ||= 176/175 ||< | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||= ||= || | ||
||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || | |||
|| 676/675 || | 2 -3 -2 0 0 2 > || 2.56 || Parizeksma || || ||</pre></div> | ||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= ||= ||</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>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006b2e;">25 tone equal temperament</span></h1> | <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>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006b2e;">25 tone equal temperament</span></h1> | ||
| Line 260: | Line 260: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>256/243<br /> | <td style="text-align: center;">256/243<br /> | ||
</td> | </td> | ||
<td>| 8 -5 &gt;<br /> | <td style="text-align: left;">| 8 -5 &gt;<br /> | ||
</td> | </td> | ||
<td>90.22<br /> | <td style="text-align: right;">90.22<br /> | ||
</td> | </td> | ||
<td>Limma<br /> | <td style="text-align: center;">Limma<br /> | ||
</td> | </td> | ||
<td>Pythagorean Minor 2nd<br /> | <td style="text-align: center;">Pythagorean Minor 2nd<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3125/3072<br /> | <td style="text-align: center;">3125/3072<br /> | ||
</td> | </td> | ||
<td>| -10 -1 5 &gt;<br /> | <td style="text-align: left;">| -10 -1 5 &gt;<br /> | ||
</td> | </td> | ||
<td>29.61<br /> | <td style="text-align: right;">29.61<br /> | ||
</td> | </td> | ||
<td>Small Diesis<br /> | <td style="text-align: center;">Small Diesis<br /> | ||
</td> | </td> | ||
<td>Magic Comma<br /> | <td style="text-align: center;">Magic Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6719816/6714445<br /> | <td style="text-align: center;">6719816/6714445<br /> | ||
</td> | </td> | ||
<td>| 38 -2 -15 &gt;<br /> | <td style="text-align: left;">| 38 -2 -15 &gt;<br /> | ||
</td> | </td> | ||
<td>1.38<br /> | <td style="text-align: right;">1.38<br /> | ||
</td> | </td> | ||
<td>Hemithirds Comma<br /> | <td style="text-align: center;">Hemithirds Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">16807/16384<br /> | ||
</td> | </td> | ||
<td>| - | <td>| -14 0 0 5 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">44.13<br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 316: | Line 316: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">49/48<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: left;">| -4 -1 0 2 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">35.70<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Slendro Diesis<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">64/63<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: left;">| 6 -2 0 -1 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">27.26<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Septimal Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Archytas' Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Leipziger Komma<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">3125/3087<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: left;">| 0 -2 5 -3 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">21.18<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Gariboh<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">50421/50000<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: left;">| -4 1 -5 5 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">14.52<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Trimyna<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">1029/1024<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: left;">| -10 1 0 3 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">8.43<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Gamelisma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">3136/3125<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: left;">| 6 0 -5 2 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">6.08<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Hemimean<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">65625/65536<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: left;">| -16 1 5 1 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">2.35<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Horwell<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">100/99<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: left;">| 2 -2 2 0 -1 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">17.40<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Ptolemisma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">176/175<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: left;">| 4 0 -2 -1 1 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: right;">9.86<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Valinorsma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>91/90<br /> | <td style="text-align: center;">91/90<br /> | ||
</td> | </td> | ||
<td>| -1 -2 -1 1 0 1 &gt;<br /> | <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br /> | ||
</td> | </td> | ||
<td>19.13<br /> | <td style="text-align: right;">19.13<br /> | ||
</td> | </td> | ||
<td>Superleap<br /> | <td style="text-align: center;">Superleap<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>676/675<br /> | <td style="text-align: center;">676/675<br /> | ||
</td> | </td> | ||
<td>| 2 -3 -2 0 0 2 &gt;<br /> | <td style="text-align: left;">| 2 -3 -2 0 0 2 &gt;<br /> | ||
</td> | </td> | ||
<td>2.56<br /> | <td style="text-align: right;">2.56<br /> | ||
</td> | </td> | ||
<td>Parizeksma<br /> | <td style="text-align: center;">Parizeksma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 22:15, 31 May 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author jdfreivald and made on 2011-05-31 22:15:33 UTC.
- The original revision id was 233347464.
- 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:
=<span style="color: #006b2e;">25 tone equal temperament</span>= 25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7. 25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]]. If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony. Some example of a keyboard in 25-EDO [[image:mm25.PNG]] ==Intervals== || Degrees of 25-EDO || Cents value || || 0 || 0 || || 1 || 48 || || 2 || 96 || || 3 || 144 || || 4 || 192 || || 5 || 240 || || 6 || 288 || || 7 || 336 || || 8 || 384 || || 9 || 432 || || 10 || 480 || || 11 || 528 || || 12 || 576 || || 13 || 624 || || 14 || 672 || || 15 || 720 || || 16 || 768 || || 17 || 816 || || 18 || 864 || || 19 || 912 || || 20 || 960 || || 21 || 1008 || || 22 || 1056 || || 23 || 1104 || || 24 || 1152 || ==Commas== 25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||= || ||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || ||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.38 ||= Hemithirds Comma ||= ||= || ||= 16807/16384 || | -14 0 0 5 > ||> 44.13 || || || || ||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= || ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || ||= 3125/3087 ||< | 0 -2 5 -3 > ||> 21.18 ||= Gariboh ||= ||= || ||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||= ||= || ||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= || ||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean ||= ||= || ||= 65625/65536 ||< | -16 1 5 1 > ||> 2.35 ||= Horwell ||= ||= || ||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||= ||= || ||= 176/175 ||< | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||= ||= || ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || ||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= ||= ||
Original HTML content:
<html><head><title>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006b2e;">25 tone equal temperament</span></h1>
<br />
25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.<br />
<br />
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.<br />
<br />
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the <a class="wiki_link" href="/k%2AN%20subgroups">2*25 subgroup</a> 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.<br />
<br />
Some example of a keyboard in 25-EDO<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:390:<img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="" title="" /> --><img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /><!-- ws:end:WikiTextLocalImageRule:390 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x25 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
<br />
<table class="wiki_table">
<tr>
<td>Degrees of 25-EDO<br />
</td>
<td>Cents value<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>48<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>96<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>144<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>192<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>240<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>288<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>336<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>384<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>432<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>480<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>528<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>576<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>624<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>672<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>720<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>768<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>816<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>864<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>912<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>960<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>1008<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>1056<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>1104<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1152<br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x25 tone equal temperament-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2>
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.)<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>Value (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
<th>Name 3<br />
</th>
</tr>
<tr>
<td style="text-align: center;">256/243<br />
</td>
<td style="text-align: left;">| 8 -5 ><br />
</td>
<td style="text-align: right;">90.22<br />
</td>
<td style="text-align: center;">Limma<br />
</td>
<td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3125/3072<br />
</td>
<td style="text-align: left;">| -10 -1 5 ><br />
</td>
<td style="text-align: right;">29.61<br />
</td>
<td style="text-align: center;">Small Diesis<br />
</td>
<td style="text-align: center;">Magic Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">6719816/6714445<br />
</td>
<td style="text-align: left;">| 38 -2 -15 ><br />
</td>
<td style="text-align: right;">1.38<br />
</td>
<td style="text-align: center;">Hemithirds Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">16807/16384<br />
</td>
<td>| -14 0 0 5 ><br />
</td>
<td style="text-align: right;">44.13<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">49/48<br />
</td>
<td style="text-align: left;">| -4 -1 0 2 ><br />
</td>
<td style="text-align: right;">35.70<br />
</td>
<td style="text-align: center;">Slendro Diesis<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">64/63<br />
</td>
<td style="text-align: left;">| 6 -2 0 -1 ><br />
</td>
<td style="text-align: right;">27.26<br />
</td>
<td style="text-align: center;">Septimal Comma<br />
</td>
<td style="text-align: center;">Archytas' Comma<br />
</td>
<td style="text-align: center;">Leipziger Komma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3125/3087<br />
</td>
<td style="text-align: left;">| 0 -2 5 -3 ><br />
</td>
<td style="text-align: right;">21.18<br />
</td>
<td style="text-align: center;">Gariboh<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">50421/50000<br />
</td>
<td style="text-align: left;">| -4 1 -5 5 ><br />
</td>
<td style="text-align: right;">14.52<br />
</td>
<td style="text-align: center;">Trimyna<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1029/1024<br />
</td>
<td style="text-align: left;">| -10 1 0 3 ><br />
</td>
<td style="text-align: right;">8.43<br />
</td>
<td style="text-align: center;">Gamelisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3136/3125<br />
</td>
<td style="text-align: left;">| 6 0 -5 2 ><br />
</td>
<td style="text-align: right;">6.08<br />
</td>
<td style="text-align: center;">Hemimean<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">65625/65536<br />
</td>
<td style="text-align: left;">| -16 1 5 1 ><br />
</td>
<td style="text-align: right;">2.35<br />
</td>
<td style="text-align: center;">Horwell<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">100/99<br />
</td>
<td style="text-align: left;">| 2 -2 2 0 -1 ><br />
</td>
<td style="text-align: right;">17.40<br />
</td>
<td style="text-align: center;">Ptolemisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">176/175<br />
</td>
<td style="text-align: left;">| 4 0 -2 -1 1 ><br />
</td>
<td style="text-align: right;">9.86<br />
</td>
<td style="text-align: center;">Valinorsma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">91/90<br />
</td>
<td style="text-align: left;">| -1 -2 -1 1 0 1 ><br />
</td>
<td style="text-align: right;">19.13<br />
</td>
<td style="text-align: center;">Superleap<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">676/675<br />
</td>
<td style="text-align: left;">| 2 -3 -2 0 0 2 ><br />
</td>
<td style="text-align: right;">2.56<br />
</td>
<td style="text-align: center;">Parizeksma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>