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Wikispaces>jdfreivald **Imported revision 233349542 - Original comment: Added comma table.** |
Wikispaces>jdfreivald **Imported revision 233349718 - 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 22:26:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233349718</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 47: | Line 47: | ||
27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.) | 27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
|| 128/125 || | 7 0 -3 > || 41.06 || Diesis || Augmented Comma || || | ||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||= || | ||
|| 20000/19683 || | 5 -9 4 > || 27.66 || Minimal Diesis || Tetracot Comma || || | ||= 20000/19683 ||< | 5 -9 4 > ||> 27.66 ||= Minimal Diesis ||= Tetracot Comma ||= || | ||
|| 78732/78125 || | 2 9 -7 > || 13.40 || Medium Semicomma || Sensipent Comma || || | ||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||= || | ||
|| 4711802/4709457 || | 1 -27 18 > || 0.86 || Ennealimma || || || | ||= 4711802/4709457 ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||= ||= || | ||
|| 686/675 || | 1 -3 -2 3 > || 27.99 || Senga || || || | ||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= || | ||
|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma || | ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||
|| 50421/50000 || | -4 1 -5 5 > || 14.52 || Trimyna || || || | ||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||= ||= || | ||
|| 245/243 || | 0 -5 1 2 > || 14.19 || Sensamagic || || || | ||= 245/243 ||< | 0 -5 1 2 > ||> 14.19 ||= Sensamagic ||= ||= || | ||
|| 126/125 || | 1 2 -3 1 > || 13.79 || Septimal Semicomma || Starling Comma || || | ||= 126/125 ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||= || | ||
|| 4000/3969 || | 5 -4 3 -2 > || 13.47 || Octagar || || || | ||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||= ||= || | ||
|| 1728/1715 || | 6 3 -1 -3 > || 13.07 || Orwellisma || Orwell Comma || || | ||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||= || | ||
|| 420175/419904 || | -6 -8 2 5 > || 1.12 || Wizma || || || | ||= 420175/419904 ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= || | ||
|| 2401/2400 || | -5 -1 -2 4 > || 0.72 || Breedsma || || || | ||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= || | ||
|| 4375/4374 || | -1 -7 4 1 > || 0.40 || Ragisma || || || | ||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||= ||= || | ||
|| 250047/250000 || | -4 6 -6 3 > || 0.33 || Landscape Comma || || || | ||= 250047/250000 ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||= ||= || | ||
|| 99/98 || | -1 2 0 -2 1 > || 17.58 || Mothwellsma || || || | ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= || | ||
|| 896/891 || | 7 -4 0 1 -1 > || 9.69 || Pentacircle || || || | ||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||= ||= || | ||
|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma || || || | ||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||= || | ||
|| 91/90 || | -1 -2 -1 1 0 1 > || 19.13 || Superleap || || || | ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || | ||
|| < 27 43 63 76 93 100 | || | || < 27 43 63 76 93 100 | ||</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>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #0061ff; font-size: 103%;">27 tone equal tempertament</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>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #0061ff; font-size: 103%;">27 tone equal tempertament</span></h1> | ||
Line 274: | Line 273: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>128/125<br /> | <td style="text-align: center;">128/125<br /> | ||
</td> | </td> | ||
<td>| 7 0 -3 &gt;<br /> | <td style="text-align: left;">| 7 0 -3 &gt;<br /> | ||
</td> | </td> | ||
<td>41.06<br /> | <td style="text-align: right;">41.06<br /> | ||
</td> | </td> | ||
<td>Diesis<br /> | <td style="text-align: center;">Diesis<br /> | ||
</td> | </td> | ||
<td>Augmented Comma<br /> | <td style="text-align: center;">Augmented Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20000/19683<br /> | <td style="text-align: center;">20000/19683<br /> | ||
</td> | </td> | ||
<td>| 5 -9 4 &gt;<br /> | <td style="text-align: left;">| 5 -9 4 &gt;<br /> | ||
</td> | </td> | ||
<td>27.66<br /> | <td style="text-align: right;">27.66<br /> | ||
</td> | </td> | ||
<td>Minimal Diesis<br /> | <td style="text-align: center;">Minimal Diesis<br /> | ||
</td> | </td> | ||
<td>Tetracot Comma<br /> | <td style="text-align: center;">Tetracot Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>78732/78125<br /> | <td style="text-align: center;">78732/78125<br /> | ||
</td> | </td> | ||
<td>| 2 9 -7 &gt;<br /> | <td style="text-align: left;">| 2 9 -7 &gt;<br /> | ||
</td> | </td> | ||
<td>13.40<br /> | <td style="text-align: right;">13.40<br /> | ||
</td> | </td> | ||
<td>Medium Semicomma<br /> | <td style="text-align: center;">Medium Semicomma<br /> | ||
</td> | </td> | ||
<td>Sensipent Comma<br /> | <td style="text-align: center;">Sensipent Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4711802/4709457<br /> | <td style="text-align: center;">4711802/4709457<br /> | ||
</td> | </td> | ||
<td>| 1 -27 18 &gt;<br /> | <td style="text-align: left;">| 1 -27 18 &gt;<br /> | ||
</td> | </td> | ||
<td>0.86<br /> | <td style="text-align: right;">0.86<br /> | ||
</td> | </td> | ||
<td>Ennealimma<br /> | <td style="text-align: center;">Ennealimma<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>686/675<br /> | <td style="text-align: center;">686/675<br /> | ||
</td> | </td> | ||
<td>| 1 -3 -2 3 &gt;<br /> | <td style="text-align: left;">| 1 -3 -2 3 &gt;<br /> | ||
</td> | </td> | ||
<td>27.99<br /> | <td style="text-align: right;">27.99<br /> | ||
</td> | </td> | ||
<td>Senga<br /> | <td style="text-align: center;">Senga<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>64/63<br /> | <td style="text-align: center;">64/63<br /> | ||
</td> | </td> | ||
<td>| 6 -2 0 -1 &gt;<br /> | <td style="text-align: left;">| 6 -2 0 -1 &gt;<br /> | ||
</td> | </td> | ||
<td>27.26<br /> | <td style="text-align: right;">27.26<br /> | ||
</td> | </td> | ||
<td>Septimal Comma<br /> | <td style="text-align: center;">Septimal Comma<br /> | ||
</td> | </td> | ||
<td>Archytas' Comma<br /> | <td style="text-align: center;">Archytas' Comma<br /> | ||
</td> | </td> | ||
<td>Leipziger Komma<br /> | <td style="text-align: center;">Leipziger Komma<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>50421/50000<br /> | <td style="text-align: center;">50421/50000<br /> | ||
</td> | </td> | ||
<td>| -4 1 -5 5 &gt;<br /> | <td style="text-align: left;">| -4 1 -5 5 &gt;<br /> | ||
</td> | </td> | ||
<td>14.52<br /> | <td style="text-align: right;">14.52<br /> | ||
</td> | </td> | ||
<td>Trimyna<br /> | <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>245/243<br /> | <td style="text-align: center;">245/243<br /> | ||
</td> | </td> | ||
<td>| 0 -5 1 2 &gt;<br /> | <td style="text-align: left;">| 0 -5 1 2 &gt;<br /> | ||
</td> | </td> | ||
<td>14.19<br /> | <td style="text-align: right;">14.19<br /> | ||
</td> | </td> | ||
<td>Sensamagic<br /> | <td style="text-align: center;">Sensamagic<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>126/125<br /> | <td style="text-align: center;">126/125<br /> | ||
</td> | </td> | ||
<td>| 1 2 -3 1 &gt;<br /> | <td style="text-align: left;">| 1 2 -3 1 &gt;<br /> | ||
</td> | </td> | ||
<td>13.79<br /> | <td style="text-align: right;">13.79<br /> | ||
</td> | </td> | ||
<td>Septimal Semicomma<br /> | <td style="text-align: center;">Septimal Semicomma<br /> | ||
</td> | </td> | ||
<td>Starling Comma<br /> | <td style="text-align: center;">Starling Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4000/3969<br /> | <td style="text-align: center;">4000/3969<br /> | ||
</td> | </td> | ||
<td>| 5 -4 3 -2 &gt;<br /> | <td style="text-align: left;">| 5 -4 3 -2 &gt;<br /> | ||
</td> | </td> | ||
<td>13.47<br /> | <td style="text-align: right;">13.47<br /> | ||
</td> | </td> | ||
<td>Octagar<br /> | <td style="text-align: center;">Octagar<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>1728/1715<br /> | <td style="text-align: center;">1728/1715<br /> | ||
</td> | </td> | ||
<td>| 6 3 -1 -3 &gt;<br /> | <td style="text-align: left;">| 6 3 -1 -3 &gt;<br /> | ||
</td> | </td> | ||
<td>13.07<br /> | <td style="text-align: right;">13.07<br /> | ||
</td> | </td> | ||
<td>Orwellisma<br /> | <td style="text-align: center;">Orwellisma<br /> | ||
</td> | </td> | ||
<td>Orwell Comma<br /> | <td style="text-align: center;">Orwell Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>420175/419904<br /> | <td style="text-align: center;">420175/419904<br /> | ||
</td> | </td> | ||
<td>| -6 -8 2 5 &gt;<br /> | <td style="text-align: left;">| -6 -8 2 5 &gt;<br /> | ||
</td> | </td> | ||
<td>1.12<br /> | <td style="text-align: right;">1.12<br /> | ||
</td> | </td> | ||
<td>Wizma<br /> | <td style="text-align: center;">Wizma<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>2401/2400<br /> | <td style="text-align: center;">2401/2400<br /> | ||
</td> | </td> | ||
<td>| -5 -1 -2 4 &gt;<br /> | <td style="text-align: left;">| -5 -1 -2 4 &gt;<br /> | ||
</td> | </td> | ||
<td>0.72<br /> | <td style="text-align: right;">0.72<br /> | ||
</td> | </td> | ||
<td>Breedsma<br /> | <td style="text-align: center;">Breedsma<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>4375/4374<br /> | <td style="text-align: center;">4375/4374<br /> | ||
</td> | </td> | ||
<td>| -1 -7 4 1 &gt;<br /> | <td style="text-align: left;">| -1 -7 4 1 &gt;<br /> | ||
</td> | </td> | ||
<td>0.40<br /> | <td style="text-align: right;">0.40<br /> | ||
</td> | </td> | ||
<td>Ragisma<br /> | <td style="text-align: center;">Ragisma<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>250047/250000<br /> | <td style="text-align: center;">250047/250000<br /> | ||
</td> | </td> | ||
<td>| -4 6 -6 3 &gt;<br /> | <td style="text-align: left;">| -4 6 -6 3 &gt;<br /> | ||
</td> | </td> | ||
<td>0.33<br /> | <td style="text-align: right;">0.33<br /> | ||
</td> | </td> | ||
<td>Landscape Comma<br /> | <td style="text-align: center;">Landscape 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>99/98<br /> | <td style="text-align: center;">99/98<br /> | ||
</td> | </td> | ||
<td>| -1 2 0 -2 1 &gt;<br /> | <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br /> | ||
</td> | </td> | ||
<td>17.58<br /> | <td style="text-align: right;">17.58<br /> | ||
</td> | </td> | ||
<td>Mothwellsma<br /> | <td style="text-align: center;">Mothwellsma<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>896/891<br /> | <td style="text-align: center;">896/891<br /> | ||
</td> | </td> | ||
<td>| 7 -4 0 1 -1 &gt;<br /> | <td style="text-align: left;">| 7 -4 0 1 -1 &gt;<br /> | ||
</td> | </td> | ||
<td>9.69<br /> | <td style="text-align: right;">9.69<br /> | ||
</td> | </td> | ||
<td>Pentacircle<br /> | <td style="text-align: center;">Pentacircle<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>385/384<br /> | <td style="text-align: center;">385/384<br /> | ||
</td> | </td> | ||
<td>| -7 -1 1 1 1 &gt;<br /> | <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br /> | ||
</td> | </td> | ||
<td>4.50<br /> | <td style="text-align: right;">4.50<br /> | ||
</td> | </td> | ||
<td>Keenanisma<br /> | <td style="text-align: center;">Keenanisma<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> | ||
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<br /> | <br /> | ||
<br /> | |||
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</table> | </table> | ||
</body></html></pre></div> |
Revision as of 22:26, 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 22:26:05 UTC.
- The original revision id was 233349718.
- The revision comment was:
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=<span style="color: #0061ff; font-size: 103%;">27 tone equal tempertament</span>= If octaves are kept pure, 27edo divides the octave in 27 equal parts each exactly 44.444... cents in size. However, 27 is a prime candidate for octave shrinking, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the third, fifth and 7/4 sharply. Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as 12edo, sharp 13 2/3 cents. The result is that 6/5, 7/5 and especially 7/6 are all tuned more accurately than this. 27edo, with its 400 cent major third, tempers out the diesis of 128/125, and also the septimal comma, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with 22edo tempering out 245/243 (allegedly a Bohlen-Pierce comma, yet hear it turns up anyway) as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4. ==Intervals== || Degrees of 27-EDO || Cents value || || 0 || 0 || || 1 || 44,44 || || 2 || 88,89 || || 3 || 133,33 || || 4 || 177,78 || || 5 || 222,22 || || 6 || 266,67 || || 7 || 311,11 || || 8 || 355,56 || || 9 || 400 || || 10 || 444,44 || || 11 || 488,89 || || 12 || 533,33 || || 13 || 577,78 || || 14 || 622,22 || || 15 || 666,67 || || 16 || 711,11 || || 17 || 755,56 || || 18 || 800 || || 19 || 844,44 || || 20 || 888,89 || || 21 || 933,33 || || 22 || 977,78 || || 23 || 1022,22 || || 24 || 1066,67 || || 25 || 1111,11 || || 26 || 1155,56 || ==Commas== 27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||= || ||= 20000/19683 ||< | 5 -9 4 > ||> 27.66 ||= Minimal Diesis ||= Tetracot Comma ||= || ||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||= || ||= 4711802/4709457 ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||= ||= || ||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= || ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || ||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||= ||= || ||= 245/243 ||< | 0 -5 1 2 > ||> 14.19 ||= Sensamagic ||= ||= || ||= 126/125 ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||= || ||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||= ||= || ||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||= || ||= 420175/419904 ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= || ||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= || ||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||= ||= || ||= 250047/250000 ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||= ||= || ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= || ||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||= ||= || ||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||= || ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || || < 27 43 63 76 93 100 | ||
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<html><head><title>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #0061ff; font-size: 103%;">27 tone equal tempertament</span></h1> <br /> If octaves are kept pure, 27edo divides the octave in 27 equal parts each exactly 44.444... cents in size. However, 27 is a prime candidate for octave shrinking, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the third, fifth and 7/4 sharply.<br /> <br /> Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as 12edo, sharp 13 2/3 cents. The result is that 6/5, 7/5 and especially 7/6 are all tuned more accurately than this.<br /> <br /> 27edo, with its 400 cent major third, tempers out the diesis of 128/125, and also the septimal comma, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with 22edo tempering out 245/243 (allegedly a Bohlen-Pierce comma, yet hear it turns up anyway) as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp<br /> 9/7 in place of meantone's 5/4.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> <table class="wiki_table"> <tr> <td>Degrees of 27-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>44,44<br /> </td> </tr> <tr> <td>2<br /> </td> <td>88,89<br /> </td> </tr> <tr> <td>3<br /> </td> <td>133,33<br /> </td> </tr> <tr> <td>4<br /> </td> <td>177,78<br /> </td> </tr> <tr> <td>5<br /> </td> <td>222,22<br /> </td> </tr> <tr> <td>6<br /> </td> <td>266,67<br /> </td> </tr> <tr> <td>7<br /> </td> <td>311,11<br /> </td> </tr> <tr> <td>8<br /> </td> <td>355,56<br /> </td> </tr> <tr> <td>9<br /> </td> <td>400<br /> </td> </tr> <tr> <td>10<br /> </td> <td>444,44<br /> </td> </tr> <tr> <td>11<br /> </td> <td>488,89<br /> </td> </tr> <tr> <td>12<br /> </td> <td>533,33<br /> </td> </tr> <tr> <td>13<br /> </td> <td>577,78<br /> </td> </tr> <tr> <td>14<br /> </td> <td>622,22<br /> </td> </tr> <tr> <td>15<br /> </td> <td>666,67<br /> </td> </tr> <tr> <td>16<br /> </td> <td>711,11<br /> </td> </tr> <tr> <td>17<br /> </td> <td>755,56<br /> </td> </tr> <tr> <td>18<br /> </td> <td>800<br /> </td> </tr> <tr> <td>19<br /> </td> <td>844,44<br /> </td> </tr> <tr> <td>20<br /> </td> <td>888,89<br /> </td> </tr> <tr> <td>21<br /> </td> <td>933,33<br /> </td> </tr> <tr> <td>22<br /> </td> <td>977,78<br /> </td> </tr> <tr> <td>23<br /> </td> <td>1022,22<br /> </td> </tr> <tr> <td>24<br /> </td> <td>1066,67<br /> </td> </tr> <tr> <td>25<br /> </td> <td>1111,11<br /> </td> </tr> <tr> <td>26<br /> </td> <td>1155,56<br /> </td> </tr> </table> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x27 tone equal tempertament-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2> 27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.)<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;">128/125<br /> </td> <td style="text-align: left;">| 7 0 -3 ><br /> </td> <td style="text-align: right;">41.06<br /> </td> <td style="text-align: center;">Diesis<br /> </td> <td style="text-align: center;">Augmented Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">20000/19683<br /> </td> <td style="text-align: left;">| 5 -9 4 ><br /> </td> <td style="text-align: right;">27.66<br /> </td> <td style="text-align: center;">Minimal Diesis<br /> </td> <td style="text-align: center;">Tetracot Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">78732/78125<br /> </td> <td style="text-align: left;">| 2 9 -7 ><br /> </td> <td style="text-align: right;">13.40<br /> </td> <td style="text-align: center;">Medium Semicomma<br /> </td> <td style="text-align: center;">Sensipent Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4711802/4709457<br /> </td> <td style="text-align: left;">| 1 -27 18 ><br /> </td> <td style="text-align: right;">0.86<br /> </td> <td style="text-align: center;">Ennealimma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">686/675<br /> </td> <td style="text-align: left;">| 1 -3 -2 3 ><br /> </td> <td style="text-align: right;">27.99<br /> </td> <td style="text-align: center;">Senga<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;">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;">245/243<br /> </td> <td style="text-align: left;">| 0 -5 1 2 ><br /> </td> <td style="text-align: right;">14.19<br /> </td> <td style="text-align: center;">Sensamagic<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">126/125<br /> </td> <td style="text-align: left;">| 1 2 -3 1 ><br /> </td> <td style="text-align: right;">13.79<br /> </td> <td style="text-align: center;">Septimal Semicomma<br /> </td> <td style="text-align: center;">Starling Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4000/3969<br /> </td> <td style="text-align: left;">| 5 -4 3 -2 ><br /> </td> <td style="text-align: right;">13.47<br /> </td> <td style="text-align: center;">Octagar<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">1728/1715<br /> </td> <td style="text-align: left;">| 6 3 -1 -3 ><br /> </td> <td style="text-align: right;">13.07<br /> </td> <td style="text-align: center;">Orwellisma<br /> </td> <td style="text-align: center;">Orwell Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">420175/419904<br /> </td> <td style="text-align: left;">| -6 -8 2 5 ><br /> </td> <td style="text-align: right;">1.12<br /> </td> <td style="text-align: center;">Wizma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">2401/2400<br /> </td> <td style="text-align: left;">| -5 -1 -2 4 ><br /> </td> <td style="text-align: right;">0.72<br /> </td> <td style="text-align: center;">Breedsma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4375/4374<br /> </td> <td style="text-align: left;">| -1 -7 4 1 ><br /> </td> <td style="text-align: right;">0.40<br /> </td> <td style="text-align: center;">Ragisma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">250047/250000<br /> </td> <td style="text-align: left;">| -4 6 -6 3 ><br /> </td> <td style="text-align: right;">0.33<br /> </td> <td style="text-align: center;">Landscape Comma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">99/98<br /> </td> <td style="text-align: left;">| -1 2 0 -2 1 ><br /> </td> <td style="text-align: right;">17.58<br /> </td> <td style="text-align: center;">Mothwellsma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">896/891<br /> </td> <td style="text-align: left;">| 7 -4 0 1 -1 ><br /> </td> <td style="text-align: right;">9.69<br /> </td> <td style="text-align: center;">Pentacircle<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">385/384<br /> </td> <td style="text-align: left;">| -7 -1 1 1 1 ><br /> </td> <td style="text-align: right;">4.50<br /> </td> <td style="text-align: center;">Keenanisma<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> </table> <br /> <br /> <table class="wiki_table"> <tr> <td>< 27 43 63 76 93 100 |<br /> </td> </tr> </table> </body></html>