27edo
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Original Wikitext content:
=<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 the allegedly Bohlen-Pierce comma 245/243 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. Though the 7-limit tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both consistently and distinctly--that is, everything in the 7-limit [[Diamonds|diamond]] is uniquely represented by a certain number of steps of 27 equal. ==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 ||= ||= || =Music= [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] by [[Gene Ward Smith]] The central portion is in 27edo, the rest in 46edo.
Original HTML content:
<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 <a class="wiki_link" href="/22edo">22edo</a> tempering out the allegedly Bohlen-Pierce comma 245/243 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. <br />
<br />
Though the 7-limit tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both consistently and distinctly--that is, everything in the 7-limit <a class="wiki_link" href="/Diamonds">diamond</a> is uniquely represented by a certain number of steps of 27 equal.<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 />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1>
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in 46edo.</body></html>