27edo
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- This revision was by author jdfreivald and made on 2011-05-31 22:25:14 UTC.
- The original revision id was 233349542.
- The revision comment was: Added comma table.
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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 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 || || || <span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 705px; width: 1px;"> || < 27 43 63 76 93 100 | || </span>
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 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>128/125<br />
</td>
<td>| 7 0 -3 ><br />
</td>
<td>41.06<br />
</td>
<td>Diesis<br />
</td>
<td>Augmented Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20000/19683<br />
</td>
<td>| 5 -9 4 ><br />
</td>
<td>27.66<br />
</td>
<td>Minimal Diesis<br />
</td>
<td>Tetracot 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>4711802/4709457<br />
</td>
<td>| 1 -27 18 ><br />
</td>
<td>0.86<br />
</td>
<td>Ennealimma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>686/675<br />
</td>
<td>| 1 -3 -2 3 ><br />
</td>
<td>27.99<br />
</td>
<td>Senga<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>64/63<br />
</td>
<td>| 6 -2 0 -1 ><br />
</td>
<td>27.26<br />
</td>
<td>Septimal Comma<br />
</td>
<td>Archytas' Comma<br />
</td>
<td>Leipziger Komma<br />
</td>
</tr>
<tr>
<td>50421/50000<br />
</td>
<td>| -4 1 -5 5 ><br />
</td>
<td>14.52<br />
</td>
<td>Trimyna<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>245/243<br />
</td>
<td>| 0 -5 1 2 ><br />
</td>
<td>14.19<br />
</td>
<td>Sensamagic<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>Septimal Semicomma<br />
</td>
<td>Starling Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4000/3969<br />
</td>
<td>| 5 -4 3 -2 ><br />
</td>
<td>13.47<br />
</td>
<td>Octagar<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1728/1715<br />
</td>
<td>| 6 3 -1 -3 ><br />
</td>
<td>13.07<br />
</td>
<td>Orwellisma<br />
</td>
<td>Orwell Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>420175/419904<br />
</td>
<td>| -6 -8 2 5 ><br />
</td>
<td>1.12<br />
</td>
<td>Wizma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2401/2400<br />
</td>
<td>| -5 -1 -2 4 ><br />
</td>
<td>0.72<br />
</td>
<td>Breedsma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4375/4374<br />
</td>
<td>| -1 -7 4 1 ><br />
</td>
<td>0.40<br />
</td>
<td>Ragisma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>250047/250000<br />
</td>
<td>| -4 6 -6 3 ><br />
</td>
<td>0.33<br />
</td>
<td>Landscape Comma<br />
</td>
<td><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>896/891<br />
</td>
<td>| 7 -4 0 1 -1 ><br />
</td>
<td>9.69<br />
</td>
<td>Pentacircle<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>385/384<br />
</td>
<td>| -7 -1 1 1 1 ><br />
</td>
<td>4.50<br />
</td>
<td>Keenanisma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>91/90<br />
</td>
<td>| -1 -2 -1 1 0 1 ><br />
</td>
<td>19.13<br />
</td>
<td>Superleap<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 705px; width: 1px;"><br />
<table class="wiki_table">
<tr>
<td>< 27 43 63 76 93 100 |<br />
</td>
</tr>
</table>
</span></body></html>