27edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Osmiorisbendi and made on 2011-03-13 16:02:35 UTC.
- The original revision id was 210042652.
- The revision comment was:
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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 ||
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>
</body></html>