27edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 145670281 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 210042652 - 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt> | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-03-13 16:02:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>210042652</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : 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> | ||
<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;white-space: pre-wrap ! important" class="old-revision-html"> | <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;white-space: pre-wrap ! important" class="old-revision-html">=<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. | 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. | ||
| Line 12: | Line 12: | ||
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. | 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.</pre></div> | 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 ||</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; | <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> | ||
<br /> | <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 /> | 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 /> | ||
| Line 20: | Line 51: | ||
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 /> | 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 /> | <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 &quot;superpythagorean&quot; fifths giving a sharp 9/7 in place of meantone's 5/4.</body></html></pre></div> | 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 &quot;superpythagorean&quot; fifths giving a sharp <br /> | ||
9/7 in place of meantone's 5/4.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><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></pre></div> | |||