Pythagorean family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 188879167 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 188879885 - 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:genewardsmith|genewardsmith]] and made on <tt>2010-12-17 03: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-17 03:55:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>188879885</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> | ||
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<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">The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12>, and hence the fifths form a closed 12-note circle of fifths, identical to [[12edo]]. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it. | <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">The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12>, and hence the fifths form a closed 12-note circle of fifths, identical to [[12edo]]. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it. | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 15.116 | ||
Map: [<12 19 0|, <0 0 1|] | Map: [<12 19 0|, <0 0 1|] | ||
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Commas: 225/224, 250047/250000 | Commas: 225/224, 250047/250000 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 16.225 | ||
Map: [<12 19 0 -22|, <0 0 1 2|] | Map: [<12 19 0 -22|, <0 0 1 2|] | ||
| Line 30: | Line 30: | ||
Commas: 225/224, 441/440, 4375/4356 | Commas: 225/224, 441/440, 4375/4356 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 16.734 | ||
Map: [<12 19 0 -22 -42|, <0 0 1 2 3|] | Map: [<12 19 0 -22 -42|, <0 0 1 2 3|] | ||
| Line 40: | Line 40: | ||
Commas: 81/80, 128/125 | Commas: 81/80, 128/125 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 26.790 | ||
Map: [<12 19 28 0|, <0 0 0 1|] | Map: [<12 19 28 0|, <0 0 0 1|] | ||
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<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>Pythagorean family</title></head><body>The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12&gt;, and hence the fifths form a closed 12-note circle of fifths, identical to <a class="wiki_link" href="/12edo">12edo</a>. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.<br /> | <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>Pythagorean family</title></head><body>The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12&gt;, and hence the fifths form a closed 12-note circle of fifths, identical to <a class="wiki_link" href="/12edo">12edo</a>. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 15.116<br /> | ||
<br /> | <br /> | ||
Map: [&lt;12 19 0|, &lt;0 0 1|]<br /> | Map: [&lt;12 19 0|, &lt;0 0 1|]<br /> | ||
| Line 61: | Line 61: | ||
Commas: 225/224, 250047/250000<br /> | Commas: 225/224, 250047/250000<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 16.225<br /> | ||
<br /> | <br /> | ||
Map: [&lt;12 19 0 -22|, &lt;0 0 1 2|]<br /> | Map: [&lt;12 19 0 -22|, &lt;0 0 1 2|]<br /> | ||
| Line 69: | Line 69: | ||
Commas: 225/224, 441/440, 4375/4356<br /> | Commas: 225/224, 441/440, 4375/4356<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 16.734<br /> | ||
<br /> | <br /> | ||
Map: [&lt;12 19 0 -22 -42|, &lt;0 0 1 2 3|]<br /> | Map: [&lt;12 19 0 -22 -42|, &lt;0 0 1 2 3|]<br /> | ||
| Line 79: | Line 79: | ||
Commas: 81/80, 128/125<br /> | Commas: 81/80, 128/125<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 26.790<br /> | ||
<br /> | <br /> | ||
Map: [&lt;12 19 28 0|, &lt;0 0 0 1|]<br /> | Map: [&lt;12 19 28 0|, &lt;0 0 0 1|]<br /> | ||
EDOs: 12, 36, 48, 132, 180</body></html></pre></div> | EDOs: 12, 36, 48, 132, 180</body></html></pre></div> | ||