Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 199233736 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 202797834 - 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>2011-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-17 12:52:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>202797834</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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==Tertiaseptal== | ==Tertiaseptal== | ||
Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well. | Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well. | ||
Commas: 2401/2400, 65625/65536 | |||
POTE generator: ~256/245 = 77.191 | |||
Map: [<1 3 2 3|, <0 -22 5 -3|] | |||
EDOs: 15, 16, 31, 109, 140, 171 | |||
Badness: 0.0130 | |||
===11-limit=== | |||
Commas: 243/242, 441/440, 65625/65536 | |||
POTE generator: ~256/245 = 77.227 | |||
Map: [<1 3 2 3 7|, <0 -22 5 -3 -55|] | |||
EDOs: 15, 16, 31, 171, 202 | |||
Badness: 0.0356 | |||
==Harry== | ==Harry== | ||
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Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. <a class="wiki_link" href="/171edo">171edo</a> makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.<br /> | Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. <a class="wiki_link" href="/171edo">171edo</a> makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id=" | Commas: 2401/2400, 65625/65536<br /> | ||
<br /> | |||
POTE generator: ~256/245 = 77.191<br /> | |||
<br /> | |||
Map: [&lt;1 3 2 3|, &lt;0 -22 5 -3|]<br /> | |||
EDOs: 15, 16, 31, 109, 140, 171<br /> | |||
Badness: 0.0130<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Tertiaseptal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h3> | |||
Commas: 243/242, 441/440, 65625/65536<br /> | |||
<br /> | |||
POTE generator: ~256/245 = 77.227<br /> | |||
<br /> | |||
Map: [&lt;1 3 2 3 7|, &lt;0 -22 5 -3 -55|]<br /> | |||
EDOs: 15, 16, 31, 171, 202<br /> | |||
Badness: 0.0356<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Harry"></a><!-- ws:end:WikiTextHeadingRule:6 -->Harry</h2> | |||
Commas: 2401/2400, 19683/19600<br /> | Commas: 2401/2400, 19683/19600<br /> | ||
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Badness: 0.0341<br /> | Badness: 0.0341<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Harry-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h3> | ||
Commas: 243/242, 441/440, 4000/3993<br /> | Commas: 243/242, 441/440, 4000/3993<br /> | ||
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Badness: 0.0159<br /> | Badness: 0.0159<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Harry-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> | ||
Commas: 243/242, 351/350, 441/440, 676/675<br /> | Commas: 243/242, 351/350, 441/440, 676/675<br /> | ||
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Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Quasiorwell"></a><!-- ws:end:WikiTextHeadingRule:12 -->Quasiorwell</h2> | ||
In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | ||
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Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.</body></html></pre></div> | Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.</body></html></pre></div> | ||