Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 204565744 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 205205024 - 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>2011-02-26 04:30:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>205205024</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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In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1>. It has a wedgie <<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&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. | In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1>. It has a wedgie <<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&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. | ||
Adding 3025/3024 extends to the 11-limit and gives <<38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.</pre></div> | Adding 3025/3024 extends to the 11-limit and gives <<38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning. | ||
==Decoid== | |||
Commas: 2401/2400, 67108864/66976875 | |||
POTE generator: ~8/7 = 231.099 | |||
Map: [<10 0 47 36|, <0 2 -3 -1|] | |||
Wedgie: <<20 -30 -10 -94 -72 61|| | |||
EDOs: 10, 120, 130, 270 | |||
Badness: 0.0339 | |||
===11-limit=== | |||
Commas: 2401/2400, 5832/5825, 9801/9800 | |||
POTE generator: ~8/7 = 231.070 | |||
Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|] | |||
EDOs: 130, 270, 940, 1210 | |||
Badness: 0.0187</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>Breedsmic temperaments</title></head><body>Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<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>Breedsmic temperaments</title></head><body>Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | ||
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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 /> | ||
<br /> | <br /> | ||
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.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Decoid"></a><!-- ws:end:WikiTextHeadingRule:18 -->Decoid</h2> | |||
Commas: 2401/2400, 67108864/66976875<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 231.099<br /> | |||
<br /> | |||
Map: [&lt;10 0 47 36|, &lt;0 2 -3 -1|]<br /> | |||
Wedgie: &lt;&lt;20 -30 -10 -94 -72 61||<br /> | |||
EDOs: 10, 120, 130, 270<br /> | |||
Badness: 0.0339<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Decoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h3> | |||
Commas: 2401/2400, 5832/5825, 9801/9800<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 231.070<br /> | |||
<br /> | |||
Map: [&lt;10 0 47 36 98|, &lt;0 2 -3 -1 -8|]<br /> | |||
EDOs: 130, 270, 940, 1210<br /> | |||
Badness: 0.0187</body></html></pre></div> | |||