87edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 149422583 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 186508351 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-08 15:39:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>186508351</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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224&87 <<27 8 -67 -1 5 ...|| | 224&87 <<27 8 -67 -1 5 ...|| | ||
87et is a particularly good tuning for rodan temperament.</pre></div> | 87et is a particularly good tuning for rodan temperament. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE]] generator and is close to the 11-limit POTE generator also.</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>87edo</title></head><body>The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so.<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>87edo</title></head><body>The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so.<br /> | ||
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224&amp;87 &lt;&lt;27 8 -67 -1 5 ...||<br /> | 224&amp;87 &lt;&lt;27 8 -67 -1 5 ...||<br /> | ||
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87et is a particularly good tuning for rodan temperament.</body></html></pre></div> | 87et is a particularly good tuning for rodan temperament. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit <a class="wiki_link" href="/POTE">POTE</a> generator and is close to the 11-limit POTE generator also.</body></html></pre></div> | ||
Revision as of 15:39, 8 December 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-12-08 15:39:29 UTC.
- The original revision id was 186508351.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so. 87et tempers out 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29|, the misty comma, <26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103. Some 13-limit rank two temperaments supported by 87et are these: tritikleismic 72&87 <<18 15 -6 9 42 ... || rodan 41&87 <<3 17 -1 -13 -22 ... || mystery 29&58 <<0 29 29 29 29 ... || countercata 34&87 <<6 5 -31 32 14 ... || luna 31&87 <<15 -2 -5 22 -23 ... || 87 can serve as a MOS in these: 270&87 <<24 -9 -66 12 27 ... || 494&87 <<51 -1 -133 11 32 ... || 224&87 <<27 8 -67 -1 5 ...|| 87et is a particularly good tuning for rodan temperament. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE]] generator and is close to the 11-limit POTE generator also.
Original HTML content:
<html><head><title>87edo</title></head><body>The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so.<br /> <br /> 87et tempers out 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29|, the misty comma, <26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103. <br /> <br /> Some 13-limit rank two temperaments supported by 87et are these:<br /> <br /> tritikleismic 72&87 <<18 15 -6 9 42 ... ||<br /> rodan 41&87 <<3 17 -1 -13 -22 ... ||<br /> mystery 29&58 <<0 29 29 29 29 ... ||<br /> countercata 34&87 <<6 5 -31 32 14 ... ||<br /> luna 31&87 <<15 -2 -5 22 -23 ... ||<br /> <br /> 87 can serve as a MOS in these:<br /> <br /> 270&87 <<24 -9 -66 12 27 ... ||<br /> 494&87 <<51 -1 -133 11 32 ... ||<br /> 224&87 <<27 8 -67 -1 5 ...||<br /> <br /> 87et is a particularly good tuning for rodan temperament. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit <a class="wiki_link" href="/POTE">POTE</a> generator and is close to the 11-limit POTE generator also.</body></html>