Kestrel chords: Difference between revisions
Wikispaces>genewardsmith **Imported revision 243852363 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 283407104 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-07 15:02:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>283407104</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">The //kestrel tetrad// is the 13-limit [[Dyadic chord|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 165, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. </pre></div> | <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 //kestrel tetrad// is the 13-limit [[Dyadic chord|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 165, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</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>kestrel chords</title></head><body>The <em>kestrel tetrad</em> is the 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrad</a> consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 165, 214, 255. 255edo is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539.</body></html></pre></div> | <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>kestrel chords</title></head><body>The <em>kestrel tetrad</em> is the 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrad</a> consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 165, 214, 255. 255edo is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</body></html></pre></div> | ||