Kestrel chords
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2013-01-31 15:50:07 UTC.
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Original Wikitext content:
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, 205, 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.Original HTML content:
<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, 205, 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>