Orwell tetrad
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-07-25 18:13:12 UTC.
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Original Wikitext content:
The //orwell tetrad// is a four-note chord which in close position (reduced to the octave) consists of a chain of three subminor thirds, thirds of approximately 7/6 in size, and a major third, of approximately 5/4 in size, which closes at the octave since the orwell comma, 1728/1715, is tempered out; in other words, a 7/6-7/6-7/6-5/4 chord. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include 22, 26, 27, 31, 53, 58, 80, 84 and 111. The orwell tetrad can in a natural way be extended to the [[11-limit]] as the [[Orwellismic family#Guanyin|guanyin]] tetrad by considering it to temper out 176/175 (and and so 540/539) as well as 1728/1715. If 540/539 is tempered out, (7/6)^2 is equated to 15/11 as well as (7/6)^3 to 8/5, so that the guanyin tetrad is a tempered verssion of 1-7/6-15/11-8/5. Equal temperaments with guanyin tetrads include 22, 31, 53, 58, 80 and 111.
Original HTML content:
<html><head><title>orwell tetrad</title></head><body>The <em>orwell tetrad</em> is a four-note chord which in close position (reduced to the octave) consists of a chain of three subminor thirds, thirds of approximately 7/6 in size, and a major third, of approximately 5/4 in size, which closes at the octave since the orwell comma, 1728/1715, is tempered out; in other words, a 7/6-7/6-7/6-5/4 chord. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include 22, 26, 27, 31, 53, 58, 80, 84 and 111. <br /> <br /> The orwell tetrad can in a natural way be extended to the <a class="wiki_link" href="/11-limit">11-limit</a> as the <a class="wiki_link" href="/Orwellismic%20family#Guanyin">guanyin</a> tetrad by considering it to temper out 176/175 (and and so 540/539) as well as 1728/1715. If 540/539 is tempered out, (7/6)^2 is equated to 15/11 as well as (7/6)^3 to 8/5, so that the guanyin tetrad is a tempered verssion of 1-7/6-15/11-8/5. Equal temperaments with guanyin tetrads include 22, 31, 53, 58, 80 and 111.</body></html>