Orwell tetrad: Difference between revisions
Wikispaces>genewardsmith **Imported revision 242799917 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 242800055 - 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>2011-07-25 18: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-25 18:13:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>242800055</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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<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 //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. | <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 //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 | 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.</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>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 /> | <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>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 /> | ||
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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 | 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></pre></div> | ||