Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 257934916 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 257936106 - 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>2011-09-25 09: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-25 09:36:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>257936106</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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Here 35/32-5/4-3/2-12/7 is the 8/7-6/5-8/7-14/11 chord. Also, in place of 1-8/7-4/3-8/5 we can use 1-6/5-3/2-12/7 => [-1 3 3]. | Here 35/32-5/4-3/2-12/7 is the 8/7-6/5-8/7-14/11 chord. Also, in place of 1-8/7-4/3-8/5 we can use 1-6/5-3/2-12/7 => [-1 3 3]. | ||
If we have a 3-tuple c representing a keenanismic tetrad, define k(c) by reversing the above correspondence, except that we assign k([3 3 3]) = [1,6/5,3/2,12/7]. If w is a keenanismic tetrad, define c(w) by taking the product w[1]*w[2]*w[3]*w[4], finding the monzo m, and returning [2-m[2] 2-m[3] 2-m[4]]. Now we may define note(n, c) by setting u = | If we have a 3-tuple c representing a keenanismic tetrad and reduce it modulo four, define k(c) by reversing the above correspondence, except that we assign k([3 3 3]) = [1,6/5,3/2,12/7]. If w is a keenanismic tetrad, define c(w) by taking the product w[1]*w[2]*w[3]*w[4], finding the monzo m, and returning [2-m[2] 2-m[3] 2-m[4]]. Define kord(c) by finding t = (c - c(k(c))/4 and setting kord(c) = 3^t[1]*5^t[2]*7^t[3]*k(c). | ||
Now we may define note(n, c) by setting u = kord(c), v = <4 6 9 11|u[1], i = v mod 4, and then setting note(n, c) = 2^((n-v-i)/4) u[i+1]. We then have our basic identity <4 6 9 11|note(n, c) = n. | |||
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Here 35/32-5/4-3/2-12/7 is the 8/7-6/5-8/7-14/11 chord. Also, in place of 1-8/7-4/3-8/5 we can use 1-6/5-3/2-12/7 =&gt; [-1 3 3].<br /> | Here 35/32-5/4-3/2-12/7 is the 8/7-6/5-8/7-14/11 chord. Also, in place of 1-8/7-4/3-8/5 we can use 1-6/5-3/2-12/7 =&gt; [-1 3 3].<br /> | ||
<br /> | <br /> | ||
If we have a 3-tuple c representing a keenanismic tetrad, define k(c) by reversing the above correspondence, except that we assign k([3 3 3]) = [1,6/5,3/2,12/7]. If w is a keenanismic tetrad, define c(w) by taking the product w[1]*w[2]*w[3]*w[4], finding the monzo m, and returning [2-m[2] 2-m[3] 2-m[4]]. Now we may define note(n, c) by setting u = | If we have a 3-tuple c representing a keenanismic tetrad and reduce it modulo four, define k(c) by reversing the above correspondence, except that we assign k([3 3 3]) = [1,6/5,3/2,12/7]. If w is a keenanismic tetrad, define c(w) by taking the product w[1]*w[2]*w[3]*w[4], finding the monzo m, and returning [2-m[2] 2-m[3] 2-m[4]]. Define kord(c) by finding t = (c - c(k(c))/4 and setting kord(c) = 3^t[1]*5^t[2]*7^t[3]*k(c).<br /> | ||
Now we may define note(n, c) by setting u = kord(c), v = &lt;4 6 9 11|u[1], i = v mod 4, and then setting note(n, c) = 2^((n-v-i)/4) u[i+1]. We then have our basic identity &lt;4 6 9 11|note(n, c) = n.</body></html></pre></div> | |||