Tablet: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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 09:36:06 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-25 09:42:17 UTC</tt>.<br>

: The original revision id was <tt>~~257936106~~</tt>.<br>

: The original revision id was <tt>257936696</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>

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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].

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).

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 q(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 = (q(k(c)) - 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 />

<br />

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 />

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 q(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 = (q(k(c)) - 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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 09:36:06 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-25 09:42:17 UTC</tt>.<br>
-: The original revision id was <tt>257936106</tt>.<br>
+: The original revision id was <tt>257936696</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>
@@ Line 165: / Line 165: @@
 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].
-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).
+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 q(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 = (q(k(c)) - 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 = &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.
@@ Line 302: / Line 302: @@
 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 =&amp;gt; [-1 3 3].&lt;br /&gt;
 &lt;br /&gt;
-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).&lt;br /&gt;
+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 q(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 = (q(k(c)) - c)/4 and setting kord(c) = 3^t[1] 5^t[2] 7^t[3] k(c).&lt;br /&gt;
 Now we may define note(n, c) by setting u = kord(c), v = &amp;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 &amp;lt;4 6 9 11|note(n, c) = n.&lt;/body&gt;&lt;/html&gt;</pre></div>