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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-13 01:32:03 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-13 02:39:27 UTC</tt>.

: The original revision id was <tt>~~264271888~~</tt>.

: The original revision id was <tt>264280030</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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[1, 655360/531441, 81920/59049, 1280/729]]

If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 < c[1] < 72, then if u = n - 6c[2] - 9c[3] ~~and~~ v = u mod 4 we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] ~~chords(c~~[1]). The steps of the 71 chords are as follows:

If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 < c[1] < 72, then if u = n - 6c[2] - 9c[3], v = u mod 4 and w = chords(c[1]), we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] w[v+1]. The steps of the 71 chords are as follows:

* 5-limit JI

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[16384/16807, 131072/117649, 5/4, 10/7, 7/4]]

If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], ~~and if~~ v ~~is the reduction of~~ u mod 5, then

If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], v = u mod 5, and w = chords(c[1]), then

note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] ~~chords(~~v+1)

note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] w[v+1].

Once again, <5 8 12 14 17|note(n, c) = c.

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[1, 655360/531441, 81920/59049, 1280/729]]

If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &lt; c[1] &lt; 72, then if u = n - 6c[2] - 9c[3] ~~and~~ v = u mod 4 we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] ~~chords(c~~[1]). The steps of the 71 chords are as follows:

If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &lt; c[1] &lt; 72, then if u = n - 6c[2] - 9c[3], v = u mod 4 and w = chords(c[1]), we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] w[v+1]. The steps of the 71 chords are as follows:

<ul><li>5-limit JI</li></ul>6/5-5/4-6/5-10/9

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chords = [[1, 131072/117649, 5/4, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 1048576/588245], [1, 131072/117649, 16384/12005, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 80/49], [1, 2048/1715, 16384/12005, 512/343, 7/4], [1, 35/32, 5/4, 512/343, 4096/2401], [1, 35/32, 5/4, 12005/8192, 7/4], [1, 35/32, 5/4, 512/343, 7/4], [1, 131072/117649, 5/4, 10/7,7/4], [1, 588245/524288, 5/4, 10/7, 7/4], [1, 131072/117649, 16384/12005, 131072/84035, 7/4], [16384/16807, 131072/117649, 5/4, 10/7, 7/4]]

If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], ~~and if~~ v ~~is the reduction of~~ u mod 5, then

If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], v = u mod 5, and w = chords(c[1]), then

note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] ~~chords(~~v+1)

note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] w[v+1].

Once again, &lt;5 8 12 14 17|note(n, c) = c.

@@ 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>2011-10-13 01:32:03 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-13 02:39:27 UTC</tt>.<br>
-: The original revision id was <tt>264271888</tt>.<br>
+: The original revision id was <tt>264280030</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 112: / Line 112: @@
 [1, 655360/531441, 81920/59049, 1280/729]]
-If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &lt; c[1] &lt; 72, then if u = n - 6c[2] - 9c[3] and v = u mod 4 we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] chords(c[1]). The steps of the 71 chords are as follows:
+If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &lt; c[1] &lt; 72, then if u = n - 6c[2] - 9c[3], v = u mod 4 and w = chords(c[1]), we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] w[v+1]. The steps of the 71 chords are as follows:
 * 5-limit JI
@@ Line 265: / Line 265: @@
 [16384/16807, 131072/117649, 5/4, 10/7, 7/4]]
-If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then
+If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], v = u mod 5, and w = chords(c[1]), then
-note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)
+note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] w[v+1].
 Once again, &lt;5 8 12 14 17|note(n, c) = c.
@@ Line 465: / Line 465: @@
 [1, 655360/531441, 81920/59049, 1280/729]]&lt;br /&gt;
 &lt;br /&gt;
-If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &amp;lt; c[1] &amp;lt; 72, then if u = n - 6c[2] - 9c[3] and v = u mod 4 we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] chords(c[1]). The steps of the 71 chords are as follows:&lt;br /&gt;
+If c is a chord identifier, [c[1] c[2] c[3]], c[2] and c[3] any integers and 0 &amp;lt; c[1] &amp;lt; 72, then if u = n - 6c[2] - 9c[3], v = u mod 4 and w = chords(c[1]), we may define note(n, c) = 2^((u-v)/4) 3^c[2] 5^c[3] w[v+1]. The steps of the 71 chords are as follows:&lt;br /&gt;
 &lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;5-limit JI&lt;/li&gt;&lt;/ul&gt;6/5-5/4-6/5-10/9&lt;br /&gt;
@@ Line 584: / Line 584: @@
 chords = [[1, 131072/117649, 5/4, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 1048576/588245], [1, 131072/117649, 16384/12005, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 80/49], [1, 2048/1715, 16384/12005, 512/343, 7/4], [1, 35/32, 5/4, 512/343, 4096/2401], [1, 35/32, 5/4, 12005/8192, 7/4], [1, 35/32, 5/4, 512/343, 7/4], [1, 131072/117649, 5/4, 10/7,7/4], [1, 588245/524288, 5/4, 10/7, 7/4], [1, 131072/117649, 16384/12005, 131072/84035, 7/4], [16384/16807, 131072/117649, 5/4, 10/7, 7/4]]&lt;br /&gt;
 &lt;br /&gt;
-If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then &lt;br /&gt;
+If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], v = u mod 5, and w = chords(c[1]), then &lt;br /&gt;
-note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)&lt;br /&gt;
+note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] w[v+1].&lt;br /&gt;
 Once again, &amp;lt;5 8 12 14 17|note(n, c) = c.&lt;br /&gt;
 &lt;br /&gt;