Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 254444868 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 254455600 - 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>2011-09-15 14: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-15 14:25:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>254455600</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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* If u mod 4 = 0, then | * If u mod 4 = 0, then | ||
note(t) = |u/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | note(t) = |u/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | ||
* If u mod 4 = 1, then | * If u mod 4 = 1, then | ||
note(t) = |(u-9)/4 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2> | note(t) = |(u-9)/4 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2> | ||
* If u mod 4 = 2, then | * If u mod 4 = 2, then | ||
note(t) = |(u-6)/4 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2> | note(t) = |(u-6)/4 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2> | ||
* If u mod 4 = 3, then | * If u mod 4 = 3, then | ||
note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | ||
If a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). Then note(t) is the note defined by the tablet t. If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w)] is a 7-limit tetrad. | If a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). Then note(t) is the note defined by the tablet t. If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w)] is a 7-limit tetrad. | ||
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* If u mod 5 = 0, then | * If u mod 5 = 0, then | ||
note(t) = |u/5 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | note(t) = |u/5 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | ||
* If u mod 5 = 1, then | * If u mod 5 = 1, then | ||
note(t) = |(u-16)/5 2+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | note(t) = |(u-16)/5 2+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | ||
* If u mod 5 = 2, then | * If u mod 5 = 2, then | ||
note(t) = |(u-12)/5 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2> | note(t) = |(u-12)/5 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2> | ||
* If u mod 5 = 3, then | * If u mod 5 = 3, then | ||
note(t) = |(u-8)/5 1+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | note(t) = |(u-8)/5 1+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2> | ||
* If u mod 5 = 4, then | * If u mod 5 = 4, then | ||
note(t) = |(u-14)/5 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2> | note(t) = |(u-14)/5 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2> | ||
Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad. | Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad. | ||
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If t = [n, [a b c]] is a tablet, define u = n - 7a - 4b - 2c. If a+b+c is even, then<br /> | If t = [n, [a b c]] is a tablet, define u = n - 7a - 4b - 2c. If a+b+c is even, then<br /> | ||
<br /> | <br /> | ||
<ul><li>If u mod 4 = 0, then</li></ul>note(t) = |u/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 4 = 0, then</li></ul>note(t) = |u/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 4 = 1, then</li></ul>note(t) = |(u-9)/4 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2&gt;<br /> | <ul><li>If u mod 4 = 1, then</li></ul>note(t) = |(u-9)/4 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 4 = 2, then</li></ul>note(t) = |(u-6)/4 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 4 = 2, then</li></ul>note(t) = |(u-6)/4 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 4 = 3, then</li></ul>note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 4 = 3, then</li></ul>note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<br /> | <br /> | ||
If a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). Then note(t) is the note defined by the tablet t. If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w)] is a 7-limit tetrad.<br /> | If a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). Then note(t) is the note defined by the tablet t. If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w)] is a 7-limit tetrad.<br /> | ||
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If we define u = n - 9a - 5b - 3c then supposing a+b+c is even,<br /> | If we define u = n - 9a - 5b - 3c then supposing a+b+c is even,<br /> | ||
<br /> | <br /> | ||
<ul><li>If u mod 5 = 0, then</li></ul>note(t) = |u/5 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 5 = 0, then</li></ul>note(t) = |u/5 (-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 5 = 1, then</li></ul>note(t) = |(u-16)/5 2+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 5 = 1, then</li></ul>note(t) = |(u-16)/5 2+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 5 = 2, then</li></ul>note(t) = |(u-12)/5 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 5 = 2, then</li></ul>note(t) = |(u-12)/5 (-a+b+c)/2 1+(a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 5 = 3, then</li></ul>note(t) = |(u-8)/5 1+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | <ul><li>If u mod 5 = 3, then</li></ul>note(t) = |(u-8)/5 1+(-a+b+c)/2 (a-b+c)/2 (a+b-c)/2&gt;<br /> | ||
<ul><li>If u mod 5 = 4, then</li></ul>note(t) = |(u-14)/5 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2&gt;<br /> | <ul><li>If u mod 5 = 4, then</li></ul>note(t) = |(u-14)/5 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2&gt;<br /> | ||
<br /> | <br /> | ||
Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad.<br /> | Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad.<br /> | ||