Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 256942682 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 256942984 - 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>2011-09-22 07: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-22 07:27:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>256942984</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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note(n, [r e3 e5]) = |(u-5)/3 e3+1 e5> | note(n, [r e3 e5]) = |(u-5)/3 e3+1 e5> | ||
Then if c is a tablet, note(n, c) gives the note belonging to the triad denoted by c, satisfying <3 5 7|note(n, c) | Then if c is a tablet, note(n, c) gives the note belonging to the triad denoted by c, satisfying <3 5 7|note(n, c) = n. | ||
=The 7-limit 4et tablet= | =The 7-limit 4et tablet= | ||
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note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 1+(a+b-c)/2> | note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 1+(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, and <4 6 9 11|note(n, t) | 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, and <4 6 9 11|note(n, t) = n. | ||
=The 7-limit 5et tablet= | =The 7-limit 5et tablet= | ||
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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, where <5 8 12 14|note(n, t) | 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, where <5 8 12 14|note(n, t) = n. | ||
=The 13-limit 7et tablet= | =The 13-limit 7et tablet= | ||
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note(n, c) = |(u-4)/5-4 c+3> | note(n, c) = |(u-4)/5-4 c+3> | ||
In all cases <5 8|note(n, c) | In all cases <5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning. | ||
=The tutone tutonic tablet= | =The tutone tutonic tablet= | ||
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<ul><li>If u mod 3 = 2, then</li></ul>note(n, [r e3 e5]) = |(u-5)/3 e3+1 e5&gt;<br /> | <ul><li>If u mod 3 = 2, then</li></ul>note(n, [r e3 e5]) = |(u-5)/3 e3+1 e5&gt;<br /> | ||
<br /> | <br /> | ||
Then if c is a tablet, note(n, c) gives the note belonging to the triad denoted by c, satisfying &lt;3 5 7|note(n, c) | Then if c is a tablet, note(n, c) gives the note belonging to the triad denoted by c, satisfying &lt;3 5 7|note(n, c) = n.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="The 7-limit 4et tablet"></a><!-- ws:end:WikiTextHeadingRule:4 -->The 7-limit 4et tablet</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="The 7-limit 4et tablet"></a><!-- ws:end:WikiTextHeadingRule:4 -->The 7-limit 4et tablet</h1> | ||
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<ul><li>If u mod 4 = 3, then</li></ul>note(t) = |(u-11)/4 (-a+b+c)/2 (a-b+c)/2 1+(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 1+(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, and &lt;4 6 9 11|note(n, t) | 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, and &lt;4 6 9 11|note(n, t) = n.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="The 7-limit 5et tablet"></a><!-- ws:end:WikiTextHeadingRule:6 -->The 7-limit 5et tablet</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="The 7-limit 5et tablet"></a><!-- ws:end:WikiTextHeadingRule:6 -->The 7-limit 5et tablet</h1> | ||
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<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, where &lt;5 8 12 14|note(n, t) | 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, where &lt;5 8 12 14|note(n, t) = n.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="The 13-limit 7et tablet"></a><!-- ws:end:WikiTextHeadingRule:8 -->The 13-limit 7et tablet</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="The 13-limit 7et tablet"></a><!-- ws:end:WikiTextHeadingRule:8 -->The 13-limit 7et tablet</h1> | ||
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<ul><li>If u mod 5 = 4 then</li></ul>note(n, c) = |(u-4)/5-4 c+3&gt;<br /> | <ul><li>If u mod 5 = 4 then</li></ul>note(n, c) = |(u-4)/5-4 c+3&gt;<br /> | ||
<br /> | <br /> | ||
In all cases &lt;5 8|note(n, c) | In all cases &lt;5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="The tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:12 -->The tutone tutonic tablet</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="The tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:12 -->The tutone tutonic tablet</h1> | ||