Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 254787718 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 254842182 - 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>2011-09-16 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-16 14:22:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>254842182</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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=The 5-limit 3et tablet= | =The 5-limit 3et tablet= | ||
If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted <* e3 e5 | If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted <* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that <r e3 e5| defines a major triad with root given by |* e3 e5> when r is even, and a minor triad when r is odd. | ||
If r is even, therefore, we will regard the | If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have | ||
* If u mod 3 = 0, then | * If u mod 3 = 0, then | ||
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=The 13-limit 7et tablet= | =The 13-limit 7et tablet= | ||
Let <r e3 e5 e7 e11 e13| denote an otonal 13-limit septad with root given by |* e3 e5 e7 e11 e13> when r is even, which in close position is 9/8-5/4-11/8-3/2-13/8-7/4-2. If r is odd, let it denote a utonal pentad which in close position is 12/11-6/5-4/3-3/2-12/7-24/13-2 | |||
We will regard the 6-tuple [r e3 e5 e7 e11 e13] as denoting a septad, and [n, [r e3 e5 e7 e11 e13]] the corresponding tablet. We first calculate u = n - 11e3 - 16e5 - 20e7 - 24e11 - 26e13. Then if r is even, we have | |||
* If u mod 7 = 0, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |u/7 e3 e5 e7 e11 e13> | |||
* If u mod 7 = 1, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-22)/7 e3+2 e5 e7 e11 e13> | |||
* If u mod 7 = 2, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-16)/7 e3 e5+1 e7 e11 e13> | |||
* If u mod 7 = 3, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-24)/7 e3 e5 e7 e11+1 e13> | |||
* If u mod 7 = 4, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-11)/7 e3+1 e5 e7 e11 e13> | |||
* If u mod 7 = 5, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-26)/7 e3 e5 e7 e11 e13+1> | |||
* If u mod 7 = 6, then | |||
note(n, [r e3 e5 e7 e11 e13]) = |(u-20)/7 e3 e5 e7+1 e11 e13> | |||
</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="The 5-limit 3et tablet"></a><!-- ws:end:WikiTextHeadingRule:4 -->The 5-limit 3et tablet</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="The 5-limit 3et tablet"></a><!-- ws:end:WikiTextHeadingRule:4 -->The 5-limit 3et tablet</h1> | ||
If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted &lt;* e3 e5 | If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted &lt;* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that &lt;r e3 e5| defines a major triad with root given by |* e3 e5&gt; when r is even, and a minor triad when r is odd.<br /> | ||
<br /> | <br /> | ||
If r is even, therefore, we will regard the | If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have<br /> | ||
<br /> | <br /> | ||
<ul><li>If u mod 3 = 0, then</li></ul>note(n, [r e3 e5]) = |u/3 e3 e5&gt;<br /> | <ul><li>If u mod 3 = 0, then</li></ul>note(n, [r e3 e5]) = |u/3 e3 e5&gt;<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="The 13-limit 7et tablet"></a><!-- ws:end:WikiTextHeadingRule:10 -->The 13-limit 7et tablet</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="The 13-limit 7et tablet"></a><!-- ws:end:WikiTextHeadingRule:10 -->The 13-limit 7et tablet</h1> | ||
</body></html></pre></div> | Let &lt;r e3 e5 e7 e11 e13| denote an otonal 13-limit septad with root given by |* e3 e5 e7 e11 e13&gt; when r is even, which in close position is 9/8-5/4-11/8-3/2-13/8-7/4-2. If r is odd, let it denote a utonal pentad which in close position is 12/11-6/5-4/3-3/2-12/7-24/13-2<br /> | ||
<br /> | |||
We will regard the 6-tuple [r e3 e5 e7 e11 e13] as denoting a septad, and [n, [r e3 e5 e7 e11 e13]] the corresponding tablet. We first calculate u = n - 11e3 - 16e5 - 20e7 - 24e11 - 26e13. Then if r is even, we have<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 0, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |u/7 e3 e5 e7 e11 e13&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 1, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-22)/7 e3+2 e5 e7 e11 e13&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 2, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-16)/7 e3 e5+1 e7 e11 e13&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 3, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-24)/7 e3 e5 e7 e11+1 e13&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 4, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-11)/7 e3+1 e5 e7 e11 e13&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 5, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-26)/7 e3 e5 e7 e11 e13+1&gt;<br /> | |||
<br /> | |||
<ul><li>If u mod 7 = 6, then</li></ul>note(n, [r e3 e5 e7 e11 e13]) = |(u-20)/7 e3 e5 e7+1 e11 e13&gt;</body></html></pre></div> | |||