Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 264271370 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 264271616 - 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>2011-10-13 01: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-13 01:30:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>264271616</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 a and b are two allowable triples of integers representing tetrads (so that their reduction modulo four is one of the seven allowed types) then we may derive a [[http://mathworld.wolfram.com/PositiveDefiniteQuadraticForm.html|positive definite quaratic form]] on 3-tuples [x y z] by Q(x, y, z) = 4x^2 + 3y^2 + 3z^2 + 4xy + 4xz + 2xy, such that Q(a-b) = 8 if a and b are 3-tuples representing tetrads with a common triad. The square root sqrt(Q(a-b)) is a Eulidean measure of distance, and sqrt(8) is the minimum distance between tetrad 3-tuples. Such 3-tuple pairs a minimum distance apart share at least an interval in common, and usually a triad, and are therefore closely related. | If a and b are two allowable triples of integers representing tetrads (so that their reduction modulo four is one of the seven allowed types) then we may derive a [[http://mathworld.wolfram.com/PositiveDefiniteQuadraticForm.html|positive definite quaratic form]] on 3-tuples [x y z] by Q(x, y, z) = 4x^2 + 3y^2 + 3z^2 + 4xy + 4xz + 2xy, such that Q(a-b) = 8 if a and b are 3-tuples representing tetrads with a common triad. The square root sqrt(Q(a-b)) is a Eulidean measure of distance, and sqrt(8) is the minimum distance between tetrad 3-tuples. Such 3-tuple pairs a minimum distance apart share at least an interval in common, and usually a triad, and are therefore closely related. | ||
==The | ==The pele tablet== | ||
This is a tablet for the rank 3 13-limit temperament [[Hemifamity family#Pele|pele]]. It is based on the following 71 chords, in the 5-limit transversal: | This is a tablet for the rank 3 13-limit temperament [[Hemifamity family#Pele|pele]]. It is based on the following 71 chords, in the 5-limit transversal: | ||
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<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#x4et tablets-The 7-limit 4et tablet">The 7-limit 4et tablet</a></div> | <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#x4et tablets-The 7-limit 4et tablet">The 7-limit 4et tablet</a></div> | ||
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#x4et tablets-The keenanismic tablet">The keenanismic tablet</a></div> | <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#x4et tablets-The keenanismic tablet">The keenanismic tablet</a></div> | ||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x4et tablets-The | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x4et tablets-The pele tablet">The pele tablet</a></div> | ||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#x5et tablets">5et tablets</a></div> | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#x5et tablets">5et tablets</a></div> | ||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#x5et tablets-The 7-limit 5et tablet">The 7-limit 5et tablet</a></div> | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#x5et tablets-The 7-limit 5et tablet">The 7-limit 5et tablet</a></div> | ||
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If a and b are two allowable triples of integers representing tetrads (so that their reduction modulo four is one of the seven allowed types) then we may derive a <a class="wiki_link_ext" href="http://mathworld.wolfram.com/PositiveDefiniteQuadraticForm.html" rel="nofollow">positive definite quaratic form</a> on 3-tuples [x y z] by Q(x, y, z) = 4x^2 + 3y^2 + 3z^2 + 4xy + 4xz + 2xy, such that Q(a-b) = 8 if a and b are 3-tuples representing tetrads with a common triad. The square root sqrt(Q(a-b)) is a Eulidean measure of distance, and sqrt(8) is the minimum distance between tetrad 3-tuples. Such 3-tuple pairs a minimum distance apart share at least an interval in common, and usually a triad, and are therefore closely related.<br /> | If a and b are two allowable triples of integers representing tetrads (so that their reduction modulo four is one of the seven allowed types) then we may derive a <a class="wiki_link_ext" href="http://mathworld.wolfram.com/PositiveDefiniteQuadraticForm.html" rel="nofollow">positive definite quaratic form</a> on 3-tuples [x y z] by Q(x, y, z) = 4x^2 + 3y^2 + 3z^2 + 4xy + 4xz + 2xy, such that Q(a-b) = 8 if a and b are 3-tuples representing tetrads with a common triad. The square root sqrt(Q(a-b)) is a Eulidean measure of distance, and sqrt(8) is the minimum distance between tetrad 3-tuples. Such 3-tuple pairs a minimum distance apart share at least an interval in common, and usually a triad, and are therefore closely related.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x4et tablets-The | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x4et tablets-The pele tablet"></a><!-- ws:end:WikiTextHeadingRule:10 -->The pele tablet</h2> | ||
This is a tablet for the rank 3 13-limit temperament <a class="wiki_link" href="/Hemifamity%20family#Pele">pele</a>. It is based on the following 71 chords, in the 5-limit transversal: <br /> | This is a tablet for the rank 3 13-limit temperament <a class="wiki_link" href="/Hemifamity%20family#Pele">pele</a>. It is based on the following 71 chords, in the 5-limit transversal: <br /> | ||
<br /> | <br /> |