Gene Ward Smith
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Gene Ward Smith (born 1947) is an American mathematician and music theorist. In mathematics he has worked in the areas of [[Galois theory]] and [[Moonshine theory]]. In music theory, he is noted for a number of innovations in the theory of musical tuning, such as the introduction of [[multilinear algebra]] and for being the first to write music in a number of exotic intonation systems. A boyhood friend of [[Steven Spielberg]], a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride.<ref>{{citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1}}.</ref> While a graduate student at [[University of California, Berkeley|Berkeley]], he and fellow mathematician Matthew P. Wiener gained online notoriety for fierce debating and frequent participation in flame wars on [[Usenet]], causing them to be nicknamed the [[Brahms Gang]] (because ''brahms.berkeley.edu'' was the name of the server they posted from).
==Music theory==
Smith introduced [[exterior algebra|wedge product]]s as a way of classifying [[regular temperament]]s, and of dealing with the problem of [[Torsion (abstract algebra)|torsion]]. In this system, a temperament is specified by means of a ''wedgie'', which technically may be identified as a point on a [[Grassmannian]].
Smith has long been drawing attention to the relationship between [[equal division of the octave|equal divisions of the octave]] and the [[Riemann zeta function]].<ref>[http://www.math.niu.edu/~rusin/uses-math/music/12 Why 12 tones per octave?], Dave Rusin. Sequence {{OEIS2C|A117536}} ''Increasingly large peaks of the Riemann zeta function on the critical line'' and {{OEIS2C|A117538}} ''Increasingly large integrals of the Z function between zeros'', [[On-Line Encyclopedia of Integer Sequences]].</ref>
Smith was among the first to consider extending the [[Tonnetz]] of [[Hugo Riemann]] beyond the [[limit (music)|5-limit]] and hence into higher dimensional [[lattice (group)|lattices]]. In three dimensions, the [[hexagonal lattice]] of 5-limit harmony extends to a lattice of type A<sub>3</sub> ~ D<sub>3</sub>.
==Mathematics==
In mathematics, Smith's most notable achievement is the construction of what has been called the Smith [[generic polynomial|generic cyclic polynomial]].<ref>{{citation|first1=Christian U.|last1=Jensen|first2=Arne|last2=Ledet|first3=Noriko|last3=Yui|title=Generic Polynomials: Constructive Aspects of the Inverse Galois Problem|publisher=Cambridge University Press|location=Cambridge|year=2002|isbn=0-521-81998-9|url=http://www.msri.org/communications/books/Book45/files/book45.pdf}}.</ref> For any integer ''n'' not divisible by eight, this constructs a polynomial which, upon specializing the values, gives all of the cyclic extensions of any given base field with [[characteristic (algebra)|characteristic]] prime to ''n''. This can then be extended to [[metacyclic]] extensions, such as [[dihedral group]]s.
Smith was also a member of the ''Amdahl Six'' group which held the largest prime record from 1989-1992.<ref>[http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html The Amdahl Six].</ref>
==References==
{{reflist}}
==External links==
*[http://lumma.org/tuning/gws/home.htm Smith's old website]
{{DEFAULTSORT:Smith, Gene Ward}}
[[Category:American music theorists]]
[[Category:American mathematicians]]
[[Category:Usenet people]]
[[Category:1947 births]]
[[Category:Living people]]
[[ht:Gene Ward Smith]]
Homepage: http://lumma.org/tuning/gws/home.htm
read on Wikipedia http://en.wikipedia.org/wiki/Gene_Ward_SmithOriginal HTML content:
<html><head><title>Gene Ward Smith</title></head><body>Gene Ward Smith (born 1947) is an American mathematician and music theorist. In mathematics he has worked in the areas of <a class="wiki_link" href="/Galois%20theory">Galois theory</a> and <a class="wiki_link" href="/Moonshine%20theory">Moonshine theory</a>. In music theory, he is noted for a number of innovations in the theory of musical tuning, such as the introduction of <a class="wiki_link" href="/multilinear%20algebra">multilinear algebra</a> and for being the first to write music in a number of exotic intonation systems. A boyhood friend of <a class="wiki_link" href="/Steven%20Spielberg">Steven Spielberg</a>, a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride.<!-- ws:start:WikiTextRefRule:2:&lt;ref&gt;<tt>citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1</tt>.&lt;/ref&gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:2 --> While a graduate student at <a class="wiki_link" href="/University%20of%20California%2C%20Berkeley">Berkeley</a>, he and fellow mathematician Matthew P. Wiener gained online notoriety for fierce debating and frequent participation in flame wars on <a class="wiki_link" href="/Usenet">Usenet</a>, causing them to be nicknamed the <a class="wiki_link" href="/Brahms%20Gang">Brahms Gang</a> (because ''brahms.berkeley.edu'' was the name of the server they posted from).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc0"><a name="x-Music theory"></a><!-- ws:end:WikiTextHeadingRule:16 -->Music theory</h2> Smith introduced <a class="wiki_link" href="/exterior%20algebra">wedge product</a>s as a way of classifying <a class="wiki_link" href="/regular%20temperament">regular temperament</a>s, and of dealing with the problem of <a class="wiki_link" href="/Torsion%20%28abstract%20algebra%29">torsion</a>. In this system, a temperament is specified by means of a ''wedgie'', which technically may be identified as a point on a <a class="wiki_link" href="/Grassmannian">Grassmannian</a>.<br /> <br /> Smith has long been drawing attention to the relationship between <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal divisions of the octave</a> and the <a class="wiki_link" href="/Riemann%20zeta%20function">Riemann zeta function</a>.<!-- ws:start:WikiTextRefRule:9:&lt;ref&gt;[http://www.math.niu.edu/~rusin/uses-math/music/12 Why 12 tones per octave?], Dave Rusin. Sequence <tt>OEIS2C|A117536</tt> ''Increasingly large peaks of the Riemann zeta function on the critical line'' and <tt>OEIS2C|A117538</tt> ''Increasingly large integrals of the Z function between zeros'', <a class="wiki_link" href="/On-Line%20Encyclopedia%20of%20Integer%20Sequences">On-Line Encyclopedia of Integer Sequences</a>.&lt;/ref&gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:9 --><br /> <br /> Smith was among the first to consider extending the <a class="wiki_link" href="/Tonnetz">Tonnetz</a> of <a class="wiki_link" href="/Hugo%20Riemann">Hugo Riemann</a> beyond the <a class="wiki_link" href="/limit%20%28music%29">5-limit</a> and hence into higher dimensional <a class="wiki_link" href="/lattice%20%28group%29">lattices</a>. In three dimensions, the <a class="wiki_link" href="/hexagonal%20lattice">hexagonal lattice</a> of 5-limit harmony extends to a lattice of type A<sub>3</sub> ~ D<sub>3</sub>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc1"><a name="x-Mathematics"></a><!-- ws:end:WikiTextHeadingRule:18 -->Mathematics</h2> In mathematics, Smith's most notable achievement is the construction of what has been called the Smith <a class="wiki_link" href="/generic%20polynomial">generic cyclic polynomial</a>.<!-- ws:start:WikiTextRefRule:13:&lt;ref&gt;<tt>citation|first1=Christian U.|last1=Jensen|first2=Arne|last2=Ledet|first3=Noriko|last3=Yui|title=Generic Polynomials: Constructive Aspects of the Inverse Galois Problem|publisher=Cambridge University Press|location=Cambridge|year=2002|isbn=0-521-81998-9|url=http://www.msri.org/communications/books/Book45/files/book45.pdf</tt>.&lt;/ref&gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:13 --> For any integer ''n'' not divisible by eight, this constructs a polynomial which, upon specializing the values, gives all of the cyclic extensions of any given base field with <a class="wiki_link" href="/characteristic%20%28algebra%29">characteristic</a> prime to ''n''. This can then be extended to <a class="wiki_link" href="/metacyclic">metacyclic</a> extensions, such as <a class="wiki_link" href="/dihedral%20group">dihedral group</a>s.<br /> <br /> Smith was also a member of the ''Amdahl Six'' group which held the largest prime record from 1989-1992.<!-- ws:start:WikiTextRefRule:15:&lt;ref&gt;[http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html The Amdahl Six].&lt;/ref&gt; --><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup><!-- ws:end:WikiTextRefRule:15 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc2"><a name="x-References"></a><!-- ws:end:WikiTextHeadingRule:20 -->References</h2> <tt>reflist</tt><br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc3"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:22 -->External links</h2> *[<!-- ws:start:WikiTextUrlRule:79:http://lumma.org/tuning/gws/home.htm --><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/home.htm" rel="nofollow">http://lumma.org/tuning/gws/home.htm</a><!-- ws:end:WikiTextUrlRule:79 --> Smith's old website]<br /> <br /> <tt>DEFAULTSORT:Smith, Gene Ward</tt><br /> <a class="wiki_link" href="http://category.wikispaces.com/American%20music%20theorists">Category/American music theorists</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/American%20mathematicians">Category/American mathematicians</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/Usenet%20people">Category/Usenet people</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/1947%20births">Category/1947 births</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/Living%20people">Category/Living people</a><br /> <br /> [[ht:Gene Ward Smith]]<br /> <br /> <br /> <br /> Homepage: <!-- ws:start:WikiTextUrlRule:80:http://lumma.org/tuning/gws/home.htm --><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/home.htm" rel="nofollow">http://lumma.org/tuning/gws/home.htm</a><!-- ws:end:WikiTextUrlRule:80 --><br /> read on Wikipedia <!-- ws:start:WikiTextUrlRule:81:http://en.wikipedia.org/wiki/Gene_Ward_Smith --><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Gene_Ward_Smith" rel="nofollow">http://en.wikipedia.org/wiki/Gene_Ward_Smith</a><!-- ws:end:WikiTextUrlRule:81 --><!-- ws:start:WikiTextReferencesRule:86: --><hr class="references" /><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <tt>citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1</tt>.</li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> [<a class="wiki_link_ext" href="http://www.math.niu.edu/~rusin/uses-math/music/12" rel="nofollow">http://www.math.niu.edu/~rusin/uses-math/music/12</a> Why 12 tones per octave?], Dave Rusin. Sequence <tt>OEIS2C|A117536</tt> ''Increasingly large peaks of the Riemann zeta function on the critical line'' and <tt>OEIS2C|A117538</tt> ''Increasingly large integrals of the Z function between zeros'', <a class="wiki_link" href="/On-Line%20Encyclopedia%20of%20Integer%20Sequences">On-Line Encyclopedia of Integer Sequences</a>.</li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <tt>citation|first1=Christian U.|last1=Jensen|first2=Arne|last2=Ledet|first3=Noriko|last3=Yui|title=Generic Polynomials: Constructive Aspects of the Inverse Galois Problem|publisher=Cambridge University Press|location=Cambridge|year=2002|isbn=0-521-81998-9|url=<a class="wiki_link_ext" href="http://www.msri.org/communications/books/Book45/files/book45.pdf" rel="nofollow">http://www.msri.org/communications/books/Book45/files/book45.pdf</a></tt>.</li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> [<a class="wiki_link_ext" href="http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html" rel="nofollow">http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html</a> The Amdahl Six].</li> </ol><!-- ws:end:WikiTextReferencesRule:86 --></body></html>