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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>2010-06-04 17:53:55 UTC</tt>.<br> | | : This revision was by author [[User:clumma|clumma]] and made on <tt>2011-08-13 15:12:43 UTC</tt>.<br> |
| : The original revision id was <tt>147075935</tt>.<br> | | : The original revision id was <tt>245783633</tt>.<br> |
| : The revision comment was: <tt></tt><br> | | : The revision comment was: <tt>Rewriting wikipedia content as appropriate for xenwiki</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> |
| <h4>Original Wikitext content:</h4> | | <h4>Original Wikitext content:</h4> |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">**Gene Ward Smith** (born 1947) is an American mathematician and music theorist. In mathematics he has worked in the areas of [[http://en.wikipedia.org/wiki/Galois_theory|Galois theory]] and [[http://en.wikipedia.org/wiki/Monstrous_moonshine|Moonshine theory]]. In music theory, he is noted for a number of innovations in the theory of musical tuning, such as the introduction of [[http://en.wikipedia.org/wiki/Multilinear_algebra|multilinear algebra]] and for being the first to write music in a number of exotic intonation systems. A boyhood friend of [[http://en.wikipedia.org/wiki/Steven_Spielberg|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 [[http://en.wikipedia.org/wiki/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 [[http://en.wikipedia.org/wiki/Usenet|Usenet]], causing them to be nicknamed the [[http://en.wikipedia.org/wiki/Brahms_Gang|Brahms Gang]] (because ''brahms.berkeley.edu'' was the name of the server they posted from). | | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">**Gene Ward Smith** (b. 1947) is a mathematician, music theorist, and composer. |
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| ==Music theory==
| | In mathematics, he has worked in the areas of [[http://en.wikipedia.org/wiki/Galois_theory|Galois theory]] and [[http://en.wikipedia.org/wiki/Monstrous_moonshine|Moonshine theory]]. |
| Smith introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge product]]s as a way of classifying [[regular temperaments]], and of dealing with the problem of [[http://en.wikipedia.org/wiki/Torsion_%28abstract_algebra%29|torsion]]. In this system, a temperament is specified by means of a ''wedgie'', which technically may be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]].
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| Smith has long been drawing attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[http://en.wikipedia.org/wiki/Riemann_zeta_function|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'', [[http://en.wikipedia.org/wiki/Online_Encyclopedia_of_Integer_Sequences|On-Line Encyclopedia of Integer Sequences]].</ref>
| | In music theory, he introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge products]] as a way of classifying [[regular temperaments]]. In this system, a temperament is specified by means of a [[Wedgies and Multivals|wedgie]], which may technically be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]]. He has long drawn attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[http://en.wikipedia.org/wiki/Riemann_zeta_function|Riemann zeta function]].<ref>Rusin, Dave "Why 12 tones per octave?" http://www.math.niu.edu/~rusin/uses-math/music/12</ref><ref>Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536</ref><ref>Increasingly large integrals of the Z function between zeros http://oeis.org/A117538</ref> |
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| Smith was among the first to consider extending the [[http://en.wikipedia.org/wiki/Tonnetz|Tonnetz]] of [[http://en.wikipedia.org/wiki/Hugo_Riemann|Hugo Riemann]] beyond the 5-limit and hence into higher dimensional [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattices]]. In three dimensions, the [[http://en.wikipedia.org/wiki/Hexagonal_lattice|hexagonal lattice]] of [[Harmonic Limit|5-limit harmony]] extends to a lattice of type A3 ~ D3.
| | Gene was among the first to consider extending the [[http://en.wikipedia.org/wiki/Tonnetz|Tonnetz]] of Hugo Riemann beyond the 5-limit and hence into higher dimensional [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattices]]. In three dimensions, the [[http://en.wikipedia.org/wiki/Hexagonal_lattice|hexagonal lattice]] of [[Harmonic Limit|5-limit harmony]] extends to a lattice of type A3 ~ D3. He is also the first to write music in a number of exotic intonation systems. See [[Microtonal Music by Gene Ward Smith]].</pre></div> |
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| ==Mathematics==
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| In mathematics, Smith's most notable achievement is the construction of what has been called the Smith [[http://en.wikipedia.org/wiki/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 [[http://en.wikipedia.org/wiki/Characteristic_%28algebra%29|characteristic (algebra)|characteristic]] prime to ''n''. This can then be extended to [[http://en.wikipedia.org/wiki/Metacyclic_group|metacyclic]] extensions, such as [[http://en.wikipedia.org/wiki/Dihedral_group|dihedral group]]s.
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| 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>
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| ==Music by Gene Ward Smith==
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| [[Microtonal Music by Gene Ward Smith]] | |
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| ==External links==
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| *[http://lumma.org/tuning/gws/home.htm Smith's old website]
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| </pre></div> | |
| <h4>Original HTML content:</h4> | | <h4>Original HTML content:</h4> |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gene Ward Smith</title></head><body><strong>Gene Ward Smith</strong> (born 1947) is an American mathematician and music theorist. In mathematics he has worked in the areas of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Galois_theory" rel="nofollow">Galois theory</a> and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monstrous_moonshine" rel="nofollow">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_ext" href="http://en.wikipedia.org/wiki/Multilinear_algebra" rel="nofollow">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_ext" href="http://en.wikipedia.org/wiki/Steven_Spielberg" rel="nofollow">Steven Spielberg</a>, a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride.<!-- ws:start:WikiTextRefRule:2:&amp;lt;ref&amp;gt;&lt;tt&gt;citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1&lt;/tt&gt;.&amp;lt;/ref&amp;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_ext" href="http://en.wikipedia.org/wiki/University_of_California,_Berkeley" rel="nofollow">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_ext" href="http://en.wikipedia.org/wiki/Usenet" rel="nofollow">Usenet</a>, causing them to be nicknamed the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Brahms_Gang" rel="nofollow">Brahms Gang</a> (because ''brahms.berkeley.edu'' was the name of the server they posted from).<br /> | | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gene Ward Smith</title></head><body><strong>Gene Ward Smith</strong> (b. 1947) is a mathematician, music theorist, and composer.<br /> |
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| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc0"><a name="x-Music theory"></a><!-- ws:end:WikiTextHeadingRule:16 -->Music theory</h2>
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| Smith introduced <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow">wedge product</a>s as a way of classifying <a class="wiki_link" href="/regular%20temperaments">regular temperaments</a>, and of dealing with the problem of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Torsion_%28abstract_algebra%29" rel="nofollow">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_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow">Grassmannian</a>.<br />
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| <br />
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| Smith has long been drawing attention to the relationship between <a class="wiki_link" href="/Equal%20Temperaments">equal divisions of the octave</a> and the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Riemann_zeta_function" rel="nofollow">Riemann zeta function</a>.<!-- ws:start:WikiTextRefRule:9:&amp;lt;ref&amp;gt;[http://www.math.niu.edu/~rusin/uses-math/music/12 Why 12 tones per octave?], Dave Rusin. Sequence &lt;tt&gt;OEIS2C|A117536&lt;/tt&gt; ''Increasingly large peaks of the Riemann zeta function on the critical line'' and &lt;tt&gt;OEIS2C|A117538&lt;/tt&gt; ''Increasingly large integrals of the Z function between zeros'', &lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Online_Encyclopedia_of_Integer_Sequences&quot; rel=&quot;nofollow&quot;&gt;On-Line Encyclopedia of Integer Sequences&lt;/a&gt;.&amp;lt;/ref&amp;gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:9 --><br />
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| Smith was among the first to consider extending the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonnetz" rel="nofollow">Tonnetz</a> of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hugo_Riemann" rel="nofollow">Hugo Riemann</a> beyond the 5-limit and hence into higher dimensional <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattices</a>. In three dimensions, the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_lattice" rel="nofollow">hexagonal lattice</a> of <a class="wiki_link" href="/Harmonic%20Limit">5-limit harmony</a> extends to a lattice of type A3 ~ D3.<br />
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| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc1"><a name="x-Mathematics"></a><!-- ws:end:WikiTextHeadingRule:18 -->Mathematics</h2>
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| In mathematics, Smith's most notable achievement is the construction of what has been called the Smith <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Generic_polynomial" rel="nofollow">generic cyclic polynomial</a>.<!-- ws:start:WikiTextRefRule:13:&amp;lt;ref&amp;gt;&lt;tt&gt;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&lt;/tt&gt;.&amp;lt;/ref&amp;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_ext" href="http://en.wikipedia.org/wiki/Characteristic_%28algebra%29" rel="nofollow">characteristic (algebra)|characteristic</a> prime to ''n''. This can then be extended to <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Metacyclic_group" rel="nofollow">metacyclic</a> extensions, such as <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Dihedral_group" rel="nofollow">dihedral group</a>s.<br />
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| Smith was also a member of the ''Amdahl Six'' group which held the largest prime record from 1989-1992.<!-- ws:start:WikiTextRefRule:15:&amp;lt;ref&amp;gt;[http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html The Amdahl Six].&amp;lt;/ref&amp;gt; --><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup><!-- ws:end:WikiTextRefRule:15 --><br />
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| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc2"><a name="x-Music by Gene Ward Smith"></a><!-- ws:end:WikiTextHeadingRule:20 -->Music by Gene Ward Smith</h2> | | In mathematics, he has worked in the areas of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Galois_theory" rel="nofollow">Galois theory</a> and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monstrous_moonshine" rel="nofollow">Moonshine theory</a>.<br /> |
| <br /> | | <br /> |
| <a class="wiki_link" href="/Microtonal%20Music%20by%20Gene%20Ward%20Smith">Microtonal Music by Gene Ward Smith</a><br /> | | In music theory, he introduced <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow">wedge products</a> as a way of classifying <a class="wiki_link" href="/regular%20temperaments">regular temperaments</a>. In this system, a temperament is specified by means of a <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, which may technically be identified as a point on a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow">Grassmannian</a>. He has long drawn attention to the relationship between <a class="wiki_link" href="/Equal%20Temperaments">equal divisions of the octave</a> and the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Riemann_zeta_function" rel="nofollow">Riemann zeta function</a>.<!-- ws:start:WikiTextRefRule:1:&amp;lt;ref&amp;gt;Rusin, Dave &amp;quot;Why 12 tones per octave?&amp;quot; http://www.math.niu.edu/~rusin/uses-math/music/12&amp;lt;/ref&amp;gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:1 --><!-- ws:start:WikiTextRefRule:3:&amp;lt;ref&amp;gt;Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&amp;lt;/ref&amp;gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:3 --><!-- ws:start:WikiTextRefRule:5:&amp;lt;ref&amp;gt;Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&amp;lt;/ref&amp;gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:5 --><br /> |
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc3"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:22 -->External links</h2> | | Gene was among the first to consider extending the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonnetz" rel="nofollow">Tonnetz</a> of Hugo Riemann beyond the 5-limit and hence into higher dimensional <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattices</a>. In three dimensions, the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_lattice" rel="nofollow">hexagonal lattice</a> of <a class="wiki_link" href="/Harmonic%20Limit">5-limit harmony</a> extends to a lattice of type A3 ~ D3. He is also the first to write music in a number of exotic intonation systems. See <a class="wiki_link" href="/Microtonal%20Music%20by%20Gene%20Ward%20Smith">Microtonal Music by Gene Ward Smith</a>.<!-- ws:start:WikiTextReferencesRule:27: --><hr class="references" /><ol class="references"> |
| *[<!-- ws:start:WikiTextUrlRule:62: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:62 --> Smith's old website]<!-- ws:start:WikiTextReferencesRule:65: --><hr class="references" /><ol class="references">
| | <li id="cite_note-1"><a href="#cite_ref-1">^</a> Rusin, Dave &quot;Why 12 tones per octave?&quot; <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></li> |
| <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> Increasingly large peaks of the Riemann zeta function on the critical line <a class="wiki_link_ext" href="http://oeis.org/A117536" rel="nofollow">http://oeis.org/A117536</a></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_ext" href="http://en.wikipedia.org/wiki/Online_Encyclopedia_of_Integer_Sequences" rel="nofollow">On-Line Encyclopedia of Integer Sequences</a>.</li>
| | <li id="cite_note-3"><a href="#cite_ref-3">^</a> Increasingly large integrals of the Z function between zeros <a class="wiki_link_ext" href="http://oeis.org/A117538" rel="nofollow">http://oeis.org/A117538</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> | | </ol><!-- ws:end:WikiTextReferencesRule:27 --></body></html></pre></div> |
| <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:65 --></body></html></pre></div> | |