Gene Ward Smith: Difference between revisions
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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:clumma|clumma]] and made on <tt>2011-08-13 15: | : This revision was by author [[User:clumma|clumma]] and made on <tt>2011-08-13 15:19:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>245784279</tt>.<br> | ||
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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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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 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 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> | 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>OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538</ref> | ||
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 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> | 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 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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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 /> | 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 /> | ||
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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 /> | 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;OEIS. 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;OEIS. 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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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 hexagonal lattice 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:26: --><hr class="references" /><ol class="references"> | 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 hexagonal lattice 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:26: --><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> 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-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> OEIS. 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-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> OEIS. 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> | ||
</ol><!-- ws:end:WikiTextReferencesRule:26 --></body></html></pre></div> | </ol><!-- ws:end:WikiTextReferencesRule:26 --></body></html></pre></div> | ||
Revision as of 15:19, 13 August 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author clumma and made on 2011-08-13 15:19:23 UTC.
- The original revision id was 245784279.
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**Gene Ward Smith** (b. 1947) is a mathematician, music theorist, and composer. 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 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>OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538</ref> 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 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]].
Original HTML content:
<html><head><title>Gene Ward Smith</title></head><body><strong>Gene Ward Smith</strong> (b. 1947) is a mathematician, music theorist, and composer.<br /> <br /> 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 /> 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:&lt;ref&gt;Rusin, Dave. &quot;Why 12 tones per octave?&quot; http://www.math.niu.edu/~rusin/uses-math/music/12&lt;/ref&gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:1 --><!-- ws:start:WikiTextRefRule:3:&lt;ref&gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&lt;/ref&gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:3 --><!-- ws:start:WikiTextRefRule:5:&lt;ref&gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&lt;/ref&gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:5 --><br /> <br /> 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 hexagonal lattice 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:26: --><hr class="references" /><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> Rusin, Dave. "Why 12 tones per octave?" <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-2"><a href="#cite_ref-2">^</a> OEIS. 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-3"><a href="#cite_ref-3">^</a> OEIS. 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> </ol><!-- ws:end:WikiTextReferencesRule:26 --></body></html>