Gene Ward Smith: Difference between revisions

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In mathematics, he worked in the areas of [[Wikipedia:Galois theory|Galois theory]] and [[Wikipedia:Monstrous moonshine|Moonshine theory]].

In music theory, he introduced [[Wikipedia:Exterior_algebra|wedge products]] as a way of classifying [[Regular_Temperaments|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 [[Wikipedia:Grassmannian|Grassmannian]]. He had long drawn attention to the relationship between [[~~Equal_Temperaments~~|equal divisions of the octave]] and the [[~~The_Riemann_Zeta_Function_and_Tuning~~|Riemann zeta function]].<ref>Rusin, Dave. "Why 12 tones per octave?" [http://www.math.niu.edu/~rusin/uses-math/music/12 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: {{OEIS|A117536}}.</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros: {{OEIS|A117538}}.</ref> He [http://www.webcitation.org/67ZUSajSK early on] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[Regular temperament|regular mapping paradigm]].

In music theory, he introduced [[Wikipedia:Exterior_algebra|wedge products]] as a way of classifying [[Regular_Temperaments|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 [[Wikipedia:Grassmannian|Grassmannian]]. He had long drawn attention to the relationship between [[Equal temperaments|equal divisions of the octave]] and the [[the Riemann zeta function and tuning|Riemann zeta function]].<ref>Rusin, Dave. "Why 12 tones per octave?" [http://www.math.niu.edu/~rusin/uses-math/music/12 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: {{OEIS|A117536}}.</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros: {{OEIS|A117538}}.</ref> He [http://www.webcitation.org/67ZUSajSK early on] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[Regular temperament|regular mapping paradigm]].

In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[Wikipedia:crystal oscillator|crystal oscillator]]. The device in turn was controlled by [[Wikipedia:HP 9800 series desktop computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].

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 In mathematics, he worked in the areas of [[Wikipedia:Galois theory|Galois theory]] and [[Wikipedia:Monstrous moonshine|Moonshine theory]].
-In music theory, he introduced [[Wikipedia:Exterior_algebra|wedge products]] as a way of classifying [[Regular_Temperaments|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 [[Wikipedia:Grassmannian|Grassmannian]].  He had long drawn attention to the relationship between [[Equal_Temperaments|equal divisions of the octave]] and the [[The_Riemann_Zeta_Function_and_Tuning|Riemann zeta function]].<ref>Rusin, Dave. "Why 12 tones per octave?" [http://www.math.niu.edu/~rusin/uses-math/music/12 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: {{OEIS|A117536}}.</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros: {{OEIS|A117538}}.</ref> He [http://www.webcitation.org/67ZUSajSK early on] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[Regular temperament|regular mapping paradigm]].
+In music theory, he introduced [[Wikipedia:Exterior_algebra|wedge products]] as a way of classifying [[Regular_Temperaments|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 [[Wikipedia:Grassmannian|Grassmannian]].  He had long drawn attention to the relationship between [[Equal temperaments|equal divisions of the octave]] and the [[the Riemann zeta function and tuning|Riemann zeta function]].<ref>Rusin, Dave. "Why 12 tones per octave?" [http://www.math.niu.edu/~rusin/uses-math/music/12 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: {{OEIS|A117536}}.</ref><ref>OEIS. Increasingly large integrals of the Z function between zeros: {{OEIS|A117538}}.</ref> He [http://www.webcitation.org/67ZUSajSK early on] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[Regular temperament|regular mapping paradigm]].
 In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[Wikipedia:crystal oscillator|crystal oscillator]]. The device in turn was controlled by [[Wikipedia:HP 9800 series desktop computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].