Gene Ward Smith: Difference between revisions

Line 3:

In mathematics, he worked in the areas of {{w|Galois theory}} and {{w|Moonshine theory}}.

In music theory, he introduced {{w|wedge product}}s as a way of classifying [[regular temperament]]s. 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 {{w|wedge product}}s as a way of classifying [[regular temperament]]s. 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 [[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 {{w|crystal oscillator}}. The device in turn was controlled by {{w|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]].

@@ Line 3: / Line 3: @@
 In mathematics, he worked in the areas of {{w|Galois theory}} and {{w|Moonshine theory}}.
-In music theory, he introduced {{w|wedge product}}s as a way of classifying [[regular temperament]]s.  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 {{w|wedge product}}s as a way of classifying [[regular temperament]]s.  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 [[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 {{w|crystal oscillator}}. The device in turn was controlled by {{w|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]].