Gene Ward Smith

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Gene Ward Smith (born 1947) is an American mathematician, composer and music theorist. In mathematics he has worked in the areas of Galois theory and Moonshine theory. As a composer, he is noted for pioneering many different tuning systems. In music theory, he is noted for a number of ideas and innovations in the theory of musical tuning, such as the introduction of multilinear algebra. A boyhood friend of Steven Spielberg, a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride.

Contents 1 Music theory 2 Mathematics 3 External links 4 Bibliography

[edit] Music theory

Smith introduced wedge products as a way of classifying regular temperaments, and of dealing with the problem of 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 divisions of the octave and the Riemann zeta function, which may be explored in the links to the On-Line Encyclopedia of Integer Sequences.

Smith was among the first to consider extending the Tonnetz of Hugo Riemann beyond the 5-limit and hence into higher dimensionsional lattices. In three dimensions, the hexagonal lattice of 5-limit harmony extends to a lattice of type A₃ ~ D₃.

[edit] Mathematics

In mathematics, Smith's most notable achievement is the construction of what has been called the Smith generic cyclic polynomial. 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 prime to n. This can then be extended to metacyclic extensions, such as dihedral groups.

Smith was also a member of the Amdahl Six group which held the largest prime record from 1989-1992.

[edit] External links

• Smith's music site
• Smith's compositions
• The Amdahl Six
• Increasingly large peaks of the Riemann zeta function on the critical line
• Increasingly large integrals of the Z function between zeros

[edit] Bibliography

Joseph McBride, Steven Spielberg: A Biography, Da Capo Press April 1999, ISBN 0-306-80900-1

Christian U. Jensen, Arne Ledet, and Noriko Yui, Generic Polynomials: Constructive Aspects of the Inverse Galois Problem, Cambridge University Press, Cambridge, 2002, ISBN 0-521-81998-9[1]