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