Abstract:The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group S 3 . The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. The left action of S 3 on the Tonnetz gives rise to interesting chord sequences. We compare the system of transformations in S 3 with the system of Schritte and Wechsel introduced by Hugo Riemann in 1880. Finally, we consider the point reflection group as it captures well… Show more
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