Diálogos entre Matemáticas y Cultura: Surface topology in the canons of J. S. Bach.

Semblanza: Investigador de la Universidad de Stony Brook en Nueva York. 

Abstract: A canon is a musical form in which one voice imitates another after a delay, and the whole composition repeats as often as desired.  Besides the "horizontal" translation in time, other symmetries can come into play; these include a shift in pitch, i.e. a "vertical" translation, and inversion (reflection in a horizontal axis). J. S. Bach used these symmetries, among others, in constructing canons, most notably in the Musical Offering and in a set of canons on the beginning of the bass line of the Goldberg Variations, BWV 1087. The symmetries imply that the musical score for one of these canons is not just a 2-dimensional loop, but has a richer topology: it can embody a Möbius band or a torus.