Speaker: Alissa Crans, Loyola Marymount University (Los Angeles)

Title: Musical Actions of Dihedral Groups

Abstract: Can we hear an action of a group? Or a centralizer? In the same way it is possible to see group structure in a crystal, it is also possible to hear group structure in music.  We will investigate two ways that the dihedral group of order 24 acts on the set of major and minor chords and illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as that of Beethoven and the Beatles.  (This is joint work with Thomas M. Fiore and Ramon Satyendra.)

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