Musical Actions of Dihedral Groups

Details Musical Actions of Dihedral Groups Musical Actions of Dihedral Groups

2007-11-12

arxiv.org/abs/0711.1873v2

Mathematics

Group Theory

27 pages, 11 figures. To appear in the American Mathematical Monthly.

Scientific paper

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

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