Musical Actions of Dihedral Groups

Authors: Crans, Alissa S.; Fiore, Thomas M.; Satyendra, Ramon

Source: American Mathematical Monthly, Volume 116, Number 6, June-July 2009 , pp. 479-495(17)

Publisher: Mathematical Association of America

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Abstract:

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 triads. 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.

Document Type: Research article

DOI: http://dx.doi.org/10.4169/193009709X470399

Publication date: 2009-06-01

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American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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