Article
Musical Actions of Dihedral Groups
The American Mathematical Monthly
Document Type
Article - post-print
Publication Date
1-1-2008
Disciplines
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 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.
Original Publication Citation
Crans, A.; Fiore, T.; and Satyendra, R. “Musical Actions of Dihedral Groups.” The American Mathematical Monthly, Vol. 116 (2009), No. 6: 479 – 495.
Citation Information
Alissa S. Crans, Thomas M. Fiore and Ramon Satyendra. "Musical Actions of Dihedral Groups" The American Mathematical Monthly (2008) Available at: http://works.bepress.com/alissa_crans/5/
This is the post-print version of the article.