2007/11/12 by Alissa S. Crans, Thomas M. Fiore, Crans, Alissa S. +3 · 3 citations
Arts and Humanities · Computer Science · Mathematics · Neuroscience · #00A08 #20-01 (Primary) #55-01 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Music Technology and Sound Studies #Musicology and Musical Analysis #Neuroscience and Music Perception #math.AT #math.GR #msc:00A08 #msc:20-01 #msc:55-01
paper · pdf · doi:10.48550/arxiv.0711.1873
27 pages, 11 figures. To appear in the American Mathematical Monthly.
openalex publication_date 2007/11/12 · arxiv created 2008/06/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.