2008/04/17 by Clifton Callender, Ian Quinn, Dmitri Tymoczko · 2 citations
Neuroscience · Computer Science · Arts and Humanities · Mathematics · #Neuroscience and Music Perception #Music and Audio Processing #Musicology and Musical Analysis #Chord (peer-to-peer) #Equivalence relation #Equivalence class (music) #Quotient #Mathematics #Inversion (geology) #Cardinality (data modeling) #Equivalence (formal languages) #Embedding #Pure mathematics #Computer science #Artificial intelligence #Data mining
paper · doi:10.1126/science.1153021
openalex publication_date 2008/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord sequences are represented. This model reveals connections between music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations, and suggests a way to understand similarity between chord types.