A graph-theoretical approach for pattern matching in post-tonal music analysis

Abstract

A graph-theoretical approach is proposed to facilitate pattern matching in post-tonal music analysis with pitchclass set theory, in which music perception is taken into account by incorporating stream segregation -a model of the perceptual organization of music. A piece of music is modelled as a graph, with each musical note presented as a vertex and the relationship between a pair of musical notes as an edge. The relationship is determined by stream segregation. According to the proposed matching conditions, searching for a musical pattern is equivalent to searching for a special subgraph called a maximal matched CRP subgraph. The comparisons are made between the patterns identified by the graph-theoretical approach and those by the musicologists.

Finding Repeated Patterns in Music: State of Knowledge, Challenges, Perspectives

“…For available reference data, several researchers evaluate the discovered patterns quantitatively by counting the number of agreements between algorithm and reference data [10,33,35,43].…”

“…Next to Collins et al [10], who introduced improvements of Meredith's Structure Induction Algorithms, we also place the studies by Buteau and Vipperman [4] and Szeto and Wong [43] in the category of geometric approaches, as both studies also use a notion of musical patterns as shapes. Szeto and Wong represent these geometric relationships as graphs [43].…”