P7-10: Polar Manhattan Displacement: Measuring Tonal Distances Between Chords Based on Intervallic Content
Jeffrey K Miller (Queen Mary University of London)*, Johan Pauwels (Queen Mary University of London), Mark B Sandler (Queen Mary University of London)
Subjects (starting with primary): Knowledge-driven approaches to MIR -> representations of music ; MIR fundamentals and methodology -> symbolic music processing ; Knowledge-driven approaches to MIR -> computational music theory and musicology ; MIR tasks -> similarity metrics ; Computational musicology -> mathematical music theory ; Musical features and properties -> harmony, chords and tonality
Presented In Person: 4-minute short-format presentation
Large-scale studies of musical harmony are often hampered by lack of suitably labelled data. It would be highly advantageous if an algorithm were able to autonomously describe chords, scales, etc. in a consistent and musically informative way. In this paper, we revisit tonal interval vectors (TIVs), which reveal certain insights as to the interval and tonal nature of pitch class sets. We then describe the qualities and criteria required to comprehensively and consistently measure displacements between TIVs. Next, we present the Polar Manhattan Displacement (PMD), a compound magnitude and phase measure for describing the displacements between pitch class sets in a tonally-informed manner. We end by providing examples of how PMD can be used in automated harmonic sequence analysis over a complex chord vocabulary.
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