Cognitive, computational, analytical, and theoretical approaches to musical rhythm can benefit greatly from signal analysis tools. This talk will explore the implications of thinking of rhythm in terms of frequency—i.e., applying Fourier transforms. Traditional theory of rhythm starts from concepts of meter grounded in European musical notation, which involves some frequency-based thinking insofar as metrical levels correspond to frequencies. However, unlike traditional meter theory, a signal-analysis approach is not restricted to discrete functions of time and hierarchically related metrical levels. The cognitive constructs typically associated with meter, sensorimotor synchronization and entrainment, are also time-continuous. Because theorists tend to equate entrainment and meter, entrainment is often assumed to be hierarchical, but there are reasons to question this assumption that have not been fully explored in the cognitive literature. In particular, the prevalence of a variety of maximally even rhythms in disparate non-Euroclassical musical traditions suggests that humans respond to rhythmic frequencies that do not fit into traditional metrical hierarchies. Fourier analysis of some rhythms commonly found in West African drum ensembles, Latin American music, Arabic traditional music, Indonesian Gamelan, and American popular music illustrate this. Fourier-based tools, rhythm spectra and coefficient spaces, also benefit from being very computationally tractable, which I will illustrate with corpus analysis of ragtime melodies and Arabic traditional rhythms, and a computational analysis of a transcription of an Adowa master drum performance. I will also define and illustrate a property called coherence derived from products of different Fourier coefficients, and show some patterns in the coherence values of the ragtime and Adowa data.

Speaker Info:

Jason Yust is Associate Professor of Music and Director of Graduate Studies at Boston University. He earned his BA in Music at Brown University and his PhD in Music Theory at the University of Washington in 2006 under the direction of John Rahn. He is the current co-Editor-in-Chief of the Journal of Mathematics and Music, an associate editor of Perspectives of New Music.

Jason Yust's research applies mathematics to topics in music theory, music analysis, and music cognition, and he is interested in how theorists, composers, and listeners conceptualise harmonic and rhythmic spaces and structures.