Rhythm and transforms, perception and mathematics

Abstract

People commonly respond to music by keeping time, tapping to the beat or swaying to the pulse. Underlying such ordinary motions is an act of perception that is not easily reproduced in a computer program or automated by machine. This paper outlines the flow of ideas in Rhythm and Transforms (Sethares 2007), which creates a device that can "tap its foot" along with the music. Such a "beat finding machine" (illustrated in Fig. 1) has implication for music theory, on the design of sound processing electronics such as musical synthesizers, on the uses of drum machines in recording and performance, and on special effects devices. The beat finder provides a concrete basis for a discussion of the relationship between the mind's processing of temporal information and the mathematical techniques used to describe and understand regularities in data. Extensive sound examples (Sethares 2008) demonstrate beatbased signal processing techniques, methods of musical (re)composition, and new kinds of musicological analysis. Fig. 1. A foot-tapping machine designed to mimic people's ability to synchronize to complex rhythmic sound must "listen" to the sound, locate the underlying rhythmic pulse, anticipate when the next beat timepoint will occur, and then provide an output © 2009 Springer-Verlag.