Music as Embodied Mathematics: A Study of a Mutually Informing Affinity

The argument examined in this paper is that music—when approached through making and responding to coherent musical structures and facilitated by multiple, intuitively accessible representations—can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students’ inquiry into the bases for their perceptions of musical coherence provides a path into the mathematics of ratio, proportion, fractions, and common multiples. In a similar manner, we conjecture that other topics in mathematics—patterns of change, transformations and invariants—might also expose, illuminate and account for more general organizing structures in music. Drawing on experience with 11-12 year old students working in a software music/math environment, we illustrate the role of multiple representations, multimedia, and the use of multiple sensory modalities in eliciting and developing students’ initially implicit knowledge of music and its inherent mathematics. “Music is the arithmetic of the soul, which counts without being aware of it.” --Leibnitz-INTRODUCTION Interest in the mutual affinities between music and mathematics has had a long history—Plato, Aristotle, Pythagoras, Leibnitz, and more recently Hofstadter (1979), Rothstein (1995), Lerdahl and Jackendoff (1983), Tanay (1998), and others. But unlike these carefully crafted and in some cases formal theories, the connections we discuss are empirical and “cognitively real” in the sense that they seem naturally embedded in the structures that generate the perception and invention of musical coherence. These functional connections initially came to the surface as college students reflected on their own creative processes during composition projects