Visualizing and sonifying mathematical music theory with software applications : implications of computer-based models for practice and education

This chapter discusses what software applications offer to the practice of mathematical music theory and, more broadly, to music education. Traditionally, mathematical music theory uses the formalisms of mathematics (such as equations and graphs) to represent and produce models of musical phenomena that serve explanatory, predictive, or generative purposes. By contrast, computer-based models use interactive elements to represent and model musical phenomena within a software environment. These two approaches support quite distinct working, thinking, and learning. The former entails process, constrained by step-wise workings and ways of a slow analytic calculations, and the latter allows for faster and more intuitive experimentation and hypothesis testing. While for most learners, learning to model musical phenomena in purely mathematical terms is cumbersome and challenging, well-designed software may enable such model-based learning to become more accessible and fluent. Thus, we argue that software can uniquely help visualize and sonify challenging concepts in mathematical music theory, helping students learn them more intuitively, and in ways that are more likely to support transfer to real musical situations.