Mathematical and Computational Modeling of Tonality: Theory and Applications

This proposed addition to the ISOR series is perhaps the most novel application of OR techniques ever conceived: the mathematical and computational modeling of tonality. This is the first book ever to apply problem-solving computational analysis to the realm of music, and author Elaine Chew is the one person in the world bringing together the mathematical and computational in a sharply focused coherent text/reference book. An accomplished scholar, pianist, and instructor (OR) at the Viterbi School of Engineering, USC, Chew has also just completed a year-long Fellowship at the Harvard University Radcliffe Institute of Advanced Studies. She is also the inventor of the Spiral Array algorithm for the study of tonality, and that is the cornerstone of her proposed book.

Taking interior point optimization methods far beyond the more traditional engineering, financial and logistics arenas, Chew applies OR techniques to the computational analysis of music, technological requirements for digital music storage and retrieval, and the study of human traits inherent in composition, performance, hearing, and analysis. Chew shows how the Spiral Array algorithm can be used in tonal analysis and solutions to music cognition phenomena. Individual sections of the book first introduce the notion of computational modeling of cognition of music structures, and then present the geometric models of tonality, including the Spiral Array, and then look at applications to specific areas like key finding; interactive visual analysis of tonal patterns; audio key finding; and segmentation and similarity assessment.

Anyone involved in research in any of these areas will likely know of Chew’s work, and will very likely want this book handy. The research and advances are applicable to a broad range of study, from digital storage and retrieval through human cognition and understanding of musical structure and form.