In time & out of tune: Some perspectives on consonance and dissonance Both of us -- a mathematician and a music theorist -- bridle when we hear someone say "music is all mathematics," but we also know that music has many mathematical secrets. Math is essential to the problem of tuning musical instruments, and helps explain which combinations of musical notes are consonant and which are dissonant. But does this determine what sounds good and what doesn't? The answer -- yes and no -- involves prime numbers, hairy ears, a brain evolved for language, and why you shouldn't pick a fight with someone who plays the kettledrum.
Thomas A. Ivey
Tom Ivey grew up in Port Dover, Ontario, graduated from Waterloo with a BMath in 1987, and obtained his PhD in mathematics from Duke University in 1992. His research concerns the connections between geometry and applied mathematics, including completely integrable systems of differential equations. Together with JM Landsberg, in 2003 he published Cartan for Beginners, a widely used reference on exterior differential systems, and has contributed to a series of monographs on the Ricci flow. Since 2000, Ivey has taught at the College of Charleston in South Carolina. He enjoys classical music, cats, and Sacred Harp singing.
Ian Quinn is Professor of Music and Cognitive Science at Yale University. His work addresses questions about whether music theory can be put on an empirical, quantitative footing. Mathematical modelling of musical concepts, computational modelling of musical repertories, and laboratory studies of human musical behaviour form a central part of this investigation. His other interests include the music of György Ligeti, Protestant folk hymnody, and musical
St. Jerome's University
University of Waterloo, Faculty of Arts
Mathematics Endowment Fund