The Musical Canon Inside Differential Equations

Donald Spector
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 323–330 Regular Papers


A musical canon contains two or more lines of music, each playing the same basic melody, but with their starting points shifted. Surprisingly, exactly this same structure emerges among an interesting set of differential equations (including some that are important for physics) that exhibit the property known as shape invariance. In this paper, I demonstrate the parallelism of these structures.