By use of sonification (the analogue of visualization, but with sound) based on familiar patterns of musical harmony, I set up a scheme to associate chord sequences with the steps in solving the mathematical puzzle known as the Tower of Hanoi. The aim is to obtain sonifications such that the harmonies generated produce a musical resolution coincident with the solution of the puzzle, and I present some examples in this vein. Such sonifications are of course not unique, and the intention is to select choices that are aesthetically pleasing while mapping information in a meaningful way. I close with some thoughts about the application of such methods to other mathematical puzzles, including the possibility of turning this relationship on its head, and using the solving of puzzles as a tool for composing music.