Joint Mathematics and Music Colloquium

Noam D. Elkies

Harvard University

Canonical forms: A mathematician's view of musical canons

Monday, February 19, 4pm, Swords 359

Musical canons, from simple rounds like Three Blind Mice to the compendium of canons Bach compiled in his Musical Offering, have a history almost as long as that of Western music itself, and continue to fascinate musical composers, performers and listeners. In a canon the same melody is played or sung in two or more parts at once; this melody must therefore make musical sense both as a tune and in harmony with a delayed or otherwise modified copy of itself. How does one go about constructing such a melody? This challenge has a mathematical flavor. It turns out that some kinds of canons are so easy to create that they can be improvised in real time, while other kinds are more demanding, and in some cases only a handful of examples are known. The talk will be illustrated with both abstract diagrams and specific musical examples, and may also digress into generalizations of canons (the forms known collectively as "invertible counterpoint") and the reasons -- besides showing off -- that so many composers incorporate canons into their music.

Sponsored by the Departments of Mathematics/Computer Science and Music