Abstract

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.

Bio: Biography: Noam D. Elkies earned his doctorate in mathematics from Harvard in 1987 under the guidance of Benedict Gross and Barry Mazur. He has been at Harvard since then; beginning as a Junior Fellow, he joined the Mathematics department in 1990 and was tenured in 1993. His work on elliptic curves, lattices and other aspects of the theory of numbers has been recognized by prizes and awards such as the Presidential Young Investigator Award of the NSF, a Packard Fellowship, and the Prix Peccot of the College de France; his expository papers won the MAA's Ford Prize and the AMS's Conant Prize.

Elkies' main interest outside mathematics is music, mainly classical composition and keyboard performance. His compositions, often but not always in styles that recognizably flow from traditional idioms, include an opera staged in 1999, and the "Brandenburg Concerto #7" premiered in 2004. Naturally there are various canons to be found in that concerto; he will try to resist the temptation of drawing on them for examples in his presentation.

Noam Elkies is also known as a chess problemist: a number of the studies and problems he composed earned awards in international contests; he won the 1996 world championship for solving chess problems, and earned the Solving Grandmaster title five years later.

FRIDAY, April 25, 2008
Time: 5:00 P.M.
Location: MM 119

Refreshments outside MM 119 at 4:30.