Wednesday, November 17th, 2010
3:00pm - 4:00pm, in Science 2-064

Matthew Lehman

Rhythm Partitions and Fibonacci Numbers (Part 1): Definitions and ur-Rhythms

Abstract: In the first of this prospective colloquium series, we’ll explore the construct of a mathematical “rhythm”, which simply consists of a string of the three elements, {0, 1, -}, along with a rule for {-} placement. We’ll first see how the concept was initially developed to answer a specific problem in modeling musical rhythms. In its generalization, we’ll find an elegant connection between these rhythms and a class of Fibonacci numbers. Generalizing further, we’ll explore a larger class of objects called “ur-rhythms”, of which standard rhythms are a specific case. After classifying all isomorphic ur-rhythms, we’ll attempt to determine whether “anti-rhythms” exist, corresponding to the complimentary class of Fibonacci numbers and the probability a random ur-rhythm is a standard rhythm.