Mathematics of Musical Rhythm

In this paper, we analyze the rhythmic structures of several pieces of music. We use two di®erent types of data reduction to reduce the signals, eliminating higher frequency information. Using algorithms written for MATLAB by Sethares and Staley, we identify dominant frequencies and periodicities using the capabilities of the Discrete Fourier Transform and the Periodicity Transform. While both the DFT and PT have certain di±culties, we conclude that each transform provides us with important information. We also touch on other applications of the analysis of rhythm.