This article demonstrates how to obtain a periodicity-based description of cyclic rhythms using the discrete Fourier transform and applies this to understanding Steve Reich's use of rhythmic canons in a series of works from the early 1970s through the 1990s. The primary analytical tool is the rhythmic spectrum, which omits phase information, but the use of plots that include phase information is also demonstrated in a few instances. The method shows a consistency in Reich's rhythmic language despite experimentations with irregular cycles, which begins with the formulation of his “signature rhythm,” the basic rhythmic pattern of Clapping Music and Music for Pieces of Wood. The article also demonstrates the evolution of Reich's rhythmic experimentation preceding these pivotal pieces, through his “phase” works of the 1960s. It discusses the relationship of the Fourier-based method and concepts of meter, especially nonisochronous meter, maximally even rhythmic patterns, and the potential of rhythmic canons to interlock and make different kinds of combinatorial patterns.