This paper presents a psychoacoustically based method of data reduction motivated by the desire to analyze the rhythm of musical performances. The resulting information is then analyzed by the “Periodicity Transform” (which is based on a projection onto “periodic subspaces”) to locate periodicities in the resulting data. These periodicities represent the rhythm at several levels, including the “pulse”, the “measure”, and larger structures such as musical “phrases.” The implications (and limitations ) of such automated grouping of rhythmic features is discussed. The method is applied to a number of musical examples, its output is compared to that of the Fourier Transform, and both are compared to a more traditional “musical” analysis of the rhythm. Unlike many methods of rhythm analysis, the techniques can be applied directly to the digitized performance (i.e., a soundfile) and do not require a musical score or a MIDI transcription. Several examples are presented that highlight both the strengths and weaknesses of the approach.