Cyclic arrays, such as clock faces, have advantages over linear arrays for conceptualizing repetitive rhythmic structures. The author maps rhythms from African and Indonesian musics into cyclic arrays and analyzes them using concepts from Gestalt psychology, mathematical group theory and psycho-acoustics. The perceptual structures thus revealed exist between the different musical parts played on various instruments and contradict the usual processes of auditory segregation according to the physical locations of instrumentation. This prompts a proposal for a theory of musical despatialization to explain the psychological efficacy of these rhythms.