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Cycle is a software tool for musical composition and improvisation that represents events along a circular timeline. In doing so, it breaks from the linear representational conventions of European Art music and modern Digital Audio Workstations. A user specifies time points on different layers, each of which corresponds to a particular sound. The layers are superimposed on a single circle, which allows a unique visual perspective on the relationships between musical voices given their geometric locations. Positions inbetween quantizations are possible, which encourages experimentation with expressive timing and machine rhythms. User-selected transformations affect groups of notes, layers, and the pattern as a whole. Past and future states are also represented, synthesizing linear and cyclical notions of time. This paper will contemplate philosophical questions raised by circular rhythmic notation and will reflect on the ways in which the representational novelties and editing functions of Cycle have inspired creativity in musical composition.