Abstract compositional spaces have long been used to illustrate structural relationships within and between musical works. However, despite robust scholarship employing spaces to depict the possibilities available to composers, space-based analytical methods have rarely been used to study the performance of music. Through case studies drawn from improvised and notated music, this article introduces the questions and methodologies by which analogous spaces for performance, which the author terms performance spaces, may be generated and analyzed. The author also considers the unique properties of hybrid spaces that combine the tools of discrete mathematics, such as graphs, with distance-based metrics.

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