This article creates transformational spaces for interpreting progressions of sets belonging to the same T/I equivalence class. Within these spaces, sets are placed in proximity based upon contextual inversion, specifically those contextual inversions that (like the familiar neo-Riemannian L, P, and R) preserve common tones. Sequential enchaining of contextual inversions will generally define simple, straight-line motions within the spaces described in this article. The musical motions of works by Webern, Schoenberg, and Stravinsky are measured against the systematic standard enshrined in the spaces, with both conformity and deviation suggesting interpretive possibilities. All appendixes for this article are available as supplementary material at

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