Increasing evidence has uncovered associations between the cognition of abstract schemas and spatial perception. Here we examine such associations for Western musical syntax, tonality. Spatial metaphors are ubiquitous when describing tonality: stable, closural tones are considered to be spatially central and, as gravitational foci, spatially lower. We investigated whether listeners, musicians and nonmusicians, indeed associate tonal relationships with visuospatial dimensions, including spatial height, centrality, laterality, and size, implicitly or explicitly, and whether such mappings are consistent with established metaphors. In the explicit paradigm, participants heard a tonality-establishing prime followed by a probe tone and coupled each probe with a subjectively appropriate location (Exp.1) or size (Exp.4). The implicit paradigm used a version of the Implicit Association Test to examine associations of tonal stability with vertical position (Exp.2), lateral position (Exp3) and size (Exp.5). Tonal stability was indeed associated with perceived physical space: the spatial distances between the locations associated with different scale-degrees significantly correlated with the tonal stability differences between these scale-degrees. However, inconsistently with musical discourse, stable tones were associated with leftward (instead of central) and higher (instead of lower) spatial positions. We speculate that these mappings are influenced by emotion, embodying the “good is up” metaphor, and by the spatial structure of music keyboards. Taken together, the results demonstrate a new type of cross-modal correspondence and a hitherto under-researched connotative function of musical structure. Importantly, the results suggest that the spatial mappings of an abstract domain may be independent of the spatial metaphors used to describe that domain.