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Musicians ubiquitously apply spatial metaphors when describing the stability hierarchy established by tonal syntax: stable tones are considered spatially central and, as gravitational foci, spatially lower. We investigated whether listeners, musicians and non-musicians, indeed associate tonal relationships with visuospatial dimensions, including spatial height, centrality, laterality, and size, and whether such mappings are consistent with tonal discourse. We examined explicit and implicit associations. In the explicit paradigm, participants heard a tonality-establishing prime followed by a probe tone and coupled each probe with a subjectively appropriate location on a two-dimensional grid (Exp. 1) or with one of 7 circles differing in 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 (Exp. 3) and object 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 the hypotheses implied by musical discourse, stable tones were associated with leftward and higher spatial positions, relative to unstable tones, rather than with central and 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, results suggest that abstract syntactical relationships may consistently map onto concrete perceptual dimensions across modalities, demonstrating a new type of cross-modal correspondence and a hitherto under-researched connotative function of musical structure.