This paper presents an overview of the epistemological grounding of the computational approach to musical syntax as a tool to advance our understanding of the cognitive underpinnings of the musical experience. From the proposed perspective, formulations of music-theoretical and analytical thinking in formal terms can be read as hypotheses on the output of computational models at different levels of description. Computational models, in turn, make it possible to derive testable predictions on observable behaviours that are available for empirical investigation. The deep connection linking music-theoretical and computational thinking is illustrated with examples drawn from analytic accounts of tonal harmonic syntax.