Pitch space and Riemannian space offer divergent perspectives on tonal space in general. This article suggests that cognitive metaphor theory offers a means of understanding Riemannian space as a metaphorical mapping from pitch space; as an extension from a “deontic” to an “epistemic” musical category. My approach differs from other theorists of musical metaphor in considering mappings not between musical structure and extra-musical “real” space, but rather mappings between musical categories themselves. I illustrate this claim by reviewing recent writings both on pitch-space and Neo-Riemannian theory, and an analytical example by Chopin.
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