Whether physical navigation shares neural substrates with mental travel in other behaviourally relevant domains is debated. With respect to sound, pure tone working memory in humans elicits hippocampal as well as auditory cortical and inferior frontal activity, and rodent work suggests that hippocampal cells that usually track an animal's physical location can also map to tone frequency when task-relevant. We generated a sound dimension based on the density of random-frequency tones in a stack, resulting in a percept ranging from low- ("beepy") to high-density ("noisy"). We established that unlike tone frequency, which listeners automatically associate with vertical position, this density dimension elicited no consistent spatial mapping. During functional magnetic resonance imaging, human participants (both sexes) held in mind the density of a series of tone stacks and, after a short maintenance period, adjusted further stacks to match the target ("navigation"). Density was represented most strongly in bilateral non-primary auditory cortex, specifically bilateral planum polare. Encoding and maintenance activity in hippocampus, inferior frontal gyrus, planum polare and posterior cingulate was positively associated with subsequent navigation success. Bilateral inferior frontal gyrus and hippocampus were among regions with elevated activity during navigation, compared to a parity-judgment condition with closely matched acoustics and motor demands. Bilateral orbitofrontal cortex was more active when navigation was toward a target density than when participants adjusted density in a control condition with no particular target. We find that self-initiated travel along a non-spatial auditory dimension engages a brain system overlapping with that supporting physical navigation.