In arbitrating between representational and relational theories of perception, perceptual illusions—cases in which a subject’s perceptual experience diverges from the way the world really is—constitute an important battleground. The debate has, however, been dominated by discussions of visual perception. In attempting to extend the debate to audition, it is appropriate to start by considering what is thought to be a key case of auditory illusion. I consider the phenomenon of the ‘missing fundamental’, as well as examining a notion that is (...) often deployed by representationalists to explain it—namely, perceptual inference. Though it is frequently deployed as an explanatory concept by inferentialists, the notion of perceptual inference is somewhat opaque. Here, I formulate a ‘job description’ for perceptual inference, involving rule-following. I then identify two sets of cases that commonly prompt the invocation of perceptual inference: namely, cases of perceptual illusion, and cases of veridical perception where the perceptual content outstrips the information present in the stimulus. I then argue that an appeal to perceptual inference is unnecessary, in the case of the missing fundamental, for two reasons. Firstly, the missing fundamental is not, after all, a clear candidate for the ascription of inferential capacity to the auditory system: it is neither an illusion, nor is it the case that the stimulus is crucially impoverished. That is, it submits to a ‘direct’ explanation. Secondly, given the adequacy of a simpler explanation, and the difficulty between distinguishing between real rule-following and the mere appearance of it, I argue that we should avoid ascribing inferential capacity to the auditory system. I close by considering objections, and offering replies. (shrink)