By Fourier's theorem, signals can be decomposed into a sum of sinusoids of different frequencies. This is especially relevant for hearing, because the inner ear performs a form of mechanical Fourier transform by mapping frequencies along the length of the cochlear partition. An alternative signal decomposition, originated by Hilbert, is to factor a signal into the product of a slowly varying envelope and a rapidly varying fine time structure. Neurons in the auditory brainstem sensitive to these features have been found in mammalian physiological studies. To investigate the relative perceptual importance of envelope and fine structure, we synthesized stimuli that we call 'auditory chimaeras', which have the envelope of one sound and the fine structure of another. Here we show that the envelope is most important for speech reception, and the fine structure is most important for pitch perception and sound localization. When the two features are in conflict, the sound of speech is heard at a location determined by the fine structure, but the words are identified according to the envelope. This finding reveals a possible acoustic basis for the hypothesized 'what' and 'where' pathways in the auditory cortex.