We use functional magnetic resonance imaging (fMRI) to analyze neural responses to natural auditory stimuli. We characterize the fMRI time series through the shape of the voxel power spectrum and find that the timescales of neural dynamics vary along a spatial gradient, with faster dynamics in early auditory cortex and slower dynamics in higher order brain regions. The timescale gradient is observed through the unsupervised clustering of the power spectra of individual brains, both in the presence and absence of a stimulus, and is enhanced in the stimulus-locked component that is shared across listeners. Moreover, intrinsically faster dynamics occur in areas that respond preferentially to momentary stimulus features, while the intrinsically slower dynamics occur in areas that integrate stimulus information over longer timescales. These observations connect the timescales of intrinsic neural dynamics to the timescales of information processing, suggesting a temporal