Auditory neuroscience has not tapped fMRI's full potential because of acoustic scanner noise emitted by the gradient switches of conventional echoplanar fMRI sequences. The scanner noise is pulsed, and auditory cortex is particularly sensitive to pulsed sounds. Current fMRI approaches to avoid stimulus-noise interactions are temporally inefficient. Since the sustained BOLD response to pulsed sounds decreases with repetition rate and becomes minimal with unpulsed sounds, we developed an fMRI sequence emitting continuous rather than pulsed gradient sound by implementing a novel quasi-continuous gradient switch pattern. Compared to conventional fMRI, continuous-sound fMRI reduced auditory cortex BOLD baseline and increased BOLD amplitude with graded sound stimuli, short sound events, and sounds as complex as orchestra music with preserved temporal resolution. Response in subcortical auditory nuclei was enhanced, but not the response to light in visual cortex. Finally, tonotopic mapping using continuous-sound fMRI demonstrates that enhanced functional signal-to-noise in BOLD response translates into improved spatial separability of specific sound representations.