Delayed auditory feedback (DAF) impairs performance in speech, music performance, and tapping, with maximal impairment in speech occurring at a delay near 200 ms. This ``critical interval" has played a central role in most explanations of the DAF effect, including both closed-loop feedback explanations and alternative proposals. We investigated the nature of the critical interval for rhythmic tapping, in particular, whether the critical interval has a constant value or is dependent on performance rate. Three experiments using a synchronization-continuation paradigm consistently showed that the critical interval shifted with different tapping rates, with maximal impairment occurring when the delay approximately equaled the tapping rate. We address the implications of these results for existing theories of DAF, and suggest a promising new direction for an explanation.