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Many previous studies have shown that a tone that is momentarily -interrupted can be perceived as continuous if the interruption is completely masked by noise. It has been suggested this "continuity illusion" occurs only when peripheral neural responses contain no evidence that the signal was interrupted. In this study, we used a combination of psychophysical measures and computational simulations of peripheral auditory responses to examine whether the continuity illusion can be experienced under conditions where peripheral neural responses contain evidence that the signal did not continue through the masker. Our results provide an example of a salient continuity illusion despite evidence of an interruption in the peripheral representation, indicating that the illusion may depend more on global features of the interrupting sound, such as its long-term specific loudness, than on its fine-grained temporal structure.