Functional specialization is a hallmark of information processing in the brain and ranges from locally very circumscribed neural populations to whole brain regions or hemispheres (Tononi and Sporns 2003; Friston 2002). For example, speech perception and comprehension involve a widespread bilateral network whose components fulfill different functions related to, for example, the acoustics, phonology, semantics, syntax, or pragmatics of spoken language (Price 2012). Similarly, different features of acoustic stimuli (like temporal or spectral information) are preferentially processed by different hemispheres (Poeppel 2003; Zatorre et al. 2002; Flinker et al. 2019). However, because the goal of an organism is to produce behaviors and percepts that allow it to successfully navigate its environment (acoustic or otherwise), the outputs that are generated by these different components need to be integrated. The question of how the brain processes and integrates information to achieve coherent and unified percepts is relevant across many domains, but it is particularly urgent in the case of auditory and speech perception where it remains largely unexplored. The current study aims to further our understanding thereof.