This paper investigates bounds on the generative capacity of prosodic processes, by focusing on the complexity of recursive prosody in coordination contexts in English (Wagner, 2010). Although all phonological processes and most prosodic processes are computationally regular string languages, we show that recursive prosody is not. The output string language is instead parallel multiple context-free (Seki et al., 1991). We evaluate the complexity of the pattern over strings, and then move on to a characterization over trees that requires the expressivity of multi bottom-up tree transducers. In doing so, we provide a foundation for future mathematically grounded investigations of the syntax-prosody interface.