The term “prosody” encompasses properties of speech that span several timescales and levels of linguistic units, from the intensity and pitch of phonemes and syllables to the overall timing and intonation of utterances and conversations. Hierarchical temporal structure was introduced as a measure of clustering in sound energy that quantifies the relationship among timescales of prosody and related aspects of speech and music. The present chapter reviews several studies showing that the degree of hierarchical temporal structure in speech signals, as measured by the rate of increase in clustering with timescale, reflects the degree of prosodic composition. Prosodic composition can serve different purposes in communication, including linguistic emphasis and chunking in infant-directed speech, scaffolding of spoken interactions with children whose speech abilities are relatively less developed, and stricter timing in formal interactions. Prosodic composition as expressed by hierarchical temporal structure may serve as a control parameter in speech production and communication.

Brain rhythms at different timescales are observed ubiquitously across cortex. Despite this ubiquitousness, individual brain areas can be characterized by "spectral profiles," which reflect distinct patterns of endogenous brain rhythms. Crucially, endogenous brain rhythms have often been explicitly or implicitly related to perceptual and cognitive functions. Regarding language, a vast amount of research investigates the role of brain rhythms for speech processing. Particularly, lower-level processes, such as speech segmentation and consecutive syllable encoding and the hemispheric lateralization of such processes, have been related to auditory cortex brain rhythms in the theta and gamma range and explained by neural oscillatory models. Other brain rhythms – particularly delta and beta – have been related to prosodic processing (delta) but also higher-level language processing, including phrasal and sentential processing. Delta and beta brain rhythms have also been related to predictions from the motor cortex, emphasizing the tight link between production and perception. More recently, neural oscillatory models were extended to include different levels of language processing.