Computation in neuronal assemblies is putatively reflected in the excitatory and inhibitory cycles of activation distributed throughout the brain. In speech and language processing, coordination of these cycles resulting in phase synchronization has been argued to reflect the integration of information on different timescales (e.g., segmenting acoustics signals to phonemic and syllabic representations; Giraud & Poeppel, 2012). A natural extension of this claim is that phase synchronization functions similarly to support the inference of more abstract higher-level linguistic structures (Martin, 2016; Martin & Doumas, 2017, 2019). Hale et al. (2018) showed that syntactically-driven parsing decisions predict EEG responses in the time domain; here we ask whether phase synchronization in the form of either inter-trial phrase coherence or cross-frequency coupling between high frequency (i.e., gamma) bursts and lower-frequency carrier signals (i.e., delta, theta), changes as the linguistic structures of compositional meaning (viz., bracket completions, as denoted by the onset of words that complete phrases) accrue. We use a naturalistic story-listening EEG dataset from Hale et al. to assess the relationship between linguistic structure and phase alignment. We observe increased phase synchronization as a function of phrase counts in the delta, theta, and gamma bands, especially for function words. A more complex pattern emerged for cross-frequency coupling as phrase count changed, possibly related to the lack of a one-to-one mapping between ‘size’ of linguistic structure and frequency band – an assumption that is tacit in recent frameworks. These results emphasize the important role that phase synchronization, desynchronization, and thus, inhibition, play in the construction of compositional meaning by distributed neural networks in the brain.