Studies in psycho-linguistics have provided compelling evidence that theoretical syntactic structures have cognitive correlates that inform and influence language perception. Generative grammar models also present a principled way to represent a plethora of hierarchical structures outside the domain of language. Hierarchical aspects of musical structure, in particular, are often described through grammar models. Whether such models carry perceptual relevance in music, however, requires further study. To address the descriptive adequacy of a grammar model in music, unfamiliar musical phrases consisting of chord progressions within the Jazz idiom were used, and zero to three chords were cut from the end of each phrase. A total of 150 participants were then presented with these stimuli and asked to provide a Closure Response, that is to predict how many more chords (0, 1, 2, or 3) were expected before the chord progression was complete. Simultaneously, a grammar model of hierarchical structure as well as a bigram model were trained over a corpus of 150 expert-annotated Jazz tunes. The models were then used to estimate probability distributions of Closure Responses in the stimuli presented to the participants. Bayesian mixed-effects models reveal that the models carry predictive value for the participants' response distributions and that the hierarchical model contains incremental predictive information over the bigram model. The present results suggest that -- akin to language -- hierarchical relationships between musical events have a cognitive correlate, which influences the perception and interpretation of music.