Keeping time is fundamental for our everyday existence. Various isochronous activities, such as locomotion, require us to use internal timekeeping. This phenomenon comes into play also in other human pursuits such as dance and music. When listening to music, we spontaneously perceive and predict its beat. The process of beat perception comprises both beat inference and beat maintenance, their relative importance depending on the salience of beat in the music. To study functional connectivity associated with these processes in a naturalistic situation, we used functional magnetic resonance imaging to measure brain responses of participants while they were listening to a piece of music containing strong contrasts in beat salience. Subsequently, we utilized dynamic graph analysis and psychophysiological interactions (PPI) analysis in connection with computational modelling of beat salience to investigate how functional connectivity manifests these processes. As the main effect, correlation analyses between the obtained dynamic graph measures and the beat salience measure revealed increased centrality in auditory-motor cortices, cerebellum, and extrastriate visual areas during low beat salience, whereas regions of the default mode- and central executive networks displayed high centrality during high beat salience. PPI analyses revealed partial dissociation of functional networks belonging to this pathway indicating complementary neural mechanisms crucial in beat inference and maintenance, processes pivotal for extracting and predicting temporal regularities in our environment.