Frequent listening to unfamiliar music excerpts forms functional connectivity in the brain as music becomes familiar and memorable. However, where these connections spectrally arise in the cerebral cortex during music familiarization has yet to be determined. This study investigates electrophysiological changes in phase-based functional connectivity recorded with electroencephalography (EEG) from twenty participants’ brains during thrice passive listening to initially unknown classical music excerpts. Functional connectivity is evaluated based on measuring phase synchronization between all pairwise combinations of EEG electrodes across all repetitions via repeated measures ANOVA and between every two repetitions of listening to unknown music with the weighted phase lag index (WPLI) method in different frequency bands. The results indicate an increased phase synchronization during gradual short-term familiarization between the right frontal and the right parietal areas in the theta and alpha bands. In addition, the increased phase synchronization is discovered between the right temporal areas and the right parietal areas at the theta band during gradual music familiarization. Overall, this study explores the short-term music familiarization effects on neural responses by revealing that repetitions form phasic coupling in the theta and alpha bands in the right hemisphere during passive listening.