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Music is often described in the laboratory and in the classroom as a beneficial tool for memory encoding and retention, with a particularly strong effect when words are sung to familiar compared to unfamiliar melodies. However, the neural mechanisms underlying this memory benefit, especially for benefits related to familiar music are not well understood. The current study examined whether neural tracking of the slow syllable rhythms of speech and song is modulated by melody familiarity. Participants became familiar with twelve novel melodies over four days prior to MEG testing. Neural tracking of the same utterances spoken and sung revealed greater cerebro-acoustic phase coherence for sung compared to spoken utterances, but did not show an effect of familiar melody when stimuli were grouped by their assigned (trained) familiarity. However, when participant's subjective ratings of perceived familiarity were used to group stimuli, a large effect of familiarity was observed. This effect was not specific to song, as it was observed in both sung and spoken utterances. Exploratory analyses revealed some in-session learning of unfamiliar and spoken utterances, with increased neural tracking for untrained stimuli by the end of the MEG testing session. Our results indicate that top-down factors like familiarity are strong modulators of neural tracking for music and language. Participants’ neural tracking was related to their perception of familiarity, which was likely driven by a combination of effects from repeated listening, stimulus-specific melodic simplicity, and individual differences. Beyond simply the acoustic features of music, top-down factors built into the music listening experience, like repetition and familiarity, play a large role in the way we attend to and encode information presented in a musical context.