Psychological and aesthetic theories predict that music is appreciated at optimal, peak levels of familiarity and complexity, and that appreciation of music exhibits an inverted U-shaped relationship with familiarity as well as complexity. Because increased familiarity conceivably leads to improved processing and less perceived complexity, we test whether there is an interaction between familiarity and complexity. Specifically, increased familiarity should render the music subjectively less complex, and therefore move the apex of the U curve toward greater complexity. A naturalistic listening experiment was conducted, featuring 40 music examples (ME) divided by experts into 4 levels of complexity prior to the main experiment. The MEs were presented 28 times each across a period of approximately 4 weeks, and individual ratings were assessed throughout the experiment. Ratings of liking increased monotonically with repeated listening at all levels of complexity; both the simplest and the most complex MEs were liked more as a function of listening time, without any indication of a U-shaped relation. Although the MEs were previously unknown to the participants, the strongest predictor of liking was familiarity in terms of having listened to similar music before, i.e., familiarity with musical style. We conclude that familiarity is the single most important variable for explaining differences in liking among music, regardless of the complexity of the music.