The inverted U hypothesis in music predicts that listeners prefer intermediate levels of complexity. However, the shape of the liking response to harmonic complexity and the effect of musicianship remains unclear. Here, we tested whether the relationship between liking and harmonic complexity in single chords shows an inverted U shape and whether this U shape is different for musicians and non-musicians. We recorded these groups' liking ratings for four levels of harmonic complexity, indexed by their level of acoustic roughness, as well as several measures of inter-individual difference. Results showed that there is an inverted U-shaped relationship between harmonic complexity and liking in both musicians and non-musicians, but that the shape of the U is different for the two groups. Non-musicians' U is more left-skewed, with peak liking for low harmonic complexity, while musicians' U is more right-skewed, with highest ratings for medium and low complexity. Furthermore, musicians who showed greater liking for medium compared to low complexity chords reported higher levels of active musical engagement and higher levels of openness to experience. This suggests that a combination of practical musical experience and personality is reflected in musicians' inverted U-shaped preference response to harmonic complexity in chords.