In this study, we investigate whether language and music share cognitive resources for structural processing. We report an experiment that used sung materials and manipulated linguistic complexity (subject-extracted relative clauses, object-extracted relative clauses) and musical complexity (in-key critical note, out-of-key critical note, auditory anomaly on the critical note involving a loudness increase). The auditory-anomaly manipulation was included in order to test whether the difference between in-key and out-of-key conditions might be due to any salient, unexpected acoustic event. The critical dependent measure involved comprehension accuracies to questions about the propositional content of the sentences asked at the end of each trial. The results revealed an interaction between linguistic and musical complexity such that the difference between the subject- and object-extracted relative clause conditions was larger in the out-of-key condition than in the in-key and auditory-anomaly conditions. These results provide evidence for an overlap in structural processing between language and music.