The relationship between structural processing in music and language has received increasing interest in the last several years, spurred by the influential Shared Syntactic Integration Resource Hypothesis (SSIRH; Patel, 2003). According to this resource-sharing framework, music and language rely on separable syntactic representations but recruit shared cognitive resources to integrate these representations into evolving structures. The SSIRH is supported by findings of interactions between structural manipulations in music and language. However, other recent evidence suggests that such interactions can also arise with non-structural manipulations, and some recent neuroimaging studies report largely non-overlapping neural regions involved in processing musical and linguistic structure. These conflicting results raise the question of exactly what shared (and distinct) resources underlie musical and linguistic structural processing. This paper suggests that one shared resource is prefrontal cortical mechanisms of cognitive control, which are recruited to detect and resolve conflict that occurs when expectations are violated and interpretations must be revised. By this account, musical processing involves not just the incremental processing and integration of musical elements as they occur, but also the incremental generation of musical predictions and expectations, which must sometimes be overridden and revised in light of evolving musical input.