Discussions of extended cognition have increasingly engaged with the empirical and methodological practices of cognitive science and psychology. One topic that has received increased attention from those interested in the extended mind is music cognition. A number of authors have argued that music not only shapes emotional and cognitive processes, but also that it extends those processes beyond the bodily envelope. The aim of this paper is to evaluate the case for extended music cognition. Two accounts are examined in detail: (...) Joel Krueger’s “musically extended emotional mind” and Tom Cochrane’s “expression and extended cognition.” Each account is evaluated using three “anti-extension” arguments. I argue that Krueger and Cochrane’s accounts offer important steps toward extended music cognition, but that each account remains underdeveloped in various ways. To supplement existing approaches, I propose a complementary extended computational approach to music cognition. The claim is that music cognition forms part of an extended system in virtue of involving computational processes that range across environmental and in-the-head elements. The paper concludes by showing how the ECMC deals with each of the three anti-extension challenges and responds to objections. (shrink)