In this article, the author defines cognitive musicology as the study of musical thinking from a computational point of view. He suggests that it is an approach that focuses on musical thinking rather than the work itself, investigating factors such as compositional processes, performance processes and listening processes, and then characterising these in computational terms. The author criticises John Myhill's claim that musical thinking can be accounted for in computational terms. He argues that there are some aspects of musical thinking that cannot be characterised in strictly computational terms and that some musical thinking requires more than computations to accurately illustrate them.