Melodic discrimination tests have been used for many years to assess individual differences in musical abilities. These tests are usually analysed using classical test theory. However, classical test theory is not well suited for optimizing test efficiency or for investigating construct validity. This paper addresses this problem by applying modern item response modelling techniques to three melodic discrimination tests. First, descriptive item response modelling is used to develop a short melodic discrimination test from a larger item pool. The resulting test meets the test-theoretic assumptions of a Rasch (1960) item response model and possesses good concurrent and convergent validity as well as good testing efficiency. Second, an explicit cognitive model of melodic discrimination is used to generate hypotheses relating item difficulty to structural item features such as melodic complexity, similarity, and tonalness. These hypotheses are then tested on response data from three melodic discrimination tests (n = 317) using explanatory item response modelling. Results indicate that item difficulty is predicted by melodic complexity and melodic similarity, consistent with the proposed cognitive model. This provides useful evidence for construct validity. This paper therefore demonstrates the benefits of item response modelling both for efficient test construction and for test validity.