Individuals differ in musical competence, which we defined as the ability to perceive, remember, and discriminate sequences of tones or beats. We asked whether such differences could be explained by variables other than music training, including socioeconomic status (SES), short-term memory, general cognitive ability, and personality. In a sample of undergraduates, musical competence had positive simple associations with duration of music training, SES, short-term memory, general cognitive ability, and openness-to-experience. When these predictors were considered jointly, musical competence had positive partial associations with music training, general cognitive ability, and openness. Nevertheless, moderation analyses revealed that the partial association between musical competence and music training was evident only among participants who scored below the mean on our measure of general cognitive ability. Moreover, general cognitive ability and openness had indirect associations with musical competence by predicting music training, which in turn predicted musical competence. Musical competence appears to be the result of multiple factors, including but not limited to music training.