Many studies have found that variation in music training is associated with intellectual abilities, but research disagrees over whether music education should primarily correlate with general intelligence (g) or with specific lower-level cognitive abilities (e.g., fluid reasoning, verbal ability, or spatial reasoning). Past research, however, has not modeled the data in ways that can separate general abilities like g from specific abilities. To examine if the associations between music training and intelligence are general, specific, or both, a bifactor modeling approach was applied to data from a sample of 237 young adults who varied substantially in musical expertise. People completed a range of tasks that measured several lower-order abilities: fluid intelligence, crystallized intelligence (vocabulary knowledge), verbal fluency, and auditory discrimination ability. Simple correlations showed that music training correlated with all 4 lower-order abilities. A bifactor model, however, found that music training had both general (a strong association with g: β = .74 [.50, .98]) and specific (a moderate association with auditory ability: β = .37 [.08, .67]) relationships. The findings reconcile past research on the breadth of music training’s relationships and illustrate a fruitful method for identifying its links with cognitive abilities.