Musical aptitude is commonly measured using tasks that involve discrimination of different types of musical auditory stimuli. Performance on such different discrimination tasks correlates positively with each other and with intelligence. However, no study to date has explored these associations using a genetically informative sample to estimate underlying genetic and environmental influences. In the present study, a large sample of Swedish twins (N = 10,500) was used to investigate the genetic architecture of the associations between intelligence and performance on three musical auditory discrimination tasks (rhythm, melody and pitch). Phenotypic correlations between the tasks ranged between 0.23 and 0.42 (Pearson r values). Genetic modelling showed that the covariation between the variables could be explained by shared genetic influences. Neither shared, nor non-shared environment had a significant effect on the associations. Good fit was obtained with a two-factor model where one underlying shared genetic factor explained all the covariation between the musical discrimination tasks and IQ, and a second genetic factor explained variance exclusively shared among the discrimination tasks. The results suggest that positive correlations among musical aptitudes result from both genes with broad effects on cognition, and genes with potentially more specific influences on auditory functions.