Young children regularly engage in musical activities, but the effects of early music education on children's cognitive development are unknown. While some studies have found associations between musical training in childhood and later nonmusical cognitive outcomes, few randomized controlled trials (RCTs) have been employed to assess causal effects of music lessons on child cognition and no clear pattern of results has emerged. We conducted two RCTs with preschool children investigating the cognitive effects of a brief series of music classes, as compared to a similar but non-musical form of arts instruction (visual arts classes, Experiment 1) or to a no-treatment control (Experiment 2). Consistent with typical preschool arts enrichment programs, parents attended classes with their children, participating in a variety of developmentally appropriate arts activities. After six weeks of class, we assessed children's skills in four distinct cognitive areas in which older arts-trained students have been reported to excel: spatial-navigational reasoning, visual form analysis, numerical discrimination, and receptive vocabulary. We initially found that children from the music class showed greater spatial-navigational ability than did children from the visual arts class, while children from the visual arts class showed greater visual form analysis ability than children from the music class (Experiment 1). However, a partial replication attempt comparing music training to a no-treatment control failed to confirm these findings (Experiment 2), and the combined results of the two experiments were negative: overall, children provided with music classes performed no better than those with visual arts or no classes on any assessment. Our findings underscore the need for replication in RCTs, and suggest caution in interpreting the positive findings from past studies of cognitive effects of music instruction.