A number of studies suggest a link between musical training and both specific and general cognitive abilities, but despite some positive results, there is disagreement about which abilities are improved. This study aims to investigate the effects of a music education program both on a domain-specific competence (meta-musical awareness), and on general domain competences, that is, cognitive abilities (logical-mathematical) and symbolic-linguistic abilities (notational). Twenty 4- to 6-year-old children participated in the research, divided into two groups (experimental and control) and the measures were administered at two different times, before and after a 6-month music program (for the experimental group) and after a sports training program (for the control group). Children performed meta-musical awareness tasks, logical-mathematical tasks, and emergent-alphabetization tasks. Non-parametric statistics show that a music program significantly improves the development of notational skills and meta-musical awareness while not the development of logical-mathematical skills. These results show that a musical program increases children’s meta-musical awareness, and their ability to acquire the notational ability involved in the invented writing of words and numbers. On the contrary, it does not affect the development of logical skills. The results are discussed in terms of transfer of knowledge processes and of specific versus general domain effects of a musical program.