This work, from of theorist perspective of Historical-Critical Pedagogy, presents the school Music Education like a social mediator environment between the practices, listening and musical everydaylife knowledges and the not-quotidian, which are constitution and accumulated, throughout the centuries of History, by the human societies. The purpose is to present a possible theorist foundation to define the importance of Music Education insert in the elementary school, like a subject destined to guarantee the whole children formation and the enrichment of their relations with the music. It is a theorist reflection that indicates the importance of observation of the quotidian and not-quotidian knowledges characteristics, moreover of complete importance of formal education and, in specific, of school Music Education on human development.