Ancient and contemporary theories of cognitive functions of music, its origins, and evolution are reviewed. A hypothesis is presented that promises to unify the field and a theory is proposed of the origin of music based on the fundamental role of music in cognition. The split is considered of the vocalizations of proto-humans into two types: one less emotional and more concretely-semantic, evolving into language, and the other preserving emotional connections along with semantic ambiguity, evolving into music. The evolution of language toward the semantically powerful tool of today required emancipation from emotional encumbrances. Opposing, but no less powerful, mechanisms required a compensatory evolution of music toward more differentiated and refined emotionality. The need for refined music is grounded in fundamental mechanisms of the mind. This is why today’s human mind and cultures cannot exist without today’s music. The hypothesis is that the fundamental cognitive function of music is to help resolve cognitive dissonances created by language. Without this ability evolution of language, cognition, culture is not possible.