Antonio Eximeno (1729-1808), a Spanish expelled Jesuit, is a prominent representative of the musical thought of the Age of Enlightenment. Eximeno, the author of diverse musical and aesthetic texts (Dell'origine e delle regole della musica, Dubbio di D. Antonio Eximeno, Las investigaciones músicas de D. Lazarillo Vizcardi), showed great interest for instrumental music precisely when this musical form was on its way to "emancipation". In this paper we analyse the position that the instrumental music occupies in Eximeno's thought, stressing his defense of this form of music, despite of those that still had doubts on its possibilities. On the other hand, we study some of his descriptions of events involving the instrumental music; plausible testimonies that contribute to the knowledge of the consumption behaviour of this type of music in the late 18th century Spain. Finally, we study the opinions of specific composers, as well as different meanings they attribute to the concept of "sublime" within their thought, up to becoming the idea that serves to justify the existence of instrumental music, and to outline the existence of two confronted schools: the Northern school (with noted representatives such as Haydn) and the Southern school (with Boccherini at the head).