[from Exposition d'une Nouvelle méthode, 1818] Inspired by the teachings of Jean-Jacques Rousseau and persuaded that traditional methods of teaching music in France were mistaken, Pierre Galin applied his training in logic and the sciences to a devising a more satisfactory teaching procedure. The unprecedented analysis of the learning process common to language and music that resulted is published here in Bernarr Rainbow's translation for the first time. It presents a challenge as valid today as when it was first written in 1818.