Founded on the mathematical concept of topos (Grothendieck) and on the philosophical concept of situation-universe (Badiou), the thesis of this paper is that music is constitutive of a world per se, satisfying the three properties of a world: infinitely vast, closed on itself, centered on an internal logic. Sociology cannot succeed in accounting for the insubordination of music, of its internal logic based on what is called "music theory".
Such a conception of music as world allows thinking it as both one and plural. It enlightens the relationship of the musicians to music, which they visit without inhabitating it. It defines the contents of musical intellectuality, that which thinks the world of music as such, and demonstrates that a history of music can be but a history for the musicians, not for the works of music.