Aspect-oriented programming is emerging as a powerful tool for system design and development. In this paper, we study aspects as primitive computational entities on par with objects, functions and horn-clauses. To this end, we introduce muABC, a name-based calculus, that incorporates aspects as primitive. In contrast to earlier work on aspects in the context of object-oriented and functional programming, the only computational entities in muABC are aspects. We establish compositional translations into muABC from a class-based language with aspects and classes, and from a functional language with aspects and higher-order functions. Further, we delineate the features required to support an aspect-oriented style by presenting a translation of muABC into an extended pi-calculus.