Smooth irreducible representations of tori over local fields have been parametrized by R. P. Langlands [“Representations of abelian algebraic groups”, Olga Taussky-Todd: In memoriam. Cambridge, MA: International Press. Pac. J. Math., Spec. Issue, 231–250 (1998; Zbl 0910.11045)], using class field theory and Galois cohomology. In this paper the author extends this parametrization to some central extensions of such tori. The central extensions that the author examines are by \(n\)th roots of unity via the Hilbert symbol. The main result is an analogue of Langlands’ parametrization mentioned above to the case when the splitting field of the torus is unramified over the base field and when the cover is tame.