A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for strong couplings between natural and forcing oscillation frequencies. The phenomenon can be exemplified in the circle map when, after q iterations of the map, the new angle differs from the initial value by a rational number θ_(n + q) = θ_n + p/q. This is the form of the unperturbed circle map with the map winding number Ω = p/q.