An ultrathin polymer sheet floating on a fluid forms a periodic pattern of parallel wrinkles when subjected to uniaxial compression. The wave number of the wrinkle pattern increases sharply near the fluid meniscus where the translational symmetry of this one-dimensional corrugated profile is broken. We show that the observed multiscale morphology is controlled by a new "softness" number that quantifies the relative strength of capillary forces at the edge and the rigidity of the bulk pattern. We discover a new elastic cascade by which the wrinkling pattern in the bulk is smoothly matched to the fine structure at the edge by a discrete series of higher Fourier modes.