  This paper introduces a chain model for the Deligne-Mumford operad formed by
homotopically trivializing the circle in a chain model for the framed little
disks. We then show that under degeneration of the Hochschild to cyclic
cohomology spectral sequence, a known action of the framed little disks on
Hochschild cochains lifts to an action of this new chain model. We thus
establish homotopy hyper-commutative algebra structures on both Hochschild and
cyclic cochain complexes, and we interpret the gravity brackets on cyclic
cohomology as obstructions to degeneration of this spectral sequence. Our
results are given in the language of deformation complexes of cyclic operads.
