  The near-horizon geometry of a large class of extremal and near-extremal
black holes in string and M theory contains three-dimensional asymptotically
anti-de Sitter space. Motivated by this structure, we are led naturally to a
discrete set of complex frequencies defined in terms of the monodromy at the
inner and outer horizons of the black hole. We show that the correspondence
principle, whereby the real part of these ``non-quasinormal frequencies'' is
identified with certain fundamental quanta, leads directly to the correct
quantum behavior of the near-horizon Virasoro algebra, and thus the black hole
entropy. Remarkably, for the rotating black hole in five dimensions we also
reproduce the fractionization of conformal weights predicted in string theory.
