  The limit of large number of dimensions localizes the gravitational field of
a black hole in a well-defined region near the horizon. The perturbative
dynamics of the black hole can then be characterized in terms of states in the
near-horizon geometry. We investigate this by computing the spectrum of
quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which
we find splits into two classes. Most modes are non-decoupled modes:
non-normalizable states of the near-horizon geometry that straddle between the
near-horizon zone and the asymptotic zone. They have frequency of order D/r_0
(with r_0 the horizon radius), and are also present in a large class of other
black holes. There also exist a much smaller number of decoupled modes:
normalizable states of the near-horizon geometry that are strongly suppressed
in the asymptotic region. They have frequency of order 1/r_0, and are specific
of each black hole. Our results for their frequencies are in excellent
agreement with numerical calculations, in some cases even in D=4.
