When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies ω=ωR+iωI. We show that this behavior is the same as that of damped harmonic oscillators whose real frequencies are (ω2R+ω2I)1/2, rather than simply ωR. Since, for highly excited modes, ωI≫ωR, this observation changes drastically the physical understanding of the black hole spectrum and forces a reexamination of various results in the literature. In particular, adapting a derivation by Hod, we find that the area of the horizon of a Schwarzschild black hole is quantized in units ΔA=8πl2Pl, in contrast with the original result ΔA=4log(3)l2Pl