  In this work we generalize the results for the entropy spectra typically
derived for black holes in general relativity to a generic horizon within the
spherically symmetric (asymptotically flat and non-flat) space-times of more
general theories of gravity. We use all the standard --- Bekenstein's universal
lower bound on the entropy transition, the highly damped quasi-normal modes and
reduced phase-space quantization --- approaches to derive the spectra. In
particular, the three approaches show that the Bekenstein-like spectra for the
horizon entropy is a robust result. Our results confirm the suggestion made
relatively recently by an independent fourth argument by Kothawala et al [1].
