  Exceptional field theories yield duality-covariant formulations of
higher-dimensional supergravity. They have proven to be an efficient tool for
the construction of consistent truncations around various background
geometries. In this paper, we demonstrate how the formalism can moreover be
turned into a powerful tool for computing the Kaluza-Klein mass spectra around
these backgrounds. Most of these geometries have little to no remaining
symmetries and their spectra are accessible to standard methods only in
selected subsectors. The present formalism not only grants access to the full
Kaluza-Klein spectra but also provides the scheme to identify the resulting
mass eigenstates in higher dimensions. As a first illustration, we rederive in
compact form the mass spectrum of IIB supergravity on $S^5$. We further discuss
the application of our formalism to determine the mass spectra of higher
Kaluza-Klein multiplets around the warped geometries corresponding to some
prominent ${\cal N}=2$ and ${\cal N}=0$ AdS vacua in maximal supergravity.
