  We analyse the spectrum of Kaluza-Klein excitations above three distinct
families of ${\cal N}=1$ AdS$_4$ solutions of type IIB supergravity of
typically non-geometric, S-fold type that have been recently found. For all
three families, we provide the complete algebraic structure of their spectra,
including the content of OSp$(4|1)$ multiplets at all Kaluza-Klein levels and
their charges under the residual symmetry groups. We also provide extensive
results for the multiplet dimensions using new methods derived from exceptional
field theory, including complete, analytic results for one of the families. All
three spectra show periodicity in the moduli that label the corresponding
family of solutions. Finally, the compactness of these moduli is verified in
some cases at the level of the fully-fledged type IIB uplifted solutions.
