  We use the covariant formulation proposed in Tattersall et al (2017) to
analyse the structure of linear perturbations about a spherically symmetric
background in different families of gravity theories, and hence study how
quasi-normal modes of perturbed black holes may be affected by modifications to
General Relativity. We restrict ourselves to single-tensor, scalar-tensor and
vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black
hole background. We show explicitly the full covariant form of the quadratic
actions in such cases, which allow us to then analyse odd parity (axial) and
even parity (polar) perturbations simultaneously in a straightforward manner.
