  Gravitational parity violation arises in a variety of theories beyond general
relativity. Gravitational waves in such theories have their propagation
altered, leading to birefringence effects in both the amplitude and speed of
the wave. In this work, we introduce a generalized, theory-motivated
parametrization scheme to study parity violation in gravitational wave
propagation. This parametrization maps to parity-violating gravity theories in
a straightforward way. We find that the amplitude and velocity birefringence
effects scale with an effective distance measure that depends on how the
dispersion relation is modified. Furthermore, we show that this generic
parametrization can be mapped to the parametrized-post-Einsteinian (ppE)
formalism with convenient applications to gravitational wave observations and
model-agnostic tests of general relativity. We derive a mapping to the standard
ppE waveform of the gravitational wave response function, and also find a ppE
waveform mapping at the level of the polarization modes, $h_+$ and $h_\times$.
Finally, we show how existing constraints in the literature translate to bounds
on our new parity-violating parameters and discuss avenues for future analysis.
