  Analytical resonance conditions for oscillation modes in stars are very
helpful both to predict and to examine their frequency spectra, as well as to
make the link with their internal properties. In this short paper, we introduce
a general quantization expression for oscillation modes accounting for the
possible existence of a local sharp variation in the equilibrium structure, a
so-called glitch. This representation is based on a direct adaptation of the
progressive-wave picture of mixed modes proposed by Takata (2016b). In this
formulation, a glitch turns out to be characterized by three parameters: its
acoustic depth, the phase lags introduced after the wave reflection at the
considered point, and a coupling factor. Such an expression has two main
advantages. First, it can be easily applicable to a lot of different structural
configurations. Second, it does not assume that the glitch is a small
perturbation. Actually, we check that the obtained expression tends to the
formulations previously derived when the glitch is weak. These research notes
represent a preliminary step towards a more generalized description of
multi-cavity oscillation modes, that was briefly addressed in the poster
presented at the PHOST conference.

Solar and Stellar Astrophysics