  Recent observations of rapidly rotating stars have revealed the presence of
regular patterns in their pulsation spectra. This has raised the question as to
their physical origin, and in particular, whether they can be explained by an
asymptotic frequency formula for low-degree acoustic modes, as recently
discovered through numerical calculations and theoretical considerations. In
this context, a key question is whether compositional/density gradients can
adversely affect such patterns to the point of hindering their identification.
To answer this question, we calculate frequency spectra using two-dimensional
ESTER stellar models. These models use a multi-domain spectral approach,
allowing us to easily insert a compositional discontinuity while retaining a
high numerical accuracy. We analyse the effects of such discontinuities on both
the frequencies and eigenfunctions of pulsation modes in the asymptotic regime.
We find that although there is more scatter around the asymptotic frequency
formula, the semi-large frequency separation can still be clearly identified in
a spectrum of low-degree acoustic modes.
