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Recently, Reese et al. (2008), Lignières & Georgeot (2008) and Lignières & Georgeot (2009) showed that the frequencies of low-degree acoustic modes in rapidly rotating stars, also known as “island modes”, follow an asymptotic formula, the coefficients of which can be deduced from ray dynamics. We investigate how this asymptotic behaviour is affected by μ gradients by comparing pulsation spectra from models with and without such a discontinuity.