Using the simple model of a spherical solid inner core oscillating in a rotating liquid outer core, we compute the frequencies of the Slichter modes of the earth. The fluid is assumed neutrally stratified (but with a radially varying density) and viscous, viscosity being taken into account non-perturbatively. The parameters are those given by earth models like PREM, 1066A or CORE11. The computed resonant frequencies are compared to those observed by Courtier et al. (2000) and claimed to be the Slichter frequencies. We show that our model cannot reproduce these frequencies and that previous models which did reproduce them are not consistent with the observed quality factors of the resonances.