Comparison of frequency spacing δ_m between island modes, computed from numerical simulations and semi-analytical formula Eq. (53) for different values of Ω/Ω_K (the frequency spacings are normalized by with R_p the polar radius). Orange/gray: semi-analytical results of Eq. (53) for n = 42 and m = 1, blue/black: numerical results. The numerical results correspond to different sets of δ_m for n ∈  [42,51] , ℓ = 0 and m ∈  {  − 1,1 } . (This figure is available in color in the electronic form.)