Comparison of frequency spacings δ_n,ℓ between island modes, computed from numerical simulations and semi-analytical formulas for different values of Ω/Ω_K (the frequency spacings are normalized by with R_p the polar radius). Circles: δ_n, triangles: δ_ℓ, orange/gray: semi-analytical results, blue/black: numerical results. Numerical results correspond to different sets of and values, with n ∈  [42,51] , ℓ ∈  { 0,1 }  for m = 0; and n ∈  [42,51] , ℓ = 0, n ∈  { 42,44,46,48,50 } , ℓ = 1 for m ∈  {  − 1,1 } . Upper panel: m = 0. Lower panel: m =  ± 1. (This figure is available in color in the electronic form.)