Assessing the tight-winding (WKB) approximation for scale-invariant spirals. The relative error of the density amplitude and the error in the phase offset δψ ≡ ψ_Ψ − ψ_Σ are plotted vs. pitch angle α for m = 2 and various values of the exponent γ (for these scale-invariant models, the errors are the same at each radius). Since the first-order approximations give δψ_approx = 0, their error reflects the actual phase offset of the models.