We study epicyclic oscillations of fluid tori around black holes (in the Paczynski-Wiita potential) and derive exact analytic expressions for their radial and vertical eigenfrequencies v_r and v_z to second-order accuracy in the width of the torus. We prove that pressure effects make the eigenfrequencies smaller than those for free particles. However, the particular ratio v_z/v_r = 3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies v_r and v_z are about 15% higher than the ones corresponding to free particles. Our results therefore suggest that previous estimates of black hole spins from QPOs have produced values that are too high.
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