  The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy $E$, the axial component of the
angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or
the inclination parameter $\theta_{-}$ are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.
