  Observations from the Rossi X-Ray Timing Explorer have shown the existence of
high frequency quasi-periodic oscillations (HFQPOs) in the X-ray flux from
accreting black hole binary systems. In at least two systems, these HFQPOs come
in pairs with a 2:3 frequency commensurability. We propose a simple ``hot
spot'' model to explain the position and amplitude of the HFQPO peaks. Using
the exact geodesic equations for the Kerr metric, we calculate the trajectories
of massive test particles, which are treated as isotropic, monochromatic
emitters in their rest frames. Photons are traced from the accretion disk to a
distant observer to produce time- and frequency-dependent images of the
orbiting hot spot and background disk. The power spectrum of the X-ray light
curve consists of multiple peaks at integral combinations of the black hole
coordinate frequencies. In particular, if the radial frequency is one-third of
the azimuthal frequency (as is the case near the inner-most stable circular
orbit), beat frequencies appear in the power spectrum at two-thirds and
four-thirds of the fundamental azimuthal orbital frequency, in agreement with
observations. We also model the effects of shearing the hot spot in the disk,
producing an arc of emission that also follows a geodesic orbit, as well as the
effects of non-planar orbits that experience Lens-Thirring precession around
the black hole axis. By varying the arc length, we are able to explain the
different QPO features observed in ``Type A'' and ``Type B'' X-ray outbursts
from XTE J1550-564. In the context of this model, the observed power spectra
allow us to infer values for the black hole mass and angular momentum, and also
constrain the parameters of the model, such as the hot spot size and
luminosity.
