  We present results from an ongoing lattice study of the lowest lying
charmonium and bottomonium level splittings using the Fermilab heavy quark
formalism. Our objective is to test the performance of this action on
MILC-collaboration ensembles of (2+1) flavors of light improved staggered
(asqtad) quarks. Measurements are done on 16 ensembles with degenerate up and
down quarks of various masses, thus permitting a chiral extrapolation, and over
lattice spacings ranging from 0.09 fm to 0.18 fm, thus permitting study of
lattice-spacing dependence. We examine combinations of the mass splittings that
are sensitive to components of the effective quarkonium potential.
