  We present results from an ongoing study of mass splittings of the lowest
lying states in the charmonium system. We use clover valence charm quarks in
the Fermilab interpretation, an improved staggered (asqtad) action for sea
quarks, and the one-loop, tadpole-improved gauge action for gluons. This study
includes five lattice spacings, 0.15, 0.12, 0.09, 0.06, and 0.045 fm, with two
sets of degenerate up- and down-quark masses for most spacings. We use an
enlarged set of interpolation operators and a variational analysis that permits
study of various low-lying excited states. The masses of the sea quarks and
charm valence quark are adjusted to their physical values. This large set of
gauge configurations allows us to extrapolate results to the continuum physical
point and test the methodology.
