  Taste symmetry violations in staggered fermion formulations correlate
strongly with the cut-off (lattice spacing) dependence in thermodynamic
quantities. Better taste symmetry on the lattice can be achieved either by
decreasing the lattice spacing and going to larger temporal extent in
finite-temperature calculations, or by further improving the action. The highly
improved staggered quark (HISQ) action offers a further degree of improvement
and substantially reduces taste violations. We report on our studies of the 2+1
flavor QCD thermodynamics with the HISQ/tree action. By systematically
comparing HISQ/tree, asqtad, p4 and stout calculations we quantify how the
cut-off effects manifest themselves in different thermodynamic quantities,
including the renormalized Polyakov loop, chiral condensate, various
fluctuations and correlations of conserved charges. The implications for the
equation of state and a comparison to the hadron resonance gas model are also
discussed. The chiral aspects of the finite-temperature transition are
discussed in the companion HotQCD contribution [1].
