We present a new lattice QCD analysis of heavy-quark pseudoscalar-pseudoscalar correlators, using gluon configurations from the MILC Collaboration that include vacuum polarization from u, d, s, and c quarks (nf=4). We extract new values for the QCD coupling and for the c quark’s MS¯ mass: αMS¯(MZ,nf=5)=0.11822(74) and mc(3  GeV,nf=4)=0.9851(63)  GeV. These agree well with our earlier simulations using nf=3 sea quarks, vindicating the perturbative treatment of c quarks in that analysis. We also obtain a new nonperturbative result for the ratio of c and s quark masses: mc/ms=11.652(65). This ratio implies ms(2  GeV,nf=3)=93.6(8)  MeV when it is combined with our new c mass. Combining mc/ms with our earlier mb/mc gives mb/ms=52.55(55), which is several standard deviations (but only 4%) away from the Georgi-Jarlskop prediction from certain grand unified theories. Finally we obtain an nf=4 estimate for mb/mc=4.528(54) which agrees well with our earlier nf=3 result. The new ratio implies mb(mb,nf=5)=4.162(48)  GeV.