A direct absorption edge tunable between 0.8 and approximately 1.4 eV is demonstrated in strain-free ternary Ge_{1-x-y}Si_{x}Sn_{y} alloys epitaxially grown on Ge-buffered Si. This decoupling of electronic structure and lattice parameter-unprecedented in group-IV alloys-opens up new possibilities in silicon photonics, particularly in the field of photovoltaics. The compositional dependence of the direct band gap in Ge_{1-x-y}Si_{x}Sn_{y} exhibits a nonmonotonic behavior that is explained in terms of coexisting small and giant bowing parameters in the two-dimensional compositional space.