The highly complex structure-property inter relationship in the lead-free piezoelectric(x)Na_1/2Bi_1/2TiO₃-(1−x)BaTiO₃ is a subject of considerable contemporary debate. Using comprehensive x-ray, neutron diffraction, dielectric, and ferroelectric studies, we have shown the existence of a new criticality in this system at x=0. 80, i.e., well within the conventional tetragonal phase field. This criticality manifests as a nonmonotonic variation of the tetragonality and coercivity and is shown to be associated with a crossover from a nonmodulated tetragonal phase (for x<0.8) to a long-period modulated tetragonal phase (for x>0.80). It is shown that the stabilization of long-period modulation introduces a characteristic depolarization temperature in the system. While differing qualitatively from the two-phase model often suggested for the critical compositions of this system, our results support the view with regard to the tendency in perovskites to stabilize long-period modulated structures as a result of complex interplay of antiferrodistortive modes.