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Advancements in many modern technologies rely on the continuous need for materials discovery. However, the design of synthesis routes leading to new and targeted solid-state materials requires understanding of reactivity patterns^{, –}. Advances in synthesis science are necessary to increase efficiency and accelerate materials discovery^{, , , , , –}. We present a highly effective methodology for the rational discovery of materials using high-temperature solutions or fluxes having tunable solubility. This methodology facilitates product selection by projecting the free-energy landscape into real synthetic variables: temperature and flux ratio. We demonstrate the effectiveness of this technique by synthesizing compounds in the chalcogenide system of A(Ba)-Cu-Q(O) (Q = S or Se; A = Na, K or Rb) using mixed AOH/AX (A = Li, Na, K or Rb; X = Cl or I) fluxes. We present 30 unreported compounds or compositions …