We combine small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS) with aerodynamic levitation techniques to study in situ phase transitions in the liquid state under contactless conditions. At very high temperatures, yttria-alumina melts show a first-order transition, previously inferred from phase separation in quenched glasses. We show how the transition coincides with a narrow and reversible maximum in SAXS indicative of liquid unmixing on the nanoscale, combined with an abrupt realignment in WAXS features related to reversible shifts in polyhedral packing on the atomic scale. We also observed a rotary action in the suspended supercooled drop driven by repetitive transitions (a polyamorphic rotor) from which the reversible changes in molar volume (1.2 +/- 0.2 cubic centimeters) and entropy (19 +/- 4 joules mole(-1) kelvin(-1)) can be estimated.