We report a measurement of the frequency spectrum of x-ray transition radiation. X rays were generated by electrons of 5 and 9 GeV in radiators of multiple polypropylene foils, and detected in the range 4 to 30 keV with a calibrated single-crystal Bragg spectrometer. The experimental results closely reproduce the features of the theoretically predicted spectrum. In particular, the pronounced interference pattern of multifoil radiators and the expected hardening of the radiation with increasing foil thickness are clearly observed. The overall intensity of the radiation is somewhat lower than predicted by calculations.