A tapered undulator, in which the entrance and exit magnetic gaps are different, will show an increase in the energy width of the harmonics compared to the nontapered case. This increase can occur without substantial broadening in the collimation of the undulator radiation. We present the spectral properties measured for a tapered 3.3-cm period prototype undulator of the Advanced Photon Source at the Cornell High Energy Synchrotron Source. The width of the on-axis first harmonic at 6.9 keV increased from 0.32 to 0.66 keV for a gap tapering of 12%. Minimal angular broadening in the first harmonic x rays was detected and measurements of off-axis radiation were also performed. The results are found to be in good agreement with model calculations.