Turbulent premixed combustion processes are inherently unsteady and, thus, a source of acoustic radiation. While prior studies have extensively characterized the total sound power radiated by turbulent flames, few measurements of their spectral characteristics exist. This article presents systematic measurements of the acoustic spectra over a 100 Hz-30 kHz frequency range from a turbulent, natural gas-fueled flame. Measurements were made in an anechoic environment at several burner diameters, flow velocities, and equivalence ratios. The results show that, for a fixed burner diameter, the turbulent flame's acoustic spectrum has a nearly universal shape whose total power is a function of equivalence ratio and flow velocity. The functional dependence of the power spectra on frequency does vary with burner diameter, however, as the frequency of peak acoustic emissions generally shifts to lower frequencies with increases in burner diameter. These trends are quite similar to those exhibited by the cold flow velocity spectra, suggesting that the flame noise is "forced" by turbulent velocity fluctuations. While this observation is consistent with prior studies, the complete independence of the flame noise spectra on such characteristics as flame length or speed is puzzling, however, and demonstrates the need for further theoretical analyses of the flame noise-turbulent flow velocity transfer function.