Monopiles and gravity base foundations (GBF) are two of the most commonly used offshore foundations for wind turbines. As resonance can cause damage and even failure of wind turbines, understanding the difference between the dynamic responses of monopiles and GBFs under free vibration is important, however there is little experimental data regarding their natural frequency, especially for model tests at correct stress levels. This paper presents the results of novel monopile and GBF tests using a centrifuge to directly determine the natural frequency (fn) of the foundation-soil system. The natural frequencies of wind turbine monopiles and GBFs in centrifuge models were measured during harmonic loading by a piezo-actuator, with the results confirming that soil-structure interaction must be considered to obtain the system natural frequency as the frequency reduces substantially from fixed-base values. These results will contribute to preventing resonance damage in designs for wind-turbine foundations.