Flame transfer function measurements of turbulent premixed flames were made in a model lean premixed, swirl-stabilized, gas turbine combustor. OH*, CH*, and CO2* chemiluminescence emissions were measured to determine heat release oscillation from a whole flame, and the two-microphone technique was used to measure inlet velocity fluctuation. 2-D CH* chemiluminescence imaging was used to characterize the flame shape: the flame length (LCH* max) and flame angle (α). Using H 2-natural gas composite fuels, XH2 = 0.00-0.60, very short flame was obtained and hydrogen enrichment of natural gas had a significant impact on the flame structure and flame attachment points. For a pure natural gas flame, the flames exhibit a "V" structure, whereas H 2-enriched natural gas flames have an "M" structure. Results show that the gain of "M" flames is much smaller than that of "V" flames. Similar to results of analytic and experimental investigations on the flame transfer function of laminar premixed flames, it shows that the dynamics of a turbulent premixed flame is governed by three relevant parameters: the Strouhal number (St = LCH* max / LCONV), the flame length (LCH*max), and the flame angle (a). Two flames with the same flame shape exhibit very similar forced responses, regardless of their inlet flow conditions. This is significant because the forced flame response of a highly turbulent, practical gas turbine combustor can be quantitatively generalized using the non-dimensional parameters which collapse all relevant input conditions into the flame shape and the Strouhal number.