In order to change the blade count (BC) of axial rotor designs, a scaling technique can be applied where the blades are scaled in axial and circumferential directions while maintaining the solidity. This technique allows to adjust the blade count without changing the steady-state aerodynamics, but the influences on the aerodynamic damping are unknown. The present study is focused on the investigation of the change in aerodynamic damping of a subsonic axial compressor rotor, if the blade count is changed between 13 and 25 blades. The investigation is focused on the first bending mode family and the influences of the hub geometry on the modes are neglected. First, a comparison between the influence coefficient (IC) method and the traveling wave mode (TWM) method is conducted, which shows that the application of the IC method in combination with harmonic balance simulations offers a fast way to compute the aerodynamic damping without introducing significant errors compared with the TWM method simulations. Regarding the aerodynamic damping of the different rotor geometries, it can be noted that the amplitude of the work per cycle influence coefficient of the center blade scales linearly with the blade scaling factor and an increase in aerodynamic damping for an increase in blade count is observed. Furthermore, a simplified analytic theory is established, which explains the phase angle change of the blade influence coefficients due to the blade scaling. In the last part of the paper, an extrapolation method is proposed for the investigated geometry and mode family, which allows for the estimation of damping S-curves for scaled rotor geometries based on only one IC method simulation.