This paper reports the results of recent experiments performed on the JET tokamak on Alfvén Eigenmodes (AEs) with toroidal mode number (n) in the range n = 3-15. The stability properties of these medium-n AEs are investigated experimentally using a new set of compact in-vessel antennas, providing a direct and real-time measurement of the frequency, damping rate and amplitude for each individual toroidal mode number. We report here the quantitative analysis of the measurements of the damping rate for stable n = 3 Toroidal AEs as function of the edge plasma elongation, and the theoretical analysis of this data with the TAEFL code. The TAEFL results are in excellent qualitative agreement with the measurements, reproducing well the experimental scaling of increasing damping rate versus increasing edge elongation, and in many cases are also quantitatively correct, with a difference with respect to the measurements below 30%, particularly for magnetic configurations that have a larger edge magnetic shear.