This paper reports on the results of recent experiments performed on the JET tokamak on Toroidal Alfvén Eigenmodes (TAEs) with toroidal mode number (n) in the range up to |n|=7. The stability properties of these medium-n TAEs are investigated experimentally using a 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. The measurements of the damping rate (g/w) for these medium-n modes reported here were obtained during a deuterium to helium to hydrogen changeover experimental campaign, and are used to assess to effect of the plasma effective isotopic composition (AEFF) on the stability properties of these medium-n TAEs. We find that the damping rate of n=1 TAEs decreases approximately as g/w~1/AEFF as reported previously, but only for modes whose frequency is close to the centre of the n=1 toroidal gap and for density and current profiles giving an open gap structure. Conversely, for n>5 TAEs we find that their damping rate approximately increases as g/w~AEFF. The turning point on the g/w vs. AEFF dependence occurs for n=3 TAEs.