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, reported here, of the damping rate (γ/ω) for these medium-n modes were obtained during a deuterium to helium to hydrogen changeover experimental campaign, and are used to infer the 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 γ/ω ∼ 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 ⩾ 3 TAEs we find that their damping rate approximately increases as γ/ω ∼ AEFF.