This paper reports on the results of recent experiments performed on the JET tokamak on Alfven 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 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. First, we describe the development of a new algorithm for real-time mode detection and discrimination using the Sparse Signal Representation theory. Second, we present measurements of the dependence of the damping rate for Toroidal AEs with |n|<=8 upon various background plasma parameters. Finally, the results of theoretical modeling of the damping rate for n=3 Toroidal AEs, performed with the LEMan, CASTOR and TAEFL codes, are shown as function of the edge plasma elongation.