The original description of alpha particle driven instabilities in the Tokamak Fusion Test Reactor (TFTR) in terms of Toroidal Alfvén Eigenmodes (TAEs) remained inconsistent with three fundamental characteristics of the observations:(i) the variation of the mode frequency with toroidal mode number; (ii) the chirping of the mode frequency for a given toroidal mode number, and (iii) the anti-ballooning density perturbation of the modes. It is now shown that these characteristics can be explained within the context of cylindrical eigenmodes and their transition to TAEs with the evolution of the central plasma current profile.