We investigate the effect of the shape of the safety factor profile on the MHD spectrum. Results from numerical simulations with the CASTOR code are presented. Two scenarios are discussed. Firstly, finite beta plasmas with a non-monotonic safety factor profile for which it will be shown that a cluster spectrum of global Alfvén waves can exist. When these modes appear in the frequency range of the toroidicity-induced Alfvén gap they are undamped and become susceptible to excitation by, for example, an external antenna. The second scenario is that of small aspect ratio plasmas with a region of low shear. In these plasmas a multiple spectrum of TAE modes is shown to occur. We show a simulation of a plasma applicable to the proposed USTX experiment. The relevance to fusion experiments, in particular in the context of MHD spectroscopy, are discussed.