A common mechanism for the observed excitation of waves at sequential multiple ion cyclotron harmonics in the JET tokamak and in various space plasmas is proposed. It is suggested that, in each case, waves on the fast Alfvén-ion Bernstein branch are excited by the magnetoacoustic cyclotron instability, which is driven by an energetic ion distribution with a local maximum at v_⊥ 0, where v_⊥ is the velocity component perpendicular to the magnetic field.