The spectrum of n = 0 Alfven modes is calculated analytically and numerically in cylindrical and toroidal geometries. It includes global Alfven eigenmodes (GAEs) and surface modes (SMs) of the fast magnetoacoustic wave. These modes are not induced by toroidicity. The n = 0 GAEs owe their existence to shear. The frequency spacing between different radial and poloidal modes and the correlation of eigenfrequencies with changes in the edge density are examined and found to be in complete agreement with experimental observations of what have been named the 'Alfven frequency modes' (AFMs) so far (Chang, Z., et al., Nucl. Fusion 35 (1995) 1469). Although the eigenfrequency is related to the edge density, the n = 0 GAEs (AFMs) are not necessarily edge localized.