The inclusion of finite pressure in ideal magnetohydrodynamic theory can explain the reversed magnetic shear Alfvén eigenmodes (RSAE) (or Alfvén cascades) that have been observed in several large tokamaks without the need to invoke an energetic particle mechanism for the existence of these modes. The chirping of the RSAE is caused by changes in the minimum of the magnetic safety factor, qmin, while finite pressure effects explain the observed non-zero minimum frequency of the RSAE when qmin has a rational value. Finite pressure effects also play a dominant role in the existence of the downward chirping RSAE branch.