A novel method for tuning the orbital angular momentum (OAM) content of a vortex beam is presented. This approach makes use of the shaping of the odd and even components of the helical phase profile associated to the vortex. A relative azimuthal shift of the components results in the harmonic variation of the magnitude of the OAM density of the beam. We calculate the OAM content and show that for a beam with a vortex of topological charge m, the OAM per photon per unit length can be tuned continuously from (formula available in manuscript). We also observe the experimental propagation of the beam and compare the propagation parameters to our theoretical predictions.