We experimentally study the phase behaviour of a charge-stabilized two-dimensional colloidal monolayer which is subjected to a one-dimensional quasiperiodic substrate potential. Upon increasing the laser intensity, we observe a transition from a periodic to a quasiperiodic state. It proceeds via the formation of an intermediate periodic average structure (PAS) which is related to the quasiperiodic lattice by a bounded 1-1 mapping. Because PAS can transform to crystals and quasicrystals by minute particle displacements, they provide a mechanism to allow for interesting insights into the relationship between periodic and quasiperiodic order.