Quantum transport through an open periodic array of up to five dots is investigated in thepresence of a magnetic field. The device spectrum exhibits clear features of the bandstructure of the corresponding one-dimensional artificial crystal which evolveswith varying field. A significant magnetically controlled current flow is inducedwith changes up to many orders of magnitude depending on temperature andmaterial parameters. We propose a simple design for measuring with currenttechnology the magnetic subband formation of quasi one-dimensional Bloch electrons.