Spin-wave excitations (magnons) are investigated in a one-dimensional (1D) magnonic crystal fabricated out of Ni80Fe20 nanowires. We find two different magnon band structures depending on the magnetic ordering of neighboring wires, i.e., parallel and antiparallel alignment. At a zero in-plane magnetic field H the modes of the antiparallel case are close to those obtained by zone folding of the spin-wave dispersions of the parallel case. This is no longer true for nonzero H which opens a forbidden frequency gap at the Brillouin zone boundary. The 1D stop band gap scales with the external field, which generates a periodic potential for Bragg reflection of the magnons.