It is shown experimentally that collective Bloch spin waves are able to propagate in a dense periodic array of nanowires with step-modulated thickness along the periodicity direction. The spin wave dispersion (frequency versus wave vector k) was measured using the Brillouin light scattering technique by sweeping the wave vector perpendicularly to the wire length. Remarkably, the mode measured at the lowest frequency exhibits an oscillating dispersion and its frequency is up-shifted with respect to the homogeneous-thickness wires of the same width. The modes located at higher frequencies have negligible dependencies on the wave number, i.e. are practically dispersionless. Complementary ferromagnetic resonance measurements enabled us to independently measure the whole set of modes at k = 0, showing a good agreement with the Brillouin light scattering data. These results have been successfully reproduced in a numerical simulation employing a two-dimensional Green's function description of the dynamic dipole field of the precessing magnetization. The theory also allowed visualizing the non-trivial distribution of dynamic magnetization across the wire cross-section and estimating the Brillouin light scattering cross-section. The analysis of these intensities suggests complicated magneto-optical coupling between the light and the dynamic magnetization in the arrays of nanowires with step-modulated thickness. This work can stimulate the design, tailoring, and characterization of three-dimensional magnonic crystals. © 2014 IOP Publishing Ltd.