A highly constrained iterative technique for the optimisation of non-periodic, (random and sparse) array geometries is presented. This approach involves establishing a set of array configurations which seek to minimise the peak sidelobe level of the array beampattern. The technique, harmonic array design, quickly produces a constrained set of near-optimal array solutions which can then be tried and tested. This is seen as an alternative to intensive computational search algorithms. Results of simulations for ten element linear non-periodic arrays are presented and their performance compared with equivalent periodic arrays. Such non-periodic arrays have the potential to offer improved angular resolution at a lower cost than periodic designs and have applications in all forms of acoustic and electromagnetic imaging. Here, the particular application of digital sonar beamforming is considered.