The modification of phononic crystals by surface structuring allows obtaining a new parameter describing the dynamics of the structure produced in this way. We have investigated the dispersion relation of surface acoustic waves propagating in a phononic material which is based on nanometer-scale surface modulation using interconnected one-dimensional array of stripes and a two-dimensional array of pillars. The influence of these two array components on the dispersion relation has been determined experimentally (Brillouin light scattering) and theoretically (Finite Element Method). The interaction of these two nanostructures supports a new mode which is not observed in independent structures of pillars and stripes. The influence of the relative position of these two nanostructures on the frequency of the new mode has been determined.