We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend our previous results [ Xuereb, Genes and Dantan Phys. Rev. Lett. 109 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes.