Block copolymer (BCP) self-assembly is of great interest as a cost-effective method for large-scale, high-resolution nanopattern fabrication. Directed self-assembly can induce long-range order and registration, reduce defect density, and enable access to patterns of higher complexity. Here we demonstrate preferential orientation of two incommensurate BCP dot arrays. A bottom layer of hexagonal silica dots is prepared via typical self-assembly from a PS-b-PDMS block copolymer. Self-assembly of a second, or top, layer of a different PS-b-PDMS block copolymer that forms a hexagonal dot pattern with different periodicity results in a predictable moir\ue9 superstructure. Four distinct moir\ue9 superstructures were demonstrated through a combinat...