In this paper the effective properties of a two-dimensional periodic binary magnetic system are studied. The magnetic system is composed by cobalt cylindrical dots embedded into a permalloy film. The dot diameter is 310 nm and the periodicity of the system is 600 nm. Since the dot diameter is smaller than the characteristic mode wavelength, it is possible to describe the collective excitations through effective quantities. In particular, for each collective mode an effective wavelength and a small effective wave vector not necessarily equal to the corresponding Bloch wavelength and Bloch wave vector can be defined. The introduction of these effective quantities characterizing collective mode dynamics allows us to describe the binary periodic magnetic system as a magnonic metamaterial.