We analyze the phonon spectra of periodic structures formed by two-dimensional mixtures of dipolar colloidal particles. These mixtures display an enormous variety of complex ordered configurations [J. Fornleitner {it et al.}, Soft Matter {bf 4}, 480 (2008)], allowing for the systematic investigation of the ensuing phonon spectra and the control of phononic gaps. We show how the shape of the phonon bands and the number and width of the phonon gaps can be controlled by changing the susceptibility ratio, the concentration and the mass ratio between the two components.
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