The current manuscript deals with the design of passive mechanical filters for vibration attenuation a low frequencies. Traditionally, this has been addressed employing dissipation as the attenuation mechanism. While such strategy provides broadfrequency effectiveness, attenuation at any given frequency is modest. Mass and stiffness-modulated periodic systems, on the other hand, exploit dispersion as the attenuation mechanism and represent an alternative to dissipation-based devices. Attenuation due to dispersion may be significantly higher than what is afforded by dissipation-based systems within a design frequency rage. The proposed assemblies, however, are not easily tailored to filter lowe-frequency vibrations. To this end, embedding such periodic systems into an elastic matrix yields a high-pass mechanical filter with tunable stop bands were waves are not allowed to propagate. Significant improvements in performance moreover may be obtained if intrinsically nonlinear devices are adopted. Specifically, a strongly nonlinear medium such as ordered granular media supports a limited number of waveforms, resulting in an efficient mechanical filter. Results reported here, in fact, suggest matrix-embedded sphere chains as highly tunable mechanical filters for vibration attenuation.