Novel tetrachiral honeycomb structures are evaluated for the first time from the vibroacoustic point of view. A numerical method based on Bloch wave approximations for Finite Element models of the unit cells is applied to simulate the pass-stop band characteristics of these cellular solids. Experimental modal analysis and modal densities are measured on honeycomb panels and sandwich plate, and the results evaluated with the experimental findings. The novel tetrachiral honeycombs show pass-stop band characteristics with isotropic acoustic signature, while sandwich structures made with the same honeycomb cores have the interesting feature of presenting a high-pass frequency behavior on the same pass-stop bands of the honeycomb.