  We find that the frequency spectra of layered phononic and photonic
composites admit a universal struc- ture, independent of the geometry of the
periodic-cell and the specific physical properties. We show that this
representation extends to highly deformable and multi-physical materials of
tunable spectra. The structure is employed to establish universal properties of
the corresponding band-gaps, and to rigorously determine their sta- tistical
and optimal characteristics. Specifically, we investigate the density of the
gaps, their maximal width and expected value. As a result, rules for tailoring
the laminate according to desired spectra properties follow. Our representation
further facilitates characterizing the tunability of the band-structure of soft
and multi-physical materials.
