THz/Far Infrared synchrotron absorption experiments on pure and doped MgB2 samples show that the absorption spectral weight at low wavenumber (i.e., <110 cm-1) evolves as the temperature is reduced to 10 K. Distinct spectral peak intensities increase as the temperature of MgB2 and doped MgB2 approaches, and then crosses, the superconducting transition temperature. These experimental data suggest a strong link to superconductivity induced by subtle shifts in structural symmetry. Significant increases in absorption are observed at frequencies that correspond to the superconducting gaps for doped and pure MgB2, and at fractions of these frequency (or energy) values. This low wavenumber spectral transition is consistent with the notion that superlattice frequencies contribute to the optic modes of the MgB2 phonon dispersion and are critical to the superconducting transition for this structure. Key integer ratios are identified in real and reciprocal spaces that link bonding character, Fermi vectors and Fermi surfaces as well as phonon properties with geometric parameters and specific superlattice symmetries for MgB2. Similarly consistent spectral data at low wavenumber are also obtained for carbon doped Mg11B2. Density Functional Theory calculations of superlattice phonon dispersions result in folded mode frequencies that match these observed low wavenumber experiments. These results show that symmetry reductions, largely electronic in character although coupled to vibrations, occur with change in temperature and imply strong links to superconductivity mechanisms.