The 105 zero-wavevector vibrational modes of an infinite sodalite framework with atomic positions corresponding to the sodalites M(8)[Al6Si6O24]Cl-2 (M = Li, Na, K) and silica sodalite are calculated by the Wilson GF matrix method. Not all of the modes which are formally infrared or Raman active have significant spectral intensity, and point-charge or bond-polarizability models are used to generate synthetic infrared or Raman spectra in order to identify the modes which give rise to the observed bands. The synthetic spectra reproduce most of the features of the experimental spectra very satisfactorily, and for the aluminosilicate sodalites the wavenumbers of the bands are simulated to within 30 cm(-1). The changes in the spectra as the framework angles change along the series M = Li, Na, K are also well reproduced. This enables an extensive analysis of the spectra to be made, including the assignment of the symmetries of the modes, and is the first detailed interpretation of the vibrational spectra of a fairly complex aluminosilicate framework. The vibrational modes involved in the observed infrared and Raman bands are analyzed in terms of the contributions from the characteristic vibrations of the TO4 and four-ring or six-ring structural subunits of the aluminosilicate framework, and each of the modes is shown to involve large contributions from only a few of the symmetry coordinates of the four-ring or six-ring subunits. The analysis has identified new relationships between both the intensities and the frequencies in the spectra and structural features of the aluminosilicate framework, notably between the intensity of an infrared band near 750 cm(-1) and the Si-O-Al angle and between the intensity of a Raman band near 1000 cm(-1) and the degree of ordering of Si and Al atoms over the tetrahedral sites of the framework.