The 27Al NMR spectra of powders of strontium chromate aluminate sodalite (SACr) and calcium tungstate aluminate sodalite (CAW) by the magic angle spinning (MAS) technique and of single-crystal SACr by a static method. It is shown that the precision in the detn. of the quadrupole coupling const. (qcc) from MAS spectra is limited by residual broadening. Both in SACr and in CAW Loewenstein's rule is violated, and the qcc's are among the largest found for Al in a tetrahedral site of an aluminosilicate framework, due to the strong tetragonal distortion that accompanies this violation. MAS spectra in cubic and tetragonal SACr are indistinguishable, compatible with a phase transition mainly due to conformational shearing of the four-membered rings of the framework. In the orthorhombic phases of CAW and SACr, at least four different Al-sites can be distinguished: the MAS spectra suggest that the Al sites in the two compds. are very similar. Due to the local character of the NMR information, this does not necessarily imply that they have the same space groups. The empirical relation between 27Al chem. shifts and bond angles established in (approx.) 1/1 aluminosilicates does not hold for these pure aluminates.