The discrimination between atomic species in light-element materials is a challenging question. An archetypal example is the resolution of the Al/Si ordering in aluminosilicates. Only an average long-range order can be deduced from powder X-ray or neutron diffraction, while magic-angle-spinning NMR provides an accurate picture of the short-range order. The long- and short-range orders thus obtained usually differ, hence raising the question of whether the difference between local and extended orders is intrinsic or caused by the difficulty of obtaining an accurate picture of the long-range order from diffraction techniques. In this communication we resolve this question for the monoclinic phases of BaAl2Si2O8 and SrAl2Si2O8 on the basis of 27Al NMR measurements and ab initio simulation of electric field gradient. Although the long- and short-range orders deduced from our XRD and NMR experiments differ, they become similar when the XRD atomic positions are optimized by ab initio electronic structure calculations.