The average structure of a mullite, Al2(Al2+xSi2−2xO10−x with composition x = 0.40, has been determined by refinement of X-ray diffraction data. Because the mullite structure is incommensurate, the average structure contains information about the modulation in the form of apparently positionally disordered atoms. Although some such atom sites may be adequately described by split-atom models in the least-squares refinement procedure, very small displacements cannot be so described. In this study, third- and fourth-order tensors are used to describe two such oxygen sites. In addition to allowing these small displacements to be identified, the results of the refinement also provide further information regarding the occupancies of the two tetrahedral sites by Si and Al.