A lattice with long-range periodic order that has two or more periodicities in which an irrational number gives the ratio between the periodicities. An example of an incommensurate lattice occurs in certain magnetic systems in which the ratio of the magnetic period to the atomic lattice is an irrational number. The phase transition between a commensurate lattice and an incommensurate lattice can be analysed using the Frenkel–Kontorowa model. In the X-ray crystallography of crystals with an incommensurate lattice, the diffraction pattern and reciprocal lattice are characterized by four numbers, with the symmetries of these crystals having four-dimensional space groups.