The results of a (57)Fe Mössbauer spectroscopy study between 2.0 and 297 K of the parent compound Fe1.09Te and the superconductor FeSe0.4Te0.6 are reported. It is shown that in both compounds the magnitude of the quadrupole splitting increases with decreasing temperature and is well described by a T(3/2) power-law relation. The presence of incommensurate spin-density-wave antiferromagnetism in Fe1.09Te is demonstrated, with the Néel temperature T(N) = 71.1(6) K. A theoretical prediction (Zhang et al 2009 Phys. Rev. B 79 012506) of the Fe magnetic moment at the 2c sites being significantly larger than that at the 2a sites in the parent compound is confirmed experimentally by showing that these moments at 4.4 K are, respectively, 3.20(4) and 1.78(3) μ(B). The absence of magnetic order in FeSe0.4Te0.6 down to 2.0 K is confirmed. The Debye temperatures of Fe1.09Te and FeSe0.4Te0.6 are found to be 290(1) and 233(1) K, respectively.