The IR and Raman spectra of spessartine garnet Mn3Al2Si3O12, are simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The frequencies of the 25 Raman active modes (3 of A(1g), 8 of E-g and 14 of F-2g symmetry) and of the two sets of 17 F-1u transverse-optical and longitudinal-optical frequencies are generated, as well as the IR oscillator strength. The agreement between calculated and experimental data is excellent: for the IR and Raman sets, the mean absolute difference (vertical bar Delta vertical bar) over bar is 4.0 and 6.8 cm(-1), respectively. Isotopic substitution permits to highlight the Mn, Al and Si participation to the various zones of the spectrum. Graphical animation, available on the authors' web-site (http://www.crystal.unito.it/vibs/garnets/spessartine/), provides a very readable description of the movement of atoms and groups in each vibrational mode