We present a generic theoretical model for torque differential magnetometry (TDM) - an experimental method for determining the magnetic properties of a magnetic specimen by recording the resonance frequency of a mechanical oscillator, on which the magnetic specimen has been mounted, as a function of the applied magnetic field. The effective stiffness change, and hence the resonance frequency shift, of the oscillator due to the magnetic torque on the specimen is calculated, treating the magnetic specimen as a single magnetic domain. Our model can deal with an arbitrary magnetic free energy density characterizing the specimen, as well as any relative orientation of the applied magnetic field, the specimen and the oscillator. Our calculations agree well with published experimental data. The theoretical model presented here allows to take full advantage of TDM as an efficient magnetometry method. ; Comment: 15 pages, 6 figures