In multifrequency atomic force microscopy higher eigenmodes are externally excited to enhance resolution and contrast while simultaneously increasing the number of experimental observables with the use of gentle forces. Here, the implications of externally exciting multiple frequencies are discussed in terms of cantilever anharmonicity, fundamental period and the onset of subharmonic and superharmonic components. Cantilever anharmonicity is shown to affect and control both the observables, that is, the monitored amplitudes and phases, and the main expressions quantified via these observables, that is, the virial and energy transfer expressions which form the basis of the theory.