A harmonic of a periodic complex tone can be heard out as a separate entity if the harmonic is slightly mistuned from its correct frequency. Pitch matching experiments show that the pitch of such a mistuned harmonic differs systematically from its frequency. The shift in pitch is found to be an exaggeration of the frequency mistuning. This article considers two classes of model for the pitch shift. In the first class are tonotopically local interaction models which attribute the pitch shift to interactions between the mistuned harmonic and neighboring harmonics, where the neighborhood is established by peripheral filtering. The second class of model attributes the pitch shift to a contrast between the mistuned harmonic and a broadband harmonic template. This article describes six pitch matching experiments using complex tones having spectral gaps, strategically chosen to compare local interaction and template models. The results show that when a competition is set up between local interactions and a template, the template proves to be dominant. A parallel between the pitch shifts of mistuned harmonics and periodicity pitch, also attributed to a harmonic template, is seen as the frequency range of the mistuned harmonic is changed. Tonotopically local influences are evident in several experiments, but they are of secondary importance.