  Fermion mass models usually contain a horizontal symmetry and therefore fail
to predict the exponential mass spectrum of the Standard Model in a natural
way. In dynamical symmetry breaking there are different concepts to introduce a
fermion mass spectrum, which automatically has the desired hierarchy. In
constructing a specific model we show that in some modified gap equations
periodic solutions with several fermion poles appear. The stability of these
excitations and the application of this toy model are discussed. The mass
ratios turn out to be approximately $e^\pi$ and $e^{2\pi}$. Thus the model
explains the large ratios of fermion masses between successive generations in
the Standard Model without introducing large or small numbers by hand.
