  We investigate the hierarchical structure of three-frequency resonances in
nonlinear dynamical systems with three interacting frequencies. We hypothesize
an ordering of these resonances based on a generalization of the Farey tree
organization from two frequencies to three. In experiments and numerical
simulations we demonstrate that our hypothesis describes the hierarchies of
three-frequency resonances in representative dynamical systems. We conjecture
that this organization may be universal across a large class of three-frequency
systems.
