Applying knowledge of the interaction between heavy quarks derived from the study of \(c\overline{c}\) and \(b\overline{b}\) bound states, we calculate the spectrum of \(c\overline{b}\) mesons. We compute transition rates for the electromagnetic and hadronic cascades that lead from excited states to the \(^1\text{S}_0\) ground state, and briefly consider the prospects for experimental observation of the spectrum.