A detailed analysis of the bound-state spectrum of HOCl (hypoclorous acid) in the ground electronic state is presented. Exact quantum mechanical calculations (filter diagonalization) are performed employing an ab initio potential energy surface, which has been constructed using the multireference configuration-interaction method and a quintuple-zeta one-particle basis set. The wave functions of all bound states up to the HO+Cl dissociation threshold are visually inspected in order to assign the spectrum in a rigorous way and to elucidate how the spectrum develops with energy. The dominant features are (1) a 2:1 anharmonic resonance between the bending mode and the OCl stretching mode, which is gradually tuned in as the energy increases, and (2) a saddle-node bifurcation, i.e., the sudden birth of a new family of states. The bifurcation is further investigated in terms of the structure of the classical phase space (periodic orbits, continuation/bifurcation diagram). It is also discussed how the spectrum of bound states persists into the continuum and how the various types of quantum mechanical continuum wave functions affect the state-specific dissociation rates.