  Resonant magnetic modes with odd and even symmetries were studied by
inelastic neutron scattering experiments in the bilayer high-$T_c$
superconductor $\rm Y_{1-x}Ca_{x}Ba_2Cu_3O_{6+y}$ over a wide doping range. The
threshold of the spin excitation continuum in the superconducting state,
deduced from the energies and spectral weights of both modes, is compared with
the superconducting d-wave gap, measured on the same samples by electronic
Raman scattering in the $B_{1g}$ symmetry. Above a critical doping level of
$\delta \simeq 0.19$, both mode energies and the continuum threshold coincide.
We find a simple scaling relationship between the characteristic energies and
spectral weights of both modes, which indicates that the resonant modes are
bound states in the superconducting energy gap, as predicted by the
spin-exciton model of the resonant mode.
