Detailed neutron scattering measurements of YBa_2Cu_3O_6.95 found that the resonance peak and incommensurate magnetic scattering induced by superconductivity represent the same physical phenomenon: two dispersive branches that converge near 41 meV and the in-plane wave-vector q_af=(pi/a, pi/a) to form the resonance peak. One branch has a circular symmetry around q_af and quadratic downward dispersion from ~41 meV to the spin gap of 33+-1meV. The other, of lower intensity, disperses from ~41 meV to at least 55 meV. Our results exclude a quartet of vertical incommensurate rods in q-w space and are incompatible with dynamical magnetic stripes as an origin of the observed incommensurate scattering in optimally-doped YBCO.