Detailed neutron scattering measurements of YBa2Cu3O6.95 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 approximately 41 meV to the spin gap of 33+/-1 meV. The other, of lower intensity, disperses from approximately 41 meV to at least 55 meV. Our results exclude a quartet of vertical incommensurate rods in q-omega space expected from spin waves produced by dynamical charge stripes as an origin of the observed incommensurate scattering in optimally doped YBCO.