  The magnetic properties of CuO encompass several contemporary themes in
condensed matter physics, including quantum magnetism, magnetic frustration,
magnetically-induced ferroelectricity and orbital currents. Here we report
polarized and unpolarized neutron inelastic scattering measurements which
provide a comprehensive map of the cooperative spin dynamics in the low
temperature antiferromagnetic (AFM) phase of CuO throughout much of the
Brillouin zone. At high energies ($E \gtrsim 100$\,meV) the spectrum displays
continuum features consistent with the des Cloizeax--Pearson dispersion for an
ideal $S=\frac{1}{2}$ Heisenberg AFM chain. At lower energies the spectrum
becomes more three-dimensional, and we find that a linear spin-wave model for a
Heisenberg AFM provides a very good description of the data, allowing for an
accurate determination of the relevant exchange constants in an effective spin
Hamiltonian for CuO. In the high temperature helicoidal phase, there are
features in the measured low-energy spectrum that we could not reproduce with a
spin-only model. We discuss how these might be associated with the
magnetically-induced multiferroic behavior observed in this phase.
