  We consider the radiation of three soft gluons in a generic process for
multiparton hard scattering in QCD. In the soft limit the corresponding
scattering amplitude has a singular behaviour that is factorized and controlled
by a colorful soft current. We compute the tree-level current for triple
soft-gluon emission from both massless and massive hard partons. The
three-gluon current is expressed in terms of maximally non-abelian irreducible
correlations. We compute the soft behaviour of squared amplitudes and the
colour correlations produced by the squared current. The radiation of one and
two soft gluons leads to colour dipole correlations. Triple soft-gluon
radiation produces in addition colour quadrupole correlations between the hard
partons. We examine the soft and collinear singularities of the squared current
in various energy ordered and angular ordered regions. We discuss some features
of soft radiation to all-loop orders for processes with two and three hard
partons. Considering triple soft-gluon radiation from three hard partons,
colour quadrupole interactions break the Casimir scaling symmetry between
quarks and gluons. We also present some results on the radiation of four soft
gluons from two hard partons, and we discuss the colour monster contribution
and its relation with the violation (and generalization) of Casimir scaling. We
also compute the first correction of ${\cal O}(1/N_c^2)$ to the eikonal formula
for multiple soft-gluon radiation with strong energy ordering from two hard
gluons.
