  We study the class of four-dimensional N=4 supergravities obtained by gauging
the axionic shift and axionic rescaling symmetries. We formulate these theories
using the machinery of embedding tensors, characterize the full gauge algebras
and discuss several specific features of this family of gauged supergravities.
We exhibit in particular a generalized duality between massive vectors and
massive two-forms in four dimensions, inherited from the gauging of the shift
symmetry. We show that these theories can be deduced from higher dimensions by
a Scherk-Schwarz reduction, where a twist with respect to a non-compact
symmetry is required. The four-dimensional generalized duality plays a crucial
role in identifying the higher-dimensional ascendent.
