  Athanasiadis studied arrangements obtained by adding shifted hyperplanes to
the braid arrangement. Similarly, Bailey studied arrangements obtained by
adding tilted hyperplanes to the braid arrangement. These two kinds of
arrangements are associated with directed graphs and their freeness was
characterized in terms of the associated graphs. In addition, there is
coincidence of freeness. Namely, if Athanasiadis' arrangement is free, then the
corresponding Bailey's arrangement is free, and vice versa.
  In this paper, we generalize this phenomenon by using gain graphs.
