  If F is a master function corresponding to a hyperplane arrangement A and a
collection of weights y, we investigate the relationship between the critical
set of F, the variety defined by the vanishing of the one-form w = d log F, and
the resonance of y. For arrangements satisfying certain conditions, we show
that if y is resonant in dimension p, then the critical set of F has
codimension at most p. These include all free arrangements and all rank 3
arrangements.
