  An empirically successful mass formula derived long ago from hadronic string
models is not explained by symmetries of the QCD lagrangian. Consider that
M(rho)^2-M(pi)^2 = M(K*)^2-M(K)^2 to a few percent accuracy. We derive this and
other equal spacing relations using chiral symmetry and a novel Z_2 symmetry.
We offer an interpretation of this Z_2 symmetry as a manifestation of chiral
anomalies in a gauge theory with an intrinsic cutoff.
