  Commensurate scale relations are perturbative QCD predictions which relate
observable to observable at fixed relative scales, independent of the choice of
intermediate renormalization scheme or other theoretical conventions. A
prominent example is the "generalized Crewther relation" which connects the
Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to
measurements of the $e^+ e^-$ annihilation cross section. Commensurate scale
relations also provide an extension of the standard minimal subtraction scheme
which is analytic in the quark masses, has non-ambiguous scale-setting
properties, and inherits the physical properties of the effective charge
$\alpha_V(Q^2)$ defined from the heavy quark potential. I also discuss a
property of perturbation theory, the "Abelian correspondence principle", which
provides an analytic constraint on non-Abelian gauge theory for $N_C \to 0.$
