  We perform a benchmark study of the step scaling procedure for the ratios of
renormalization constants extracted from position space correlation functions.
We work in the quenched approximation and consider the pseudoscalar, scalar,
vector and axial vector bilinears. The pseudoscalar/scalar cases allow us to
obtain the non-perturbative running of the quark mass over a wide range of
energy scales - from around 17 GeV to below 1.5 GeV - which agrees well with
the 4-loop prediction of continuum perturbation theory. We find that step
scaling is feasible in X-space and we discuss its advantages and potential
problems.
