  The structural distortion and magnetoelastic coupling induced through
commensurate magnetism has been investigated by neutron diffraction in
structurally related MnWO$_4$ and NaFe(WO$_4$)$_2$. Both systems exhibit a
competition of incommensurate spiral and commensurate spin up-up-down-down
ordering along the magnetic chains. In the latter commensurate phases, the
alternatingly parallel and antiparallel arrangement of Fe$^{3+}$ respectively
Mn$^{2+}$ moments leads to sizeable bond-angle modulation and thus to magnetic
dimerization. For NaFe(WO$_4$)$_2$ this structural distortion has been
determined to be strongest for the low-field up-up-down-down arrangement, and
the structural refinement yields a bond-angle modulation of $\pm 1.15(16)$
degrees. In the commensurate phase of MnWO$_4$, superstructure reflections
signal a comparable structural dimerization and thus strong magneto-elastic
coupling different to that driving the multiferroic order. Pronounced
anharmonic second- and third-order reflections in the incommensurate and
multiferroic phase of MnWO$_4$ result from tiny commensurate fractions that can
depin multiferroic domains.
