  In this paper we use observations of molecular tracers in metal rich and
alpha-enhanced galaxies to study the effect of abundance changes on molecular
chemistry. We selected a sample of metal rich spiral and star bursting objects
from the literature, and present here new data for a sample of early-type
galaxies (ETGs). We conducted the first survey of CS and methanol emission in
ETGs, detecting 7 objects in CS, and 5 in methanol emission. We find evidence
to support the hypothesis that CS is a better tracer of dense star-forming gas
than HCN. We suggest that the methanol emission in these sources is driven by
dust mantle destruction due to ionisation from high mass star formation, but
cannot rule out shocks dominating in some sources. The derived source averaged
CS/methanol column densities and rotation temperatures are similar to those
found in normal spiral and starburst galaxies, suggesting dense clouds are
little affected by the differences between galaxy types. Finally we used the
total column density ratios for our galaxy samples to show for the first time
that some molecular tracers do seem to show systematic variations that appear
to correlate with metallicity, and that these variations roughly match those
predicted by chemical models. Using this fact, the chemical models of Bayet et
al. (2012b), and assumptions about the optical depth we are able to roughly
predict the metallicity of our spiral and ETG sample, with a scatter of ~0.3
dex. We provide the community with linear approximations to the relationship
between the HCN and CS column density ratio and metallicity. Further study will
clearly be required to determine if this, or any, molecular tracer can be used
to robustly determine gas-phase metallically, but that a relationship exists at
all suggests that in the future it may be possible to calibrate a metallicity
indicator for the molecular interstellar medium (abridged).
