  The presence of possible correlations between stellar rotation rate $\Omega$
and the frequency of the activity cycle $\omega_\mathrm{cyc}$ is still much
debated. We implement a new Bayesian classification algorithm based on a
simultaneous regression analysis of multiple scaling laws and we demonstrate
the existence of two different scalings in the $\log_{10} \omega_\mathrm{cyc}$
-- $\log_{10} \Omega$ plane for an extended Mt.~Wilson sample of 67 stars.
Thanks to metallicity measurements obtained from both ESA Gaia and
high-resolution spectroscopy, we argue that the origin of this dichotomy is
likely related to the chemical composition: stars whose magnetic cycle
frequency increases with rotation rate are less metallic than stars whose
magnetic cycle frequency decreases with stellar rotation rates. On the
contrary, no clear difference in chromospheric magnetic activity indicators
characterizes the two branches.
