  Kinetic mixing between the metric and scalar degrees of freedom is an
essential ingredient in contemporary scalar-tensor theories. This often makes
hard to understand their physical content, especially when derivative mixing is
present, as it is the case for Horndeski action. In this work we develop a
method that allows to write a Ricci curvature-free scalar field equation and
discuss some of the advantages of such rephrasing in the study of stability
issues in the presence of matter, the existence of an Einstein frame and the
generalization of the disformal screening mechanism. For quartic Horndeski
theories, such procedure leaves, in general, a residual coupling to curvature,
given by the Weyl tensor. This gives rise to a binary classification of
scalar-tensor theories into stirred theories, for which the curvature can be
substituted for, and shaken theories for which a residual coupling to curvature
remains. Quite remarkably, we have found that generalized DBI Galileons belong
to the first class. Finally, we discuss kinetic mixing in quintic theories for
which non-linear mixing terms appears and in the recently proposed theories
beyond Horndeski which display a novel form of kinetic mixing, in which the
field equation is sourced by derivatives of the energy-momentum tensor.
