  In recent years the global seismic scaling relations for the frequency of
maximum power and for the large frequency separation have caught the attention
of various fields of astrophysics. With the exquisite photometry of
\textit{Kepler}, the uncertainties in the seismic observables are small enough
to estimate masses and radii with a precision of only a few per cent. Even
though this seems to work quite well for main-sequence stars, there is
empirical evidence, mainly from studies of eclipsing binary systems, that the
seismic scaling relations overestimate the mass and radius of red giants by
about 15 and 5\%, respectively. Model-based corrections of the $\Delta\nu
-$scaling reduce the problem but do not solve it. We re-examine the global
oscillation parameters of the giants in the binary systems in order to
determine their seismic fundamental parameters and find them to agree with the
dynamic parameters from the literature if we adopt nonlinear scalings. We note
that a curvature and glitch corrected $\Delta\nu_\mathrm{cor}$ should be
preferred over a local or average values. We then compare the observed seismic
parameters of the cluster giants to those scaled from independent measurements
and find the same nonlinear behaviour as for the eclipsing binaries. Our final
proposed scaling relations are based on both samples and cover a broad range of
evolutionary stages from RGB to RC stars: $g/\sqrt{T_\mathrm{eff}} =
(\nu_\mathrm{max}/\nu_\mathrm{max,\odot})^{1.0075\pm0.0021}$ and
$\sqrt{\bar\rho} = (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})[\eta -
(0.0085\pm0.0025) \log^2
(\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})]^{-1}$, where $g$,
$T_\mathrm{eff}$, and $\bar\rho$ are in solar units,
$\nu_\mathrm{max,\odot}=3140\pm5\mu$Hz and
$\Delta\nu_\mathrm{cor,\odot}=135.08\pm0.02\mu$Hz , and $\eta$ is equal to one
in case of RGB stars and $1.04\pm0.01$ for RC stars.
