  The masses and radii of solar-like oscillators can be estimated through the
asteroseismic scaling relations. These relations provide a direct link between
observables, i.e. effective temperature and characteristics of the oscillation
spectra, and stellar properties, i.e. mean density and surface gravity (thus
mass and radius). These scaling relations are commonly used to characterize
large samples of stars. Usually, the Sun is used as a reference from which the
structure is scaled. However, for stars that do not have a similar structure as
the Sun, using the Sun as a reference introduces systematic errors as large as
10\% in mass and 5\% in radius. Several alternatives for the reference of the
scaling relation involving the large frequency separation (typical frequency
difference between modes of the same degree and consecutive radial order) have
been suggested in the literature. In a previous paper, we presented a reference
function with a dependence on both effective temperature and metallicity. The
accuracy of predicted masses and radii improved considerably when using
reference values calculated from our reference function. However, the residuals
indicated that stars on the red-giant branch possess a mass dependence that was
not accounted for. Here, we present a reference function for the scaling
relation involving the large frequency separation that includes the mass
dependence. This new reference function improves the derived masses and radii
significantly by removing the systematic differences and mitigates the trend
with $\nu_{\rm max}$ (frequency of maximum oscillation power) that exists when
using the solar value as a reference.
