  Continuing the work of \cite{7} and \cite{8}, we derive an analogue of the
classical "$k/12$-formula" for Drinfeld modular forms of rank $r \geq 2$. Here
the vanishing order $\nu_{\omega}(f)$ of one modular form at some point
$\omega$ of the complex upper half-plane is replaced by the intersection
multiplicity $\nu_{\bo}(f_1,\ldots,f_{r-1})$ of $r-1$ independent Drinfeld
modular forms at some point $\bo$ of the Drinfeld symmetric space $\OM^r$. We
apply the formula to determine the common zeroes of $r-1$ consecutive
Eisenstein series $E_{q^{i}-1}$, where $n-r<i<n$ for some $n \geq r$.
