  Building on Pierre Simon's notion of distality, we introduce distality rank
as a property of first-order theories and give examples for each rank $m$ such
that $1\leq m \leq \omega$. For NIP theories, we show that distality rank is
invariant under base change. We also define a generalization of type
orthogonality called $m$-determinacy and show that theories of distality rank
$m$ require certain products to be $m$-determined. Furthermore, for NIP
theories, this behavior characterizes $m$-distality. If we narrow the scope to
stable theories, we observe that $m$-distality can be characterized by the
maximum cycle size found in the forking "geometry," so it coincides with
$(m-1)$-triviality. On a broader scale, we see that $m$-distality is a
strengthening of Saharon Shelah's notion of $m$-dependence.
