  Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the
restriction $A''$ of $A$ to any hyperplane endowed with the natural
multiplicity is then a free multiarrangement. We initiate a study of the
stronger freeness property of inductive freeness for these canonical free
multiarrangements and investigate them for the underlying class of reflection
arrangements.
  More precisely, let $A = A(W)$ be the reflection arrangement of a complex
reflection group $W$. By work of Terao, each such reflection arrangement is
free. Thus so is Ziegler's canonical multiplicity on the restriction $A''$ of
$A$ to a hyperplane. We show that the latter is inductively free as a
multiarrangement if and only if $A''$ itself is inductively free.
