A co-analytic maximal set of orthogonal measures

We prove that if $V=L$ then there is a ${\mathrm{\Pi }}_1^1$ maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known Theorem of Preiss and Rataj that no analytic set of measures can be maximal orthogonal.