We prove that if V=L then there is a Π11 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.
"A co-analytic maximal set of orthogonal measures." J. Symbolic Logic 75 (4) 1403 - 1414, December 2010. https://doi.org/10.2178/jsl/1286198154