There are cases in pieces where the pitch of the basis of a mode changes slightly because of intermediate modulations during the piece. Chrysanthos claims that this is the case in Iakovos' Protopsaltis Doxastikon "To tritto tis erotiseos". The relevant part of Chrysanthos' "Mega Theoretikon" (p. 172) has been scanned here [jpg] by Georgios Michalakis. This page presents more information and recordings on this topic.