The pitches in alternate tuning systems like JI and maqam are sometimes, but not always, denoted with extra information. Quarter-flats, cent indicators, and so on, distinguish the note-pitch representations. While tuning systems can indeed be transposed or converted to unmodified standard (ET) staff notation, that's more of a convenience that has its own learning curve.

So, in JI you wouldn't simply use 'A' to represent (e.g.) 440Hz, it might be A 4, for the "A" key (or "A" staff position) having a 4 cent difference than ET A.[1]

1. http://lilypondblog.org/wp-content/uploads/2015/11/example.p...