I am writing an instrumental orchestration of De Machaut's Messe de Nostre Dame, Kyrie. I found scores in IMSLP here and here.
These scores show accidentals above notes, sometimes in parenthesis. I am not sure how to treat those. Listening to performances, it seems that some are used and some are not, notably, the ones in parenthesis aren't while the ones without sound like "regular" accidentals before the note.
I believe that the harmony is hexachordal, however, any analysis I try to make in order to explain which accidentals should appear where fails at some point (can provide details if needed).
What are the rules for the accidental placements and their performance?
Also, in the first link, the score has "bridges" over groups of notes which I understood to be modernized ligatures. How should those be treated? (I can ask a separate question on this if requested.)
Edit: apparently Wikipedia has the answer.