" To Volgadon - I myself, just above, posted that very question and, apart from barber-shop songs (plus someone on another thread, I think, suggesting bawdy songs), we are still not sure..? It has, however, been said that they were very common in the taverns and barber-shops of 17th century England. Were traditionally unaccompanied English folk-songs SOMETIMES accompanied with a cittern, whilst courtly songs were accompanied on a lute..? "

WAV, the vast majority of music for the cittern is italianate. That is, cittern players were copying French/Italian court culture instead of putting their skills into the English tradition.
So, what we have here is a German instrument brought over to England by Italians and used to play songs in an Italian and French style. Why should it be any more a part of the 'tradition' than the electric guitar?

Maybe a cittern player strummed along to Barbarah Allen once in a rare while, but we do have many, many more recorded instances of Eng trad songs being played on electric guitar!!!!!