"I'll ask the question one last time, and of course we are talking here about songs (or tunes) written in the 'traditional idiom' or 'imitating' or 'influenced by the tradition' (Songs that maintain that tradition and keep it alive)"

Ignoring the obvious fact that there is no one "tradition", "Folkish" is a term from the late 1940s that seemed to work. As sis "Folk idiom"