If you include "anything that has been through the folk process"--i.e. anything that has been anonymously altered from the original and taken up by others, then your spoof jingles qualify; so do soccer chants, traditional songs/tunes, children's songs and so on. We can avoid unpleasantness by recognising "contemporary" songs/tunes as being by known writers/composers. A contemporary song can get folk-processed too, copyright considerations notwithstanding (you could get sued--eek!)

Steve