A hink-pink for an incorrect melody could be "wrong song." In hink-pink riddles, the goal is to find a pair of rhyming words that describe a specific word or phrase. In this case, "wrong" and "song" rhyme and accurately describe an incorrect melody.
grim hymn
wrong song
wrong song
worn horn
lathering gathering is the hink pink for a group of men shaving
lunch bunch
a rank bank
news crews
news crews
Lunch Bunch.Lunch Bunch.
loud crowd
loud crowd
loud crowd
loud crowd
loud crowd
loud crowd