I accidentally came across the following while doing a Wikipedia search:

Explorers reported seeing aborigines jumping with vines in the 16th century. European boys started jumping rope in the early 17th century. The activity was considered indecent for girls because they might show their ankles. There were no associated chants. This changed in the early 18th century. Girls began to jump rope.^[1] They added the chants, owned the rope, controlled the game, and decided who participated.^[2]

Another source suggests that, prior to 1833, the invention of pantaloons, enabled girls to jump rope without displaying ankles.^[3]

These chants are unusual inasmuch as they were transmitted from child to child usually without an underlying reason, as opposed to nursery rhymes which were transmitted from adult to child and often contained a moral