There is also a dance to the same music called Contrapasso Nuovo, for three couples.
A version of this dance can also be found in Nobilta di Dame, where it is referred to as "Contrapasso to be danced in a circle". In the later version Caroso calls for the dance to be done by several couples in a circle, though the couples do not appear to interact with each other. He also makes many revisions to the steps, with references to how the original dance was "imperfect".
Nobilta di Dame
Translation
Terpsichore at the Tower XIV (PDF)
Del's Dance Book
Dragonscale Consort (CD)