My curiosity about the change in step vocabulary between the cotillons of the 1760s and 1770s and the quadrilles of the early 1800s has been further piqued by information from an additional source. I had heard of Josson’s Traité abrégé de la danse of 1763 – I had even seen and catalogued a copy in a private collection – but I had never really taken note of its contents. Catherine Turocy of the New York Baroque Dance Company drew my attention to the digital copy on Gallica, prompting me to take a proper look. Josson is probably best known for what he has to say about the minuet but his Traité also deals with ‘les différens pas & figures des contre-danses en usage’. At the time he was writing, I think we can assume that these contredanses were in fact cotillons.
Josson lists as the basic steps – ‘les pas dont on fait usage dans les Contre-danses’ – balancé, pas de rigaudon, pas de gavotte, chassés and pirouettes. He also describes how they should be performed and there are some interesting differences from what is said elsewhere, notably by De la Cuisse. I will not go into detail here, but I will mention the pas de gavotte. Josson’s version is not the same as that of De la Cuisse (who equates it to the demi-contretems). This is what Josson says (p. 77):

This isn’t the pas de gavotte I was taught in years past either – a contretems forwards or backwards followed by an assemblé into first position, with or without a pas marché to fill the upbeat – although it obviously relates to that pas composé.
My attention was also drawn to Josson’s supplementary list of steps (p. 81):

The entre-chat, sissonne brisé and jetté battu can claim to be steps for the stage, although there is evidence beyond Josson’s Traité they were also used in the ballroom. However, I am now wondering about the term brisé. So far as I know, it isn’t found in the early 18th-century treatises, although it certainly appears in Magri’s Trattato teorico-prattico di ballo as well as some of the various treatises on the cotillon and the quadrille. In the context of social dancing, what is a brisé? Also, why does Josson list the demi-contretems here? It presumably isn’t the step described by de La Cuisse as ‘le Pas fondamental de la Contredanse’ but something altogether more demanding.
Josson has upset my notion of the cotillon as a dance with a circumscribed step vocabulary in which the emphasis is on the figures. His Traité raises questions about the range of steps actually used in these contredanses. How could this showy vocabulary be fitted into the tight figures and relentless momentum of cotillons? We still have much to learn about these demanding little choreographies.