The work contains the usual five numbers of the quadrille as they were standardized in the early 19th century, plus a specific genre dance appended, as was the custom in published quadrilles at least through mid-century. In this case it's a galop; it might also have been a waltz or, after 1840, a polka.
The interesting feature of Hünten's quadrille is that the alternate strains in all five numbers are varied when repeated but the refrain (first strain) is not. The design of each number is ABACABACA. This provides 72 bars of music for the dance, or 8 for the promenade and 64 for the figures. See the graphic below for incipits of the refrain, B, C, and the variants of B & C.
I suspect that the composer is duplicating a common practice of performers (most often pianists) in house balls and similar dancing occasions (as with the post-Schubertiade dancing of Schubert's friends, for example). The unembellished refrain provides a stable guidepost for the design -- and therefore for the dancing -- while the variations on the alternate strains not only provide additional contrast with the refrain but also reflect what a creative (or bored) pianist very probably did in the course of dancing that could go on for a half hour to an hour at a time.
