Sixteenth-century Europe had many improvisatory genres of dance, and sixteenth-century Italy was no exception.
The popularity of the passo e mezo, tordiglione and canario were outmatched only by that of the gagliarda. The corranto, nizzarda, and alemana, though scantily described in our sources, also deserve a spot here. If only there were any description of the calata!
These dances survive both as choreographies and as selections of mutanze and passeggii. It seems that contemporary dancers would use the standard format (of which the written choreographies are exemplars, by notable dance-masters) but supplement them with their own mutanze, whether learned in advance or invented on the fly.