In several of Frei Otto’s early membrane structures, acoustics was a rather relevant design aspect that could not be controlled through classical form-finding approaches based on physical models. Moreover, it is possible to add that, geometrically speaking, Frei Otto’s membranes could naturally perform acoustically, because of their anticlastic shape and the ability of the convex areas to scatter sound. In this paper, two of Frei Otto’s key projects are revisited and redesigned parametrically using mathematical optimisation: first, the Dance Pavilion that was conceived for the Federal Garden Exhibition in Cologne (1957); and, second, the large umbrellas that were built at the same venue in 1971. His architectural form of “necessity” represents the structural optimum, that is, a buildable technology, which can now be informed by other performance criteria, such as acoustics. The work described in this paper could show a possible way of expanding Frei Otto’s two-step design method, which was based on the sequential use of a form-finding model first – to literally “find” structural form – and then a technological model – to study the tectonic aspects of the structure and endow it with materiality. This paper was inspired by the rock set designs of Mark Fisher and – in particular – by the retractable umbrellas that Frei Otto designed, in 1977, for the second leg of Pink Floyd’s “In the Flesh Tour”, which was also known as the “Animals Tour”.