From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury

Abstract

Many Western art music composers have taken advantage of tabulated data for nourishing their creative practices, particularly since the early twentieth century. The arrival of atonality and serial techniques was crucial to this shift. Among the authors dealing with these kinds of tables, some have considered the singular mathematical properties of magic squares. This paper focuses on a particular case study in this sense: Philippe Manoury's Third String Quartet, entitled Melencolia. We mainly analyse mainly several strategies conceived by the French composer – through his own sketches – in order to manipulate pitches and pitch-classes over time. For that purpose, we take advantage of Klumpenhouwer networks as a way to settle wide and dense isographic relationships. Our hyper-K-nets sometimes reach a total of 32 arrows that allow geometrical arrangements as tesseracts in which their different dimensions cluster related families of isographies. In doing so, we aim to provide an instructive example of how to contextualise K-nets and isographies as powerful tools for the analysis of compositional practices.