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Article Dans Une Revue Music Analysis Année : 2022

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

Résumé

Magic squares stand as some of the most popular objects in recreational mathematics. They probably first appeared in China-the earliest unambiguous reference dates from the first century CE (Cammann 1960, pp. 116-18). Although their origins were intrinsically rooted in religious and esoteric contexts, magic squares gradually became an autonomous mathematical entity. In particular, several Arabic treatises from the Middle Ages propounded fairly accurate algorithms which demonstrated how to build them (Sesiano 2017). These sources probably had an impact in Europe during the Renaissance, where they penetrated by way of Andalusia (Comes 2016), and later in the specific field of compositional practices. As the history of Western music reveals, many musicians of different periods, including those living in recent times, have allowed mysticism and occultism to nourish their theoretical conceptions. It is not surprising, therefore, that some of these musicians have dealt with magic squares for esoteric purposes (Hasler 2007). Conversely, many other composers have regarded tabulated data as a device which could help them clarify and objectify their musical practice. The source of this readiness is partly to be found in the research in combinatorics and music which arose in Europe during the seventeenth and eighteenth centuries (Knobloch 2001). To these combinatorial devices belongs dice music, which was mainly an amusement for dilettantes during the second half of the eighteenth century (Hedges 1978). Tabulated diagrams became less anecdotal, however, with the end of the common practice period, after which composers sought new methods to stimulate their creative thoughts. Latin and magic squares, as well as other related numerical constructions, are therefore found in several composers' sketches of the twentieth and twenty-first centuries. A representative but non-exhaustive list of European composers includes
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hal-03872865 , version 1 (25-11-2022)

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José L Besada, Corentin Guichaoua, Moreno Andreatta. From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury. Music Analysis, 2022, 41 (1), pp.145 - 182. ⟨10.1111/musa.12176⟩. ⟨hal-03872865⟩
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