Mathématiques de la musique idéale : Harmonie cosmique et proportions architecturales en Europe et aux États-Unis dans les années 1950-1960 - Jules-Valentin Boucher (Etudes Epistémè)
The idea that the proportions of a building are to be set on mathematical ratios that arise from musical harmony – itself being the image of a cosmic harmony inaudible to our mortal ears – was brought back to the forefront of the architectural scene in the fifties and sixties, in Europe and in the United States of America. At the same time, many composers questioned the twelve-tone equal temperament, and developed their own systems of octave division. In the first part, we will focus on Le Corbusier’s Modulor, a sizing system that aimed to standardize architectural beauty in a universal way. Iannis Xenakis used this system in his compositions, but for opposite purposes: his ambition was to put the music in tune with quantum physics and our relativistic cosmos. The composer John Cage, who was very interested in architecture, formulated a sharp criticism of the Modulor, the latter being contrary to his political convictions. We will then focus on North-American creators and, in the second part, on the ones who invented new proportional systems: first, John Cage, who was interested in the random aspect of chaosmos; Louis Kahn who, through his spiritual architecture, intended to express a higher order; Tony Smith, whose architecture and sculptures were also, but in a very different way, the expression of a cosmic order, notably through the use of three-dimensional modules. In the third part, we will take a closer look at some composers who have developed their own tuning systems, idiosyncratic expressions of their visions of the cosmos: Harry Partch, Lou Harrison and, finally, La Monte Young.