Envelopes of time: Drawing Boulez’s third milieu

Abstract

Abstract French composer Pierre Boulez first formulated the concepts of the ‘smooth and the striated’ in his musical oeuvre as an expression of his concerns regarding the interaction between continuous and discontinuous musical parameters referred to time and space. Later on, Deleuze and Guattari further established new applications for these ideas relating them to a wide range of non-musical purposes. However, several questions arise such as how the smooth-striated communicate, transform and remain different; is there a third space that intermingles with the system ‘smooth-striated’? And in this instance, how could it be visualized? In order to give answers to these questions, this article explores a third milieu, also introduced by Boulez: the ‘fixed’ space-time that would allow the perception of the communication between the ‘smooth and the striated’. Additionally, this article argues that there is a strong link between the ‘fixed’ and the Deleuzian diagrams, through which the musical concepts could be visualized, presenting a series of drawings as case studies developed using analogical and digital techniques.