The composer-performer collective l’Itinéraire, founded in 1973 by Murail and Tessier, was the de facto platform for spectral music in France. This chapter shows how l’Itinéraire formed with the aim of establishing an organ for the music of the youngest generation of French composers, and how, with the demise of Boulez’s Domaine Musical ahead of the opening of IRCAM, l’Itinéraire fortuitously found itself positioned as the successor to that Parisian new music series, endorsed by Messiaen and recipient of a state subsidy. The chapter details how Grisey composed Périodes, a l’Itinéraire commission and the first work composed from his Les Espaces acoustiques cycle, and how Grisey attended the acoustics laboratory at the Université Paris VI Jussieu, where, alongside lessons in musical acoustics, he absorbed the work of Abraham Moles on the application of information theory to art. The chapter also shows how Murail began to incorporate the models of spectral harmonicity and periodicity into his music from Tigres de verre onwards, and it explores the relationship of these instrumental compositional techniques to the computer sound synthesis work of Risset and Chowning.