By the end of the 1970s, the spectral composers were being invited to speak at the Darmstadt Summer Courses and were enjoying favourable press coverage in France. Recognising the need for a common epithet for their musical movement, they discussed a few possibilities: ’spectral’, ’liminal’, and ’vectorial’. This chapter explores, in turn, Dufourt’s concept of spectral music, which signified a compositional approach recognising and drawing on the microscopic scale of sound as the composer’s true material; Murail’s more technical vision of spectral music, and how, at IRCAM from the beginning of the 1980s, beginning with the electroacoustic work Désintégrations, Murail developed a sophisticated music drawing on computational resources; and Grisey’s notion of écriture liminale, a psychoacoustics-informed approach to compositional writing based on blurred statistical parameters and musical mutation. The chapter ends by detailing how the Darmstadt Summer Courses in 1982, at which the composers of l’Itinéraire gave a joint seminar, were the end of their common movement and the beginning of spectral music as an internationally known compositional attitude.