"Spiral" was composed in Madison, Connecticut in September 1968 and was premiered on 15 May 1969 at the Muzički Biennale Zagreb, with the oboist Heinz Holliger as the soloist. Holliger performed it subsequently in Saint-Paul de Vence, and on 10 July 1969 at the Cheltenham Music Festival. Between 14 March and 14 September 1970, "Spiral" was given 1300 times at Expo '70 in Osaka, Japan, in daily performances by twenty different musicians including the composer. The score is dedicated to the other nineteen: the six singers of the Collegium Vocale Köln (Dagmar Apel, Gaby Rodens, Helga Albrecht, Wolfgang Fromme, Siegfried Bernhöft, and Hans Alderich Billig), and instrumentalists David C. Johnson (flute with synthesizer), Michael Vetter (electric recorder), Edward Tarr (trumpet), Karlheinz Böttner (electric guitar), Christoph Caskel and Michael Ranta (percussion), Rolf Gehlhaar (tamtam), (electronium and piano), Peter Eötvös (55-chord and piano), Gérard Frémy and Aloys Kontarsky (piano), Johannes Fritsch (electric viola), and Mesías Maiguashca (sound direction).