[2][3] After military service and being a prisoner of war in the United States, he studied voice with Gerhard Hüsch and choral conducting with Kurt Thomas.

[6] Among the composers who wrote music for the ensemble are Pierre Boulez, Brian Ferneyhough, Vinko Globokar, Gérard Grisey, Heinz Holliger, Mauricio Kagel, Helmut Lachenmann, György Ligeti, Krzysztof Penderecki, Steve Reich, Dieter Schnebel, and Hans Zender.

Notably, Gottwald conducted the Schola Cantorum in a performance of Ligeti's Lux aeterna, which was later used in the Stanley Kubrick film 2001: A Space Odyssey.

[7] He had the initial idea at a workshop of Pierre Boulez, "transcribing" Ravel's Soupir from his Trois poèmes de Mallarmé similarly to Ligeti's use of voices in Lux aeterna.

[8] In particular, his arrangement of Gustav Mahler's Rückert song "Ich bin der Welt abhanden gekommen" for voices (1985) was popularized by Swedish choral conductor Eric Ericson and has been performed by many leading choirs.