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Metzger studied piano under Carl Seemann in Freiburg and composition under Max Deutsch in Paris. Later, attending a summer course for new music in Darmstadt, he met Theodor W. Adorno, Edgard Varèse, Karlheinz Stockhausen and Luigi Nono. Here he found his role as a notable theoretician and proponent of Serialism in musical theory. He participated as a distinguished contributor to a series of important texts called Die Reihe. Metzger was among the first critics to promote Stockhausen's music, but was soon a substantial critic of Stockhausen's compositional development.
In the 1960s, Metzger was one of the first European commentators on John Cage, and spokesman of the movement called compositional Anarchy, which resulted in the so-called Kölner Manifest of 1960, and serving as a copy editor of the magazine Collage in Palermo. From 1965 until 1969 he worked as a music critic for the Zürcher Weltwoche (Zürich world weekly). In 1969, he founded, together with his partner, composer and conductor Rainer Riehn, the 'Ensemble Musica Negativa', where they embraced the performance of radical new music. In 1987, Metzger and Riehn became the chief dramatic advisors of the Frankfurt opera under Gary Bertini. During their tenure, the Frankfurt Opera commissioned and premiered John Cage's Europeras 1 & 2.
From 1977 to 2002 Metzger and Riehn founded, edited, researched, and provided texts criticism for the musicology series "Musik-Konzepte" (The concepts of music), Munich text+kritik-edition; for this they received the Deutscher Kritikerpreis (German critics prize) in 1983. Also, they edited the two first volumes of the Kompositionen von Adorno (Compositions of Adorno). Metzger has received honorary doctorates from the Berlin University of the Arts and from the University of Palermo.
- Musik wozu. Literatur zu Noten, with Rainer Riehn, Frankfurt a.M.: Suhrkamp 1980
- Die freigelassene Musik. Schriften zu John Cage, Rainer Riehn and Florian Neuner (editors), Wien: Klever Verlag 2012