[2][1] His uncle, Bernhard Dessau [de], was Konzertmeister at the Staatskapelle Berlin;[3] his cousin, Max Winterfeld, became known under the name Jean Gilbert as a composer of operettas;[2] and his second cousin, Robert Gerson Müller-Hartmann, was a composer and collaborator with Ralph Vaughan Williams.

[5] He studied the work of the conductors Felix Weingartner and Arthur Nikisch and took classes in composition from Max Julius Loewengard [de].

[2] After World War I he became conductor at the Kammerspiele Hamburg and was répétiteur and later Kapellmeister at the Cologne Opera under Otto Klemperer between 1919 and 1923.

[2] Dessau returned to Germany with his second wife, the writer Elisabeth Hauptmann, and settled in East Berlin in 1948.

[5] Starting in 1952, he taught at the Staatliche Schauspielschule (State drama school) in Berlin-Oberschöneweide where he was appointed professor in 1959.

At the same time he lobbied for the avant-garde music (e.g. Witold Lutosławski, Alfred Schnittke, Boris Blacher, Hans Werner Henze and Luigi Nono).