[3] His career as a soloist started in 1964 when he won first prize in the ARD International Music Competition in Munich.

[1] Baumann taught at the Folkwang Hochschule in Essen from 1969[3] for 30 years[1][2] and at horn conventions around the world.

[1][3] The quality of human singing was partly achieved by a specific vibrato, adequate in lyrical passages.

1 by Richard Strauss for the broadcaster WDR with the Kölner Rundfunk-Sinfonieorchester conducted by Günter Wand in 1975; it was later issued on CD.

[4] His 1985 recording of Villanelle by Paul Dukas in an arrangement by Vitaly Bujanovsky, with the Gewandhaus Orchestra conducted by Masur, was included in 2002 in a collection The World of the French Horn.

[5] He was the hornist in the world premiere and first recording of Ligeti's 1982 Horn Trio, with violinist Saschko Gawriloff and pianist Eckart Besch who had commissioned the work.

[11] He recorded chamber music in 1977, evening songs and love songs (Abendlieder, Liebeslieder und Romanzen) sung by Klesie Kelly and Ian Partridge, and other instrumental soloists, clarinetist Dieter Klöcker, bassoonist Karl-Otto Hartmann and pianist Werner Genuit.