Baumgarten was born in Lübeck, and was a pupil of the organist Johann Paul Kunzen [de].
Haydn wrote in his diary that Baumgarten led "a sleepy orchestra".
[1] Carl Ferdinand Pohl wrote "he does not seem to have possessed the art of making use of his advantages, and was quickly forgotten.
"[3] Baumgarten's compositions include keyboard works, an oboe concerto, and six quartets for various instruments.
[2] He also wrote some material for the theatre, including the music for Carlo Antonio Delpini's Blue Beard (1791), the overture for Harlequin, Junior (Covent Garden 1784) and some of the music for Netley Abbey (Covent Garden 1794).