Klengel was born in Leipzig, and studied with Emil Hegar in his youth. His father was a lawyer and an amateur musician, and was friend of Mendelssohn.[2] After his 15th birthday, Klengel joined the Leipzig Gewandhaus Orchestra where Klengel played first cello, and began touring in Europe and Russia. Klengel also became a soloist at that point, frequently giving solo performances.
Klengel rose to become principal cellist of the orchestra, aged 22, in 1881.[2] There he remained for over four decades: to celebrate his fifty years of service, Wilhelm Furtwängler conducted a jubilee concert, in which Klengel played the cello part in a double concerto he composed for the occasion. During that time period, Klengel became professor at the Leipzig Conservatory, where he was briefly a member of Adolph Brodsky's string quartet,[3] and began composing. He ultimately composed hundreds of pieces for the cello, including four cello concertos, two double cello concertos, cello quartets, a cello sonata, as well as numerous caprices, etudes and other technical pieces. Of his music, the two volumes of etudes ("Technical Studies") for cello remain in the repertory; three concertos were recorded in 2000 by Christoph Richter and NDR Radiophilharmonie under Bjarte Engeset.
^*Ginsburg, Lev (1983). "Cellists of the Viennese School and Other German Cellists of the 19th century, German Violoncellists of the end of the 19th and the beginning of the 20th century". In Axelrod, Herbert R. (ed.). History of the Violoncello. Translated by Tchistyakova, Tanya. Neptune City, New Jersey: T.F.H. Publications. p. 76. ISBN978-0-87666-597-8. In 1889, [Klengel] was invited to Russia as a member of the famous Brodsky Quartet of Leipzig ... the four concerts of the Quartet [were] given excellent reviews in the Russian press. The program of the series featured works by Haydn, Mozart, Beethoven, Schumann, Grieg, Rubenstein and Tchaikovsky. The Tchaikovsky Trio was played by Tanjeef, Brodsky, and Klengel.