In the winter semester 1910/11, Künneth joined the students' fraternity “Studentengesangverein Erlangen“, now “Akademisch-Musikalische Verbindung Fridericiana Erlangen“ (“Students' Choral Society Erlangen“, now “Akademic Musical Fraternity Fridericiana Erlangen“). He carried out a variety of posts during his studies as well as after having left university in 1914. He participated in the First World War and was captured by British forces. From 1923, he was a teacher at secondary schools in Kronach and Erlangen. After retiring, he became professor at the University of Erlangen.