Specht is most well-known for his writings on classical music, and in his time was seen as a leading music journalist. He was a great authority on the music of Gustav Mahler, and in later life became a regular acquaintance of his widow, Alma Mahler-Werfel.
He was, amongst other things, a contributor to the Wiener Illustrierten Extrablatts and other Viennese newspapers. From 1910, he worked at the Merker publishing house. In 1925, he was appointed to a professorship at the institution that is now the University of Music and Performing Arts, Vienna.