Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. He was educated in theory by Frankenberger, studied the piano with Barthel and Ratzenberger, studied law, and finally philosophy and history at Berlin and Tübingen. After going through the Franco-German war he decided to devote his life to music, and studied accordingly at the Leipzig Conservatory. He then went to Bielefeld for some years as a teacher and conductor, but in 1878 returned to Leipzig as Privatdozent at the University.
As a much-desired appointment at the Conservatory did not materialize, Riemann went to Bromberg in 1880, but 1881-90 he was a teacher of piano and theory at Hamburg Conservatory. After a short time at the Sondershausen Conservatory, he held a post in the conservatory at Wiesbaden (1890-95), but eventually returned to Leipzig University as lecturer in 1895. In 1901, he was appointed professor.
In addition to his work as a teacher, lecturer and composer of pedagogical pieces, Riemann had a worldwide reputation as a writer on musical subjects. His best known works are Musik-Lexikon (1882; 5th ed. 1899; Eng. trans., 1893-96), a complete dictionary of music and musicians, the Handbuch der Harmonielehre, a work on the study of harmony, and the Lehrbuch des Contrapunkts, a similar work on counterpoint, all of which have been translated into English. One of his inventions, the Tonnetz, is the predecessor of the modern idea of pitch spaces, and is a fundamental analytical tool of the current field of neo-Riemannian theory.
He wrote many pieces for piano, songs, a piano sonata, six sonatinas, a violin sonata, and a string quartet.
See also 
- Riemannian theory
- Neo-Riemannian theory
- Chordal space
- Modulatory space
- Functional harmony
- Counter parallel
- Alexander Rehding: Hugo Riemann and the birth of modern musical thought. Cambridge: Cambridge University Press, 2003. ISBN 0-521-82073-1
- "Riemann, Hugo". New International Encyclopedia. 1905.