Hugo Riemann was educated by Heinrich Frankenberger, the Sondershausen Choir Master, in Music theory.

After participating in the Franco-Prussian 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 a visiting professor ("Privatdozent") at the University.

In addition, the term and theory of the metric and rhythmic phrase, a basic element of today's music education, originate in Riemann.

The feelings generated by sounds and chords are just an intuitive rediscovery of a reality, a mathematical harmony, that is already there in the human being.

He also elaborated a set of harmonic transformations that was adapted by the American theorist David Lewin, and eventually evolved into a significant strain of neo-Riemannian theory.

Another pillar of modern neo-Riemannian theory, the Tonnetz, was not Riemann's own invention, but he played an important role in popularizing and disseminating it.