Hugo Riemann

He wrote many pieces for piano, songs, a piano sonata, six sonatinas, a violin sonata, and a string quartet.

Riemann is one of the most influential music theorists. In his publications and lectures he coined various terms which are still in everyday use, such as functional harmony (therein popular terms such as the tonic, the dominant, the subdominant and the parallel). In addition, the term and theory of the metric and rhythmic phrase, a basic element of today's music education, originate in Riemann. Among his best-known works are the Musik-Lexikon (1882; 5th ed. 1899; Eng. trans., 1893–96), a complete dictionary of music and musicians, the Geschichte der musiktheorie im IX.-XIX. jahrhundert(1898), a history of music theory in Europe through the 19th century, 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. The Geschichte was widely used among lecturers of music for around half a century after it was written. In his book, he meticulously documented the development of polyphonic theory from the ancient times to the 16th century. With this, he concluded that common intervals heard in polyphonic music were used intuitively in folk practices due to the ostensibly "natural" element of these intervals. As he developed as a theorist, he focused more and more on human nature, using psychology as the basis of his ideas. His philosophical background exposed him to Pitagorean musical philosophy, which states that the natural harmony of the macrocosmos, or the world outside, is reflected in the microcosmos, or the world inside. 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. Thus, what humans feel when hearing music is alike the acoustical phenomenon of sympathetic resonance. He was an advocate of harmonic dualism, and his theory of harmonic function is the foundation of harmonic theory as it is still taught in Germany. 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. He authored many works on many different branches of music. His pupils included the German composer, pianist, organist, and conductor Max Reger and the musicologist and composer Walter Niemann.