Riemannian theory

For the mathematical conjecture, see Riemann hypothesis.
Illustration of Riemann's "dualist" system: minor as upside down major. Half-steps are indicated by slur marks, other notes are separated by whole steps. The descending melodic minor scale shown has the same order of half steps and whole steps as the ascending major scale.

Riemannian theory, in general, refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics, including musical logic,[1] notation,[2] harmony,[3] melody,[4] phraseology,[5] the history of music theory,[6] etc. More particularly, the term Riemannian theory often refers to his theory of harmony, characterized mainly by its dualism and by a concept of harmonic functions.

  1. ^ Musikalische Logik. Hauptzüge der physiologischen und psychologischen Begründung unseres Musik-systems, Leipzig, 1873.
  2. ^ Studien zur Geschichte der Notenschrift, Leipzig, 1878; Die Entwickelung unserer Notenschrift, Leipzig, 1881; Notenschrift und Notendruck, Leipzig, 1896.
  3. ^ Skizze einer neuen Methode der Harmonielehre, Leipzig, 1880; Handbuch der Harmonielehre, Leipzig, 1887; Vereinfachte Harmonielehre, London/New York, 1893.
  4. ^ Neue Schule der Melodik, Hamburg, 1883.
  5. ^ Katechismus der Phrasierung, Leipzig, 1890, 2d edition Vademecum der Phrasierung, 1900, 8th edition as Handbuch der Phrasierung.
  6. ^ Geschichte der Musiktheorie im IX.–XIX. Jahrhundert, Berlin, 1898.