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.
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.
Riemann's "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists. The term "dualism" refers to the emphasis on the inversional relationship between major and minor, with minor triads being considered "upside down" versions of major triads; this "harmonic dualism" (harmonic polarity) is what produces the change-in-direction described above. See also the related term utonality.[7]
Transformationsedit
In the 1880s, Riemann proposed a system of transformations that related triads directly to each other. Riemann's system had two classes of transformations: "Schritt" and "Wechsel".[7] A Schritt transposed one triad into another, moving it a certain number of scale steps. For example, the "Quintschritt" (literally "five-step" in a mixture of Latin and German) transposed a triad by a perfect fifth, transforming C major into G major (up) or F major (down). A Wechsel inverted a triad according to the Riemann's theory of dualism, mapping a major triad to a minor triad. For example, Seitenwechsel ("die Seiten wechseln" translates as "to exchange sides") mapped a triad on to its parallel minor or major, transforming C major to C minor and conversely.[7] Riemann's theory of transformations formed the basis for Neo-Riemannian theory, which expanded the idea of transformations beyond the basic tonal triads that Riemann was mostly concerned with.
^Musikalische Logik. Hauptzüge der physiologischen und psychologischen Begründung unseres Musik-systems, Leipzig, 1873.
^Studien zur Geschichte der Notenschrift, Leipzig, 1878; Die Entwickelung unserer Notenschrift, Leipzig, 1881; Notenschrift und Notendruck, Leipzig, 1896.
^Skizze einer neuen Methode der Harmonielehre, Leipzig, 1880; Handbuch der Harmonielehre, Leipzig, 1887; Vereinfachte Harmonielehre, London/New York, 1893.
riemannian, theory, mathematical, conjecture, riemann, hypothesis, general, refers, musical, theories, german, theorist, hugo, riemann, 1849, 1919, theoretical, writings, cover, many, topics, including, musical, logic, notation, harmony, melody, phraseology, h. For the mathematical conjecture see Riemann hypothesis 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 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 Contents 1 Dualism 2 Transformations 3 See also 4 SourcesDualism editRiemann s dualist system for relating triads was adapted from earlier 19th century harmonic theorists The term dualism refers to the emphasis on the inversional relationship between major and minor with minor triads being considered upside down versions of major triads this harmonic dualism harmonic polarity is what produces the change in direction described above See also the related term utonality 7 Transformations editIn the 1880s Riemann proposed a system of transformations that related triads directly to each other Riemann s system had two classes of transformations Schritt and Wechsel 7 A Schritt transposed one triad into another moving it a certain number of scale steps For example the Quintschritt literally five step in a mixture of Latin and German transposed a triad by a perfect fifth transforming C major into G major up or F major down A Wechsel inverted a triad according to the Riemann s theory of dualism mapping a major triad to a minor triad For example Seitenwechsel die Seiten wechseln translates as to exchange sides mapped a triad on to its parallel minor or major transforming C major to C minor and conversely 7 Riemann s theory of transformations formed the basis for Neo Riemannian theory which expanded the idea of transformations beyond the basic tonal triads that Riemann was mostly concerned with See also editSchenkerian analysis Undertone seriesSources edit Musikalische Logik Hauptzuge der physiologischen und psychologischen Begrundung unseres Musik systems Leipzig 1873 Studien zur Geschichte der Notenschrift Leipzig 1878 Die Entwickelung unserer Notenschrift Leipzig 1881 Notenschrift und Notendruck Leipzig 1896 Skizze einer neuen Methode der Harmonielehre Leipzig 1880 Handbuch der Harmonielehre Leipzig 1887 Vereinfachte Harmonielehre London New York 1893 Neue Schule der Melodik Hamburg 1883 Katechismus der Phrasierung Leipzig 1890 2d edition Vademecum der Phrasierung 1900 8th edition as Handbuch der Phrasierung Geschichte der Musiktheorie im IX XIX Jahrhundert Berlin 1898 a b c Klumpenhouwer Henry Some Remarks on the Use of Riemann Transformations Music Theory Online 0 9 1994 nbsp This music theory article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Riemannian theory amp oldid 1186602115, wikipedia, wiki, book, books, library,
