Dualism (music theory)

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In music theory, dualism , also known as harmonic dualism , describes the view that the major and minor triads are categories of equal rank. In contrast, so-called "monistic" theories represent a priority position of the major triad, from which the minor triad is a derivative, for example by "clouding" the third of the major triad.

The term was coined by Arthur von Oettingen , who "for the harmony system a [...] dual, d. H. A twofold, contradicting form of development, which was manifested in a symmetrical structure of all tone structures and sound sequences. Accordingly, the major and minor triads arise from processes that are opposed to each other. This justifies their conception as structures that are symmetrical to one another.

In addition to Oettingen, Moritz Hauptmann , Hugo Riemann and Sigfrid Karg-Elert are also important representatives of dualistic theories . Since 1950, their approaches in German-language music theory have only been pursued in isolated cases. a. by Martin Vogel . In American music theory, however, there has recently been an increased interest in this tradition.


According to Hermann von Helmholtz , the minor triad is less consonant than the major triad. Arthur von Oettingen counters this by stating that the minor triad consonates not less, but differently. The major chord is said to be “tonic consonant”, whereby Oettingen defines the “tonicity” of an interval or a chord as its property “to be understood as a sound component of a fundamental”. The minor chord, on the other hand, is "phonic consonant", since its "phonic overtone" (defined as the lowest common overtone of the components of an interval or chord) consonates with the triad. Conversely, however, the major triad is "phonic dissonant", since its "phonic overtone" dissonates, while the minor triad is "tonic dissonant".

Oettingen describes minor chords according to their "phonic overtone": c – es – g receives the symbol g °, where g is the “main tone”, it is the “major third” and c is the “fifth”. On the other hand, he describes a major chord like c – e – g as c + :

<< \ new Staff \ with {instrumentName = \ markup {\ column {\ right-align {"phonic" "overtone"}}}} << \ set Score.tempoHideNote = ## t \ tempo 4 = 100 \ override Staff .TimeSignature.transparent = ## t \ relative c '' '' {\ ottava # 2 b'1 \ bar "||"  \ ottava # 1 g, \ bar "||"  } >> \ new Staff << \ override Staff.TimeSignature.transparent = ## t \ relative c '{<ce g> 1_ \ markup {c +} <c es g> 1_ "g °"} >> \ new Staff \ with {instrumentName = \ markup {\ column {\ right-align {"tonic" "root"}}}} << \ override Staff.TimeSignature.transparent = ## t \ clef "bass" \ relative c, {c1 \ ottava # -1 as,} >> >> \ layout {indent = 2.2 \ cm}
  • The tonic root of c + in the example is C , since the triad notes are interpreted as the 4th, 5th and 6th partial of this tone.
  • The tones of g ° are considered the partial tones 10, 12 and 15 of the tonic root As '.
  • The phonic overtone of c + is h '' '' as the 15th partial of c ', 12th partial of e ' and 10th partial of g '.
  • The phonic overtone of g ° g '' 'as the sixth partial tone of c' , the fifth partial tone of it ', and the fourth partial tone of g '.


Hugo Riemann derives the minor triad from an undertone series , which he sees as a reflection of the overtone series :

  \ new Staff {\ clef bass \ time 6/1 \ override Staff.TimeSignature.transparent = ## t \ relative c, {c1 ^ overtone series c 'g' \ clef treble ceg% Remove bar line at the end of the current line \ once \ override Score.BarLine.break-visibility = # '# (# f #t #t) \ break}}

  \ new Staff {\ time 6/1 \ override Staff.TimeSignature.transparent = ## t \ relative c '' '{e1 ^ undertone series e, a, eca% Remove bar line at the end of the current line \ once \ override Score.BarLine.break-visibility = # '# (# f #t #t) \ break}}

For a long time, Riemann was convinced that such a series of undertones could be heard. Instead, towards the end of his life, he presented a psychological rationale for her.

One consequence of this is u. a. that Riemann thinks of the minor triad as a “sub-tone” composed of a “prime”, “lower terez” and “lower fifth”. He describes the sound ace as " e lower sound " and takes over the symbol ° e from Oettingen (the " c upper sound" is also referred to as c + or simply c ) as in Oettingen . The sub-fifth of a sub-sound is still considered to be its “keynote”.

Sources and literature (chronological)

  • Moritz Hauptmann: The nature of harmony and metrics. Breitkopf and Härtel, Leipzig 1853 ( online ).
  • Hermann von Helmholtz: The theory of tone sensations as a physiological basis for the theory of music . Vieweg, Braunschweig 1863 ( online ).
  • Arthur von Oettingen: harmony system in dual development. Studies on the theory of music. Glasses, Dorpat / Leipzig 1866 ( online ); Revised second edition as: The dual harmony system. Leipzig 1913.
  • Hugo Riemann: Musical Syntaxis. Outline of a harmonic sentence formation theory . Breitkopf and Härtel, Leipzig 1877.
  • Hugo Riemann: Simplified harmony theory or the theory of the tonal functions of chords. 1893, 2nd edition Augener, London 1903 ( online ).
  • Hugo Riemann: The problem of harmonic dualism. Leipzig 1905.
  • Hugo Riemann: Ideas for a 'Doctrine of Sound Concepts' . In: Yearbook of the Music Library Peters 21, 1914, pp. 1–26.
  • Sigfrid Karg-Elert: Polaristic theory of sound and tonality. Leipzig 1930.
  • Dale Jorgenson: A Résumé of Harmonic Dualism . In: Music & Letters 44, 1963, pp. 31-42.
  • Martin Vogel (Hrsg.): Contributions to the music theory of the 19th century. Gustav Bosse Verlag, Regensburg 1966.
  • Daniel Harrison: Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents . University of Chicago Press 1994, ISBN 9780226318097 .
  • Henry Klumpenhouwer: Dualist tonal space and transformation in nineteenth-century musical thought . In: Thomas Christensen (Ed.): The Cambridge History of Western Music Theory . Cambridge University Press, Cambridge 2002, ISBN 978-0-521-62371-1 , pp. 456-476.
  • Alexander Rehding: Hugo Riemann and the birth of modern musical thought . Cambridge University Press, Cambridge 2003, ISBN 978-0-521-09636-2 .
  • Edward Gollin: Neo-Riemannian Theory . In: Journal of the Society for Music Theory 2 / 2-3 (2005), pp. 153–155 ( online ).
  • Andreas Jakubczik: The "harmonious dualism" from Arthur von Oettingen to Martin Vogel . GRIN, Munich 2005, ISBN 978-3-638-33969-8 .

Individual evidence

  1. Klumpenhouwer 2002, p. 459.
  2. Helmholtz 1863, pp. 451f.
  3. Oettingen 1866, IV.
  4. See also Jorgenson 1963, p. 31: "Harmonic dualism has been defined as a means of explaining the minor triad in a reverse sense from the explanation of the major triad."
  5. See e.g. B. Harrison 1994 and Gollin 2005.
  6. Helmholtz 1863, pp. 451f.
  7. Oettingen 1866, pp. 32–33, 45.
  8. Riemann 1877, p. 121. See u. a. Rehding 2003, p. 16.
  9. Riemann 1914.
  10. Riemann 1903, p. 11.
  11. Riemann 1903, p. 14. See also Elmar Seidel: Die Harmonielehre Hugo Riemanns . In: Vogel (Ed.) 1966, p. 45: "Significantly, Riemann never calls the reference tone (" main tone ") of the minor chord the root tone."

See also