The Origin of the Dominant: Schoenberg's ‘Strong Progression’ and the Realisation of Implied Virtual Pitches

Abstract

ABSTRACTIn major‐minor tonality, V implies I, and rising fourths, falling thirds and rising seconds between successive chord roots are more common than falling fourths, rising thirds and falling seconds respectively. Possible explanations involve history (in two‐part medieval counterpoint, harmonic major sixths resolved to octaves – maintained in V–I); the rising leading note (V–I includes it, IV–I does not); acoustic speculation (in V–I, the third harmonic of resolves to the second); voice leading (in V7–I, a tritone resolves to a third by contrary step); melodic closure (a rising melodic leap implies subsequent falling steps, and melodies often end with –, harmonised V–I); root newness (chords ‘progress’ if the second chord's root is not part of the first); and tonal stability (V is less stable than IV, giving it a stronger ‘urge’ to resolve). An additional possibility combines the ‘virtual‐pitch’ theory of Ernst Terhardt with the ‘implication‐realisation’ theory of Leonard B. Meyer and Eugene Narmour. Major and minor triads imply subsidiary virtual pitches (missing fundamentals; see Rameau's ‘fundamental bass’) at third and fifth intervals below the root. These weakly perceived pitches are realised in the next chord if the root falls by a third or rises a fourth or major second, creating a feeling of forward progression – while also facilitating intonation for singers and melodic instrumentalists. The theory correctly predicts that successive harmonic complex (but not pure) tones an octave apart sound more similar if rising, and rising octaves are more common than falling in melody. It also explains why Classical modulations are asymmetrical in the opposite direction, major keys tending to modulate to V (not IV) and minor to III (not VI): accidental flats tend to be more perceptually salient or stable than sharps.