Conditional Asymmetry and Spontaneous Asymmetry of Harmonic Progressions

The theory of harmonic vectors (THV) postulates that, of the six possible root progressions in a given tonality, those up a fourth, down a third, and up a second (+4, -3, +2) are present in significantly greater numbers than the complementary root motions down a fourth, up a third, and down a second (-4, +3, -2) (Meeùs 1988; 1989; 2000). This imbalance sheds light on a specific aspect of the tonal system (Meeùs 2001, 63). The progressions +4, -3, +2 arise almost accidentally in pre-tonal polyphony through the constraints of contrapuntal rules, but in later repertoires they become a decisive syntactical feature that actively constrains tonality. A model combining voice leading and harmonic progression is tested against a body of madrigal cycles by Verdelot, Arcadelt, Lassus, Rore, Wert, and Monteverdi. These cycles, published between c. 1530 and 1638, contain about 50,000 chord progressions, permitting a close examination of the phenomena that reflect the changing status of the prevalent root progressions, the technical aspects that may have fostered it, and the compositional possibilities that result from the evolution outlined.