The theory of harmonic tension and resolution during the 20th century

Once the tonal system was overstepped, how did the composers solve the problem of ‘harmonic tension and resolution’? Why does a complex harmony create stress or quietness? What is the role of harmonic partials and what that of symmetries? How much does the context may change the perception of tension? What happens between chords and how to establish the degree of tension in the psychoacoustic shadow of the fi rst chord which fades into the second? Is it possible to calculate the vector of harmonic connection? How to get the maximal correlation of harmonic succession? How does the placement of the notes in acoustic space alter the synchronic tension? Is there a clear line of demarcation between consonance and dissonance? The concept of harmonic tension and resolution has intrigued music theorists and composers of all eras, but the radial explosion of numerous harmonic theories which began during the late 19th century created a basis for a diversifi ed contrast in positions, later resumed or thoroughly developed during the 20th century. The doctrinal progress that took place between the late 19th and early 20th centuries brought on a violent bifurcation. From then on, some composers and theorists pursued a strict analysis of symmetries while others explored the nuances of overtone harmony and timbre. Some of them focused their efforts on the theory of harmonic tension and resolution. The time has come to get answers and to acquire a perspective of the harmonic universe in its structural entirety.