Perspectives of chord classification

Since ancient times, music theorists have been trying to classify intervals. The original approach is based on the relative simplicity of vibration ratios. Intervals whose ratios could be derived from the Tetraktys, i.e. which could be represented by the numbers 1 to 4, were classified as perfect and thus delimited. In the octave frame this concerns the octave itself (ratio 2:1), the fifth (3:2) and the fourth (4:3). This model was adapted by the theorists of the Middle Ages. The Tetraktys intervals were termed perfect consonances; the other consonances, major and minor thirds, major and minor sixths, were termed imperfect consonances. Opposed to the consonances, the remaining intervals werde termed dissonant: minor and major second, minor and major seventh, and the tritone. Throughout the centuries, the distinction between perfect and imperfect consonances weakened. The opposition of consonance and dissonance, on the other hand, developed into a central means of representing major-minor tonality with its harmonics based on the triadic model. As a result of this development, the term consonance was also applied to the major and minor triads.

From the perspective of major-minor tonality, dissonance is a chordal tension striving to dissolve into consonance. Thus, terminology moves away from its origins even more than it might seem at first sight. The criterion of dissolution is not a purely acoustic, but above all a semantic one. It evaluates the chord in dependence of its context. As a result, the triad e-g-c is classified as consonant in the function first inversion of the C major triad, but as dissonant in the interpretation of Neapolitan E minor. The triad g-c-e is labeled consonant in the function second inversion of the C major triad, but as a dominant sixth-fourth chord, it is a distinct dissonance due to the double suspension.

As long as music unfolds within the framework of the classical-romantic patterns, the immanent category error even allows heuristic gain, because composers like to juggle with the ambivalence of functional chords. A new situation arises when the concept of the dissolution of the semantic category dissonance is put up for discussion. Arnold Schönberg describes this process as the emancipation of dissonance, but argues from the perspective of the classical concept: dissonance in itself is not emancipatable.

In the 19th century, counter-designs to the aesthetics of tonal consolidation gained in importance. The spectrum extends from the concealment of the tonal intention to the tonal questioning to the temporary or even complete suspension of the tonal orientation. In order to be able to take this development into account, a procedure is needed to break down the respective tonal disposition. Instead of developing an awareness of the challenge that arises from this, music theory has limited itself to a descriptive approach, vaguely distinguishing between tonality, atonality and some area of transition. This is just as ineffective as the equation of atonality and dissonance that is sometimes encountered: the criterion of consonance or dissonance is irrelevant for determining a tonal steering effect. Ci-analysis starts at this point. It identifies complementary intervals (ci) as creators of the tonal space of possibilities: the ci minor second/major seventh, minor third/major sixth, fourth/fifth are suitable for tonal steering effects, the other intervals are not. Starting from the interval as a basic tonal building block, the tonal potential of a more complex chord results from the intervallic relationships contained within it. As a result of the assignment of the keys to K-structures and their ci, tonal paths can be determined and complex tonal-harmonic constellations can be broken down. Ci-analysis not only allows the tonal situation in the works of the classical period to be determined much more precisely, it also opens up the tonal concepts of the Romantic period and Arnold Schönberg’s tonal strategy based on complementary series.