Emilios Cambouropoulos/Maximos Kaliakatsos-Papakostas/Costas Tsougras

The General Chord Type Representation: An Algorithm for Root Finding and Chord Labelling in Diverse Harmonic Idioms

In this study we focus on issues of harmonic representation and computational analysis.  Encodings such as guitar style chord labels or roman numeral analysis notation that are meaningful for representing tonal music, are inadequate for non-tonal musics; conversely, pc-set theoretic encodings that are employed for atonal and other non-tonal musics are inadequate for tonal music. Is it possible to devise a ‘universal’ chord representation that adapts to different harmonic idioms? In this paper, a new idiom-independent representation of chord types is proposed that is appropriate for encoding tone simultaneities in any harmonic context (such as tonal, modal, jazz, octatonic, atonal). The General Chord Type (GCT) representation, allows the re-arrangement of the notes of a harmonic simultaneity such that abstract idiom-specific types of chords may be derived; this encoding is inspired by the standard roman numeral chord type labeling, but is more general and flexible. Given a consonance-dissonance classification of intervals (that reflects culturally-dependent notions of consonance/dissonance), and a scale/key, the GCT algorithm computes, for a given multi-tone simultaneity, the ‘optimal’ ordering of pitches such that a maximal subset of consonant intervals appears at the ‘base’ of the ordering in the most compact form. The lowest tone in the base is the ‘root’ of the chord. If a tonal centre (key) is given, the position within the given scale is automatically calculated. The proposed representation is ideal for hierarchic harmonic systems such as the tonal system and its many variations, but adjusts to any other harmonic system such as post-tonal, atonal music, or traditional polyphonic systems (in the case of atonal music, the GCT amounts to the ‘normal order’ typology of pc-set theory). The proposed GCT algorithm is applied to and tested qualitatively against a set of examples from diverse musical idioms (medieval, baroque, classical, romantic, octatonic, atonal, traditional), showing its potential, especially, for computational music analysis & music information retrieval.