Symbolic Encoding of Simultaneities: Re-designing the General Chord Type Representation

Abstract

Encoding note simultaneities (chords) has been approached in different ways, such as Roman numerals for tonal harmony, or pitch class sets encountered in atonal and non-tonal music. A novel chord representation, the General Chord Type (GCT) representation, was developed to be adaptable to a broad variety of harmonic idioms from tonal to atonal. Given a binary classification of intervals into consonant or dissonant, GCT rearranges the notes of a given simultaneity such that the base of the chord encoding is consonant. This study proposes a refined elegant version of the GCT algorithm that takes into account a graded raking of intervallic consonance, maintains the core characteristics of GCT and resolves known problems such as certain types of chord ambiguities (more than one chord types for a single pitch collection) and orderings of intervals (wrong base/root and chord extensions). To evaluate the performance of the new version, common tonal chords, whose encodings are well established, are compared with encodings from both versions, as well with other existing encoding systems. In the novel algorithm, ambiguous outputs are reduced significantly, inversions are correctly identified, and foreign chord notes are organised towards the most dissonant top end of the encodings. The algorithm performs well in atonal contexts by encoding Tn-Types with great accuracy.