The Computational Analysis of Harmony in Western Art Music.

Abstract

This thesis describes research in the computational analysis of harmony in western art music, focussing particularly on improving the accuracy and information-richness of key and chord extraction from digital score data. It is argued that a greater sophistication in automatic harmony analysis is an important contribution to the field of computational musicology. Initial experiments use hidden Markov models to predict key and modulation from automatically labelled chord sequences. Model parameters are based on heuristically formulated chord and key weightings derived from Sch¨onberg’s harmonic theory and the key and chord ratings resulting from perceptual experiments with listeners. The music theory models are shown to outperform the perceptual models both in terms of key accuracy and modelling the precise moment of key change. All of the models perform well enough to generate descriptive data about modulatory frequency, modulatory type and key distance. A robust method of classifying underlying chord types from elaborated keyboard music is then detailed. The method successfully distinguishes between essential and inessential notes, for example, passing notes and neighbour notes, and combines note classification information with tertian chord potential to measure the harmonic importance of a note. Existing approaches to automatic chord classification are unsuitable for use with complex textures and are restricted to triads and simple sevenths. An important goal is therefore to recognise a much broader set of chords, including complex chord types such as 9ths, 11ths and 13ths. This level of detail is necessary if the methods are to supply sophisticated information about the harmonic techniques of composers. Testing on the first twenty-four preludes of J. S. Bach’s Well Tempered Clavier, hand annotated by the author, a state of the art approach achieves 22.1% accuracy; our method achieves 55% accuracy.