Richard Groult

Subject and Counter-Subject Detection for Analysis of the Well-Tempered Clavier Fugues

Fugue analysis is a challenging problem. We propose an algorithm that detects subjects and counter-subjects in a symbolic score where all the voices are separated, determining the precise ends and the occurrence positions of these patterns. The algorithm is based on a diatonic similarity between pitch intervals combined with a strict length matching for all notes, except for the first and the last one. On the 24 fugues of the first book of Bachs Well-Tempered Clavier, the algorithm predicts 66% of the subjects with a musically relevant end, and finally retrieves 85% of the subject occurrences, with almost no false positive.

Computational Analysis of Musical Form

Can a computer understand musical forms? Musical forms describe how a piece of music is structured. They explain how the sections work together through repetition, contrast, and variation: repetition brings unity, and variation brings interest. Learning how to hear, to analyse, to play, or even to write music in various forms is part of music education. In this chapter, we briefly review some theories of musical form, and discuss the challenges of computational analysis of musical form. We discuss two sets of problems, segmentation and form analysis. We present studies in music information retrieval (MIR) related to both problems. Thinking about codification and automatic analysis of musical forms will help the development of better MIR algorithms.

Computational fugue analysis

One of the pinnacles of form in classical Western music, the fugue is often used in the teaching of music analysis and composition. Fugues alternate between instances of a subject and other patterns and modulatory sections, called episodes. Musicological analyses are generally built on these patterns and sections. We have developed several algorithms to perform an automated analysis of a fugue, starting from a score in which all the voices are separated. By focusing on the diatonic similarities between pitch intervals, we detect subjects and countersubjects, as well as partial harmonic sequences inside the episodes. We also implemented tools to detect subject scale degrees, cadences, and pedals, as well as a method for segmenting the fugue into exposition and episodic parts. Our algorithms were tested on a corpus of 36 fugues by J. S. Bach and Dmitri Shostakovich. We provide formalized ground-truth data on this corpus as well as a dynamic visualization of the ground truth and of our computed results. The complete system showed acceptable or good results for about one half of the fugues tested, enabling us to depict their design.