Harmonic analysis of music using combinatory categorial grammar
Granroth-Wilding, Mark Thomas
Wilding, Mark Thomas Granroth
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Various patterns of the organization of Western tonal music exhibit hierarchical structure, among them the harmonic progressions underlying melodies and the metre underlying rhythmic patterns. Recognizing these structures is an important part of unconscious human cognitive processing of music. Since the prosody and syntax of natural languages are commonly analysed with similar hierarchical structures, it is reasonable to expect that the techniques used to identify these structures automatically in natural language might also be applied to the automatic interpretation of music. In natural language processing (NLP), analysing the syntactic structure of a sentence is prerequisite to semantic interpretation. The analysis is made difficult by the high degree of ambiguity in even moderately long sentences. In music, a similar sort of structural analysis, with a similar degree of ambiguity, is fundamental to tasks such as key identification and score transcription. These and other tasks depend on harmonic and rhythmic analyses. There is a long history of applying linguistic analysis techniques to musical analysis. In recent years, statistical modelling, in particular in the form of probabilistic models, has become ubiquitous in NLP for large-scale practical analysis of language. The focus of the present work is the application of statistical parsing to automatic harmonic analysis of music. This thesis demonstrates that statistical parsing techniques, adapted from NLP with little modification, can be successfully applied to recovering the harmonic structure underlying music. It shows first how a type of formal grammar based on one used for linguistic syntactic processing, Combinatory Categorial Grammar (CCG), can be used to analyse the hierarchical structure of chord sequences. I introduce a formal language similar to first-order predicate logical to express the hierarchical tonal harmonic relationships between chords. The syntactic grammar formalism then serves as a mechanism to map an unstructured chord sequence onto its structured analysis. In NLP, the high degree of ambiguity of the analysis means that a parser must consider a huge number of possible structures. Chart parsing provides an efficient mechanism to explore them. Statistical models allow the parser to use information about structures seen before in a training corpus to eliminate improbable interpretations early on in the process and to rank the final analyses by plausibility. To apply the same techniques to harmonic analysis of chord sequences, a corpus of tonal jazz chord sequences annotated by hand with harmonic analyses is constructed. Two statistical parsing techniques are adapted to the present task and evaluated on their success at recovering the annotated structures. The experiments show that parsing using a statistical model of syntactic derivations is more successful than a Markovian baseline model at recovering harmonic structure. In addition, the practical technique of statistical supertagging serves to speed up parsing without any loss in accuracy. This approach to recovering harmonic structure can be extended to the analysis of performance data symbolically represented as notes. Experiments using some simple proof-of-concept extensions of the above parsing models demonstrate one probabilistic approach to this. The results reported provide a baseline for future work on the task of harmonic analysis of performances.