Logic-based Modelling of Musical Harmony for Automatic Characterisation and Classification
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Harmony is the aspect of music concerned with the structure, progression, and relation of chords. In Western tonal music each period had different rules and practices of harmony. Similarly some composers and musicians are recognised for their characteristic harmonic patterns which differ from the chord sequences used by other musicians of the same period or genre. This thesis is concerned with the automatic induction of the harmony rules and patterns underlying a genre, a composer, or more generally a ‘style’. Many of the existing approaches for music classification or pattern extraction make use of statistical methods which present several limitations. Typically they are black boxes, can not be fed with background knowledge, do not take into account the intricate temporal dimension of the musical data, and ignore rare but informative events. To overcome these limitations we adopt first-order logic representations of chord sequences and Inductive Logic Programming techniques to infer models of style. We introduce a fixed length representation of chord sequences similar to n-grams but based on first-order logic, and use it to characterise symbolic corpora of pop and jazz music. We extend our knowledge representation scheme using context-free definite-clause grammars, which support chord sequences of any length and allow to skip ornamental chords, and test it on genre classification problems, on both symbolic and audio data. Through these experiments we also compare various chord and harmony characteristics such as degree, root note, intervals between root notes, chord labels and assess their characterisation and classification accuracy, expressiveness, and computational cost. Moreover we extend a state- of-the-art genre classifier based on low-level audio features with such harmony-based models and prove that it can lead to statistically significant classification improvements. We show our logic-based modelling approach can not only compete with and improve on statistical approaches but also provides expressive, transparent and musicologically meaningful models of harmony which makes it suitable for knowledge discovery purposes.
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