A Robust Parser-Interpreter for Jazz Chord Sequences

Abstract

Hierarchical structure similar to that associated with prosody and syntax in language can be identified in the rhythmic and harmonic progressions that underlie Western tonal music. Analysing such musical structure resembles natural language parsing: it requires the derivation of an underlying interpretation from an unstructured sequence of highly ambiguous elements—in the case of music, the notes. The task here is not merely to decide whether the sequence is grammatical, but rather to decide which among a large number of analyses it has. An analysis of this sort is a part of the cognitive processing performed by listeners familiar with a musical idiom, whether musically trained or not. Our focus is on the analysis of the structure of expectations and resolutions created by harmonic progressions. Building on previous work, we define a theory of tonal harmonic progression, which plays a role analogous to semantics in language. Our parser uses a formal grammar of jazz chord sequences, of a kind widely used for natural language processing (NLP), to map music, in the form of chord sequences used by performers, onto a representation of the structured relationships between chords. It uses statistical modelling techniques used for wide-coverage parsing in NLP to make practical parsing feasible in the face of considerable ambiguity in the grammar. Using machine learning over a small corpus of jazz chord sequences annotated with harmonic analyses, we show that grammar-based musical interpretation using simple statistical parsing models is more accurate than a baseline HMM. The experiment demonstrates that statistical techniques adapted from NLP can be profitably applied to the analysis of harmonic structure.

Keywords:

• harmony
• expectation
• grammars
• machine learning
• cognition

Acknowledgements

We thank the referees for JNMR. We also thank Martin Rohrmeier for his helpful input and discussion.

Notes

1 Throughout this paper, the term cadence will be used precisely to refer to connected structures of expectation-resolution patterns and not to refer to resolutions at points of particular significance in the global structure of a piece.

2 This is a result of the fact that the analysis, which represents harmonic expectation, is inevitably forward-looking. The few backward slash categories used handle tonic elaborations and do not contribute any relations to the analysis structure.

3 This approach to interrupted cadences differs from that most commonly seen in music theory (Piston, 1949) and is advocated by, among others, Keiler (1978) and Rohrmeier (2011).

4 Chord types have further influence on the interpretation through the statistical models introduced below.

5 Mean CPU time was 9:22 min (s.d. 33:32) with the supertagger, and 34:17 (s.d. 75:23) without, running on a 2.6 GHz AMD Opteron 6212 CPU.

6 Strictly speaking, this would only be a tritone substitution if it also had a dominant function.

7 http://www.cis.upenn.edu/~dbikel/software.html, accessed Oct 2012.

The work was supported by ERC Advanced Fellowship 249520 GRAMPLUS and ESRC Postgraduate Studentship ES/H012648/1.