Schenkerian Analysis by Computer: A Proof of Concept

Abstract

A system for automatically deriving a Schenkerian reduction of an extract of tonal music is described. Schenkerian theory is formalised in a quasi-grammatical manner, expressing a reduction as a binary-tree structure. Computer software which operates in the manner of a chart parser using this grammar has been implemented, capable of deriving a matrix of reduction possibilities, in polynomial time, from a representation of the score. A full reduction of the extract can be discovered by selecting a tree from this matrix. The number of possible valid reductions for even short extracts is found to be extremely large, so criteria are required to distinguish good reductions from bad ones. To find such criteria, themes from five Mozart piano sonatas are analysed and samples of ‗good' reductions (defined by reference to pre-existing analyses of these themes) are compared with randomly sampled reductions. Nine criteria are thereby derived, which can be applied in the process of parsing and selecting a reduction. The results are promising, but the process is still too computationally expensive-only extracts of a few bars in length can be reduced-and more extensive testing is required before the system can be properly claimed to perform automatic Schenkerian analysis.

Automatic Functional Harmonic Analysis

“…Pachet furthermore shows that these rules can be learned from chord sequence data in an automated fashion. Additionally, quasi-grammatical systems for Schenkerian analysis have been proposed recently (Marsden 2010). Furthermore, Choi (2011) developed a system for analyzing the harmony of jazz chord sequences; this system identifies common harmonic phenomena, like secondary dominants and tritone substitutions, and labels the chords involved accordingly.…”

Voice-Leading Transformation and Generative Theories of Tonal Structure

“…The best-known formal description of tonal hierarchy comes from Lerdahl and Jackendoff 's Generative Theory of Tonal Music. The basic form of hierarchy described there is also used by many others before and after, such as Komar (1971), Keiler (1977), and Marsden (2005Marsden ( , 2010. Although all of these theories are strongly influenced by Schenker, and might be seen to have had an impact on how Schenkerian analysis is currently taught and understood, none of them are, strictly speaking, formalizations of Schenkerian analysis itself.…”

“…For instance, one usually considers the neighbor note to be a unitary phenomenon, but under a representational model of hierarchy there are two distinct neighbor-note operations, left-branching and right-branching. The added complexity of the representational model leads to a large number of possible analyses, as noted by Marsden (2005Marsden ( , 2010, and at least partly accounts for the excessive number of satisfactory structural descriptions found by Marsden (2010) in algorithmic applications of Schenkerian analysis using representational hierarchies.…”

SymCHM—An Unsupervised Approach for Pattern Discovery in Symbolic Music with a Compositional Hierarchical Model

“…Although a common problem, its definition, as well as pattern discovery algorithms, significantly differs across these fields. In music, the importance of repetition has been addressed and discussed by a number of music theorists (e.g., [17]) and, more recently, also by researchers who develop algorithms for semi-automatic music analysis, such as one described by Marsden [4]. In the MIR field, an initiative for a common definition of different tasks was formalized into the Music Information Retrieval Evaluation eXchange (MIREX), in an attempt to compare different approaches.…”

“…Although GTTM mostly relies on expert rules, the concept of hierarchical structuring seems reasonable, derived from the humans' search for structure in consciously perceived surroundings. There are several attempts to build a system capable of automatic analysis supported by the GTTM and Schenkerian analysis [2][3][4]. Several other rule-based models were also researched in Music Information Retrieval (MIR) and related fields [5,6].…”