Using Geometric Symbolic Fingerprinting to Discover Distinctive Patterns in Polyphonic Music Corpora

Abstract

Did Ludwig van Beethoven (1770–1827) re-use material when composing his piano sonatas? What repeated patterns are distinctive of Beethoven’s piano sonatas compared, say, to those of Frédéric Chopin (1810–1849)? Traditionally, in preparation for essays on topics such as these, music analysts have undertaken inter-opus pattern discovery—informally or systematically—which is the task of identifying two or more related note collections (or phenomena derived from those collections, such as chord sequences) that occur in at least two different movements or pieces of music. More recently, computational methods have emerged for tackling the inter-opus pattern discovery task, but often they make simplifying and problematic assumptions about the nature of music. Thus a gulf exists between the flexibility music analysts employ when considering two note collections to be related, and what algorithmic methods can achieve. By unifying contributions from the two main approaches to computational pattern discovery—viewpoints and the geometric method—via the technique of symbolic fingerprinting, the current chapter seeks to reduce this gulf. Results from six experiments are summarized that investigate questions related to borrowing, resemblance, and distinctiveness across 21 Beethoven piano sonata movements. Among these results, we found 2–3 bars of material that occurred across two sonatas, an andante theme that appears varied in an imitative minuet, patterns with leaps that are distinctive of Beethoven compared to Chopin, and two potentially new examples of what Meyer and Gjerdingen call schemata. The chapter does not solve the problem of inter-opus pattern discovery, but it can act as a platform for research that will further reduce the gap between what music informaticians do, and what musicologists find interesting.