A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Segmentation, Similarity and Lexicon-Abstraction

This paper attempts to mediate between music theory and analysis, music psychology, computer assisted music analysis and the neurobiology of musical perception and memory. As part of his interrelated research programmes of computer analysis and synthesis of musical patterns, and the formalization and computer analysis of similarity in music, Cope used his Sorcerer program to track the pattern-antecedents to the opening phrase of the fi nale of Beethoven’s Piano Sonata op. 13 (Pathétique, 1798). This phrase is interpreted as being made up from several discrete patterns arising from a variety of different antecedent works by Bach and Mozart, Beethoven’s phrase constituting a meeting point for their later incarnations. While Cope does not formalize his project in these terms, such patterns are musical memes (or “musemes”), transmitted from antecedent composers to Beethoven by imitation. The same approach, conducted more explicitly and comprehensively in the light of memetics, is employed to analyse a phrase from Beethoven’s Piano Sonata in A∫ major, op. 110 (1822), revealing numerous possible antecedents, many from the works of Mozart, to Beethoven’s phrase. Some of these antecedents are foreground-level musemes, but others are situated at deeper structural levels, representing examples of middleground-level musemes and “musemeplexes” (complexes of evolutionarily independent musemes). This analysis also involves the sort of music-psychological determinations long advocated by such commentators as Gjerdingen and seemingly essential to prevent theory and analysis from degenerating into apophenia.
In an attempt to mediate between such analytical discourse, the computational approaches which motivated it, and the psychological and physiological processes ultimately underpinning them, the neurobiological encoding of memes is then explored, using William Calvin’s Hexagonal Cloning Theory (HCT). This theory (building on a long tradition of columnar models of cerebral functioning) contends that attributes of objects and phenomena are represented in the brain by resonating triangular arrays of neuronal “minicolumns” distributed across cerebral cortex, the association of such arrays into hexagonal groupings allowing the attributes of an object or entity – such as a physical object or a museme – to be represented. Such hexagonal groupings form plaques which compete for cortical territory in explicitly Darwinian fashion. The HCT appears to be a strong candidate theory for understanding both the representation of musical patterns by the brain and the perception and cognition of segmentation and similarity. It also offers a mechanism for the operation of Cope’s concept of the “lexicon”, a set of musical patterns related by abstraction of similarity relationships, the lexicon conceived here as a meme allele-class by analogy to the gene allele-classes of biology.