This article investigates the sources of the recapitulation using statistical methods. The recapitulation has traditionally been viewed as an expansion of small ternary forms, resulting in a top-down approach, whereby the repeat of expositional material is explained in rotational terms. Here I present a bottom-up approach, demonstrating that the recapitulation arose as a concatenation between two previously independent practices: the double return of the opening theme in the tonic in the middle of the second half of a two-part form, and the thematic matching between the ends of the two halves of two-part form. Drawing on a corpus of more than seven hundred instrumental works dated 1650-1770, I demonstrate that these two practices arose and functioned independently from each other, increasing in frequency and in length, before being subsumed into an overarching rotational practice.

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Recent literature has demonstrated the difficulty of classifying between composers who write in extremely similar styles (homogeneous style). Additionally, machine learning studies in this field have been exclusively of technical import with little musicological interpretability or significance. We present a supervised machine learning system which addresses the difficulty of differentiating between stylistically homogeneous composers using foundational elements of music, their complexity and interaction. Our work expands on previous style classification studies by developing more complex features as well as introducing a new class of musical features which focus on local irregularities within musical scores. We demonstrate the discriminative power of the system as applied to Haydn and Mozart's string quartets. Our results yield interpretable musicological conclusions about Haydn's and Mozart's stylistic differences while distinguishing between the composers with higher accuracy than previous studies in this domain.

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This chapter considers negative interaction, whereby two elements or more may have contradictory implications, analogous to the case of rivalry over resources in ecological systems. In the case of negative interaction, one element will inevitably prevail over the other in the long term. In the short term, however, any movement including rival elements will pose a compositional challenge to the composer. Using popular elements will be advantageous for communication with the audience, yet their contradictory implications forces the composer to find solutions. In the chapter I survey a number of compositional solutions that arose as responses to such tension, particularly in the works of Wilhelm Friedemann Bach and Carl Philipp Emanuel Bach.