Abstract
This study proposes a fine-tuned approach to modeling musical form in Classical repertoires by analyzing pitch-class distributions in symbolic data using machine learning algorithms. Results suggest that sliding-window histograms, which take the temporal component into account, palpably improve algorithms’ performance in assigning form labels to pieces. Pitch-class histograms were extracted from major-mode piano-sonata movements by W. A. Mozart and L. v. Beethoven according to two methods: whole-piece histograms and sliding-window histograms. In the latter method, richer features were obtained by calculating histograms for 9–90 partially overlapping windows per piece. Supervised learning methods, such as Support Vector Machines (SVMs) and Artificial Neural Networks (ANNs), yield a good separation of data points according to three distinct form labels: sonata form, ABA (ternary) form, and variation form. For both models, using sliding-window histograms significantly improves performance with regard to the whole-piece histogram data. Unsupervised clustering into three components employing a Gaussian Mixture Model (GMM), on the other hand, yields no successful results. Finally, we offer an in-depth exploration of our findings, and propose some directions for further research based on sliding-window data.
Highlights
The concept of musical form refers to a variety of structural phenomena; most typically, it is used to designate the way musical pieces are organized at various hierarchical levels, such as the level of individual phrases, themes, sections, and movements (Caplin et al, 2009; Schoenberg, 1967)
In the remainder of this paper, we first discuss the ways the differences among musical forms are expected to manifest themselves in pitch-class histograms derived from movements in these forms (Section 2); we describe our approach to classifying musical forms using both whole-piece and sliding-window histograms in combination with various machine learning algorithms (Section 3); we describe and discuss our results and their possible implications (Sections 4 and 5)
∼90% 90 58 40 the feature vectors, we reduced the training set’s dimensionality to 26 using Principal Component Analysis (PCA) to match the number of dimensions of the whole-piece histogram representation
Summary
The concept of musical form refers to a variety of structural phenomena; most typically, it is used to designate the way musical pieces are organized at various hierarchical levels, such as the level of individual phrases, themes, sections, and movements (Caplin et al, 2009; Schoenberg, 1967). Given that a piece’s formal layout—by and large—manifests itself in its tonal trajectory, one may opt for modeling musical form on the succession of local keys throughout a given piece (rather than the distribution of pitch classes, as we propose to do here). We assigned a total of twenty one unique form labels to individual movements across the corpus, representing a high-resolution differentiation among formal subcategories Fourteen of these twenty one subcategories map onto the three main form categories discussed in the previous section: sonata, ABA, and variations. Since pitch-class histograms are crucially influenced by the choice of a movement’s mode, and, certain forms— such as the sonata form—have different tonal trajectories in major and in minor, incorporating minor-mode movements in the corpus under analysis would interfere critically with the ability to perform separation on the basis of a movement’s form. A particular type of repetition in conjunction with repeat signs involves additional bits of music known as “voltas.” our decision to ignore repeat signs renders “voltas” redundant, we retain these bits, while omitting the literally repeated measures
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