Learning Sonata Form Structure on Mozart’s String Quartets Pierre Allegraud, Louis Bigo, Laurent Feisthauer, Mathieu Giraud, Richard Groult, Emmanuel Leguy, Florence Levé To cite this version: Pierre Allegraud, Louis Bigo, Laurent Feisthauer, Mathieu Giraud, Richard Groult, et al.. Learning Sonata Form Structure on Mozart’s String Quartets. Transactions of the International Society for Music Information Retrieval (TISMIR), Ubiquity Press, 2019, 2 (1), pp.82-96. 10.5334/tismir.27. hal-02366640 HAL Id: hal-02366640 https://hal.archives-ouvertes.fr/hal-02366640 Submitted on 9 Sep 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Allegraud, P., et al. (2019). Learning Sonata Form Structure on Mozart’s String Quartets. Transactions of the International Society for Music Information 7,60,5 Retrieval, 2(1), pp. 82–96. DOI: https://doi.org/10.5334/tismir.27 RESEARCH Learning Sonata Form Structure on Mozart’s String Quartets Pierre Allegraud*, Louis Bigo*, Laurent Feisthauer*, Mathieu Giraud*, Richard Groult†, Emmanuel Leguy* and Florence Levé*,† The musical analysis of large-scale structures, such as the classical sonata form, requires to integrate multiple analyses of local musical events into a global coherent analysis. Modelling large-scale structures is still a challenging task for the research community. It includes building large and accurate annotated corpora, as well as developing practical and efficient tools in order to visualize the analyses of these corpora. It finally requires the conception of effective and properly evaluated MIR algorithms. We propose a machine learning approach for the sonata form structure on 32 movements from Mozart’s string quartets. We release an open dataset, encoding two reference analyses of these 32 movements, totaling more than 1800 curated annotations, as well as flexible visualizations of these analyses. We discuss the occurrence in this corpus of melodic, harmonic, and rhythmic features induced by pitches, durations, and rests. We investigate whether the presence or the absence of these features can be characteristic of the different sections forming a sonata form. We then compute the emission and transition probabilities of several Hidden Markov Models intended to match the structure of sonata forms at several resolutions. Our results confirm that the sonata form is better identified when the parameters are learned rather than manually set up. These results open perspectives on the computational analysis of musical forms by mixing human knowledge and machine learning from annotated scores. Keywords: Computational Music Analysis; Music Structure; Musical Form; Sonata Form 1 Introduction early golden era (Reicha, 1824; Marx, 1845; Czerny, 1848). 1.1 Sonata form One of its earliest formalizations seems to be the grande The large-scale structure referred to as sonata form is a coupe binaire that Reicha (1824) described 30 years after post-hoc formalization of a widely used composer practice Mozart died. The sonata form finally became a normative since the middle of the 18th century. It is built on a piece- structure for several generations of romantic composers, level tonal path concept involving both a primary thematic being transmitted both through explicit teaching as well zone (P) and a contrasting secondary thematic zone (S) as implicit exposure. (Figure 1). This creates a polarization between two Nowadays, sonata forms are still taught in music tonalities and induces a dramatic turn to the piece. The analysis, music history and composition lectures. They sonata form can be viewed as an evolution of both aria are also the focus of recent academic studies (Ratner, and concerto Baroque forms (Rosen, 1980; Hepokoski and 1980; Rosen, 1980; Hepokoski and Darcy, 1997; Caplin, Darcy, 2006). Greenberg (2017) investigated how sonata- 1998, 2001; Hepokoski, 2002; Larson, 2003; Miyake, form recapitulation may have come from both the double 2004; Hepokoski and Darcy, 2006; Gjerdingen, 2007; return of the tonic key and the parallel endings in a two- Greenberg, 2017). The past decades have seen a revival part movement. of the Formenlehre tradition in the classical era (Caplin et A number of works composed by Haydn, Mozart and al., 2009). In Caplin (1998)’s theory of formal functions, Beethoven are recognized as in sonata forms, especially first small functional units at the idea level (e.g., basic idea, movements of string quartets, concerti, symphonies, and contrasting idea) are combined to form units at the phrase piano sonatas. However, the theories about the classical level (e.g., presentation, antecedent), which in turn are sonata form were introduced almost fifty years after its combined to form units at the theme level (e.g., sentence, period, etc.). This bottom-up approach builds up to the whole sonata form, paving the way to the three large-scale * CRIStAL, UMR 9189, CNRS, Université de Lille, FR functions that are characteristic of sonata form: Exposition, † MIS, Université de Picardie Jules Verne, Amiens, FR Development, and Recapitulation, possibly including two Corresponding author: Mathieu Giraud other functions, Introduction and Coda. In this study, we ([email protected]) rathe follow the Sonata Theory of Hepokoski and Darcy Allegraud et al: Learning Sonata Form Structure on Mozart’s String Quartets 83 Figure 1: Andante con moto of the String Quartet #16 in E♭ Major, K 428, 2nd movement. Encoded in Lilypond by Maurizio Tomasi for the Mutopia Project. This slow movement has a sonata form, as detailed in Section 2.1. Following notations of Hepokoski and Darcy (2006), the primary themes (P/P’) are followed by transitions (TR/TR’), ended with Medial Caesuras (MC/MC’) – they are here Half Cadences (HC) in the main tonality (I). In the exposition, the second- ary theme (S) and the conclusion (C) are here in the tonality of the dominant (V, E♭ major). In the recapitulation, both S’ and C’ come back to the main tonality. In the exposition, the S theme ends with a perfect authentic cadence (PAC) named essential expositional closure (EEC), whereas, in the recapitulation, the S’ theme ends with an essential structural closure (ESC). Between the exposition and the recapitulation, the development (Dev) moves to other keys and is concluded by a retransition (RT) focusing on the dominant of the primary key. 84 Allegraud et al: Learning Sonata Form Structure on Mozart’s String Quartets (2006), where sonata form is viewed as an “ordered system 1.3 Contributions of generically available options permitting the spanning of Reproducible MIR research needs to be grounded on ever larger expanses of time” (ibid., p. 15). Their detailed publicly available datasets. Here, we systematically study formalization of the successive sections of the sonata form a corpus containing most of the sonata-form movements seems adequate to develop computational models. in Mozart’s string quartets, and we release an open dataset providing two independent analyses of each movement, 1.2 MIR, high-level structure, and sonata form encoded manually, based on formal modeling of sonata form On the one hand, “analyzing a sonata form”, which implies (Section 2). Extending the approach we introduced before identifying the boundaries of its successive sections, often (Bigo et al., 2017), we propose several models of sonata requires a number of musicological judgments that are form using Hidden Markov Models for which parameters, piece-specific, which makes its automation difficult. Being emission probabilities, and transition probabilities are strongly linked to music history, music analysis may indeed automatically learned on the corpus. The states of the include ideas that involve the singularity of the piece, a HMMs represent the different sections of a sonata form comparison between composers as well as some aesthetic and the observations consist of binary analytical features considerations. On the other hand, music analyses are computed through the pieces (Section 3). We discuss the often built upon specific analytical elements, like themes relationship between the occurrences of these features or patterns that structure the harmony and the texture of and the sonata form sections. the piece. Analyses can therefore be modelled with Music The results show that the sonata form is better identified Information Retrieval (MIR) algorithms that can be properly when the parameters are learned rather than manually set evaluated. Finally, the identification of a large-scale structure up. We also study how the granularity of the model (i.e. such as the sonata form requires the combination of these the number of possible states) influences the success of local features to reach a piece-level analysis, which is itself a the detection (Section 4). challenge for MIR research. We previously reviewed research on computational analysis of musical form (Giraud et al., 2 The Mozart Sonata-Form String Quartet 2015). Chen et al. (2004) proposed to segment the musical Corpus piece into sections called “sentences”, clustering phrases 2.1 Annotating