SKETCHING SONATA FORM STRUCTURE IN SELECTED CLASSICAL STRING QUARTETS Louis Bigo1 Mathieu Giraud1 Richard Groult2 Nicolas Guiomard-Kagan2 Florence Leve´2;1 1 CRIStAL, UMR 9189, CNRS, Universite´ de Lille, France 2 MIS, Universite´ de Picardie Jules Verne, Amiens, France flouis,mathieu,richard,nicolas,[email protected] ABSTRACT possibly new themes are introduced, finished by a re- transition (R), that focus back to the main tonality; Many classical works from 18th and 19th centuries are sonata forms, exhibiting a piece-level tonal path through • a recapitulation of the themes P and S, both in the an exposition, a development and a recapitulation and in- tonality of the tonic, possibly including elements volving two thematic zones as well as other elements. The that were added throughout the development. computational music analysis of scores with such a large- Several striking events are found between these sec- scale structure is a challenge for the MIR community and tions, in particular cadences. The transition (TR) between should gather different analysis techniques. We propose the P and S zones often ends on a Medial Caesura (MC), first steps in that direction, combining analysis features on that is often a Half Cadence (HC) with additional break symbolic scores on patterns, harmony, and other elements features [14]. The S zone generally concludes with a Per- into a structure estimated by a Viterbi algorithm on a Hid- fect Authentic Cadence (PAC), and is followed by conclud- den Markov Model. We test this strategy on a set of first ing patterns (C) without thematic content. movements of Haydn and Mozart string quartets. The pro- There are many possible variations on this basic struc- posed computational analysis strategy finds some pertinent ture. Somehow, the “regular” sonata form does not exist, features and sketches the sonata form structure in some and is merely a reconstruction. Some forms even do not pieces that have a simple sonata form. have two contrasting themes but rather a “continuous ex- position”, such as in several Haydn string quartets or in the 1. INTRODUCTION first movement of Mozart’s “The Hunt” K 458 [15]. 1.1 Sonata Forms More than a rigid framework between sections, what constitutes the essence of a sonata form is a high-level bal- Sonata form is a large-scale structure that can be found ance in the whole piece: the tonal tension (the auxiliary in many works from early Classical (18th century) to late tonality) and the rhetorical tension (textures, themes) cre- Romantic period (end of 19th century). Sonata forms can ated by the exposition and the development are resolved be found in almost all first movements (and, often, in other during the recapitulation. The development of sonata form movements) on Haydn, Mozart and Beethoven works. was consubtantial to the emergence of instrumental mu- Figure 1 shows an example of a very reduced sonata sic, this high-level balance enabling the design of musical form in a piano sonatina by Kuhlau. Basically, a sonata works at a larger scale than before. form is built on a piece-level tonal path involving a pri- mary thematic zone (P) and a contrasting secondary the- matic zone (S). It contains the following parts [15]: 1.2 Sonata Forms, Musicology and Pedagogy • an exposition, often repeated, containing the the- The term “Sonata form” was first coined in mid-1820s, matic zone P in the main tonality (denoted by I), and in the A. B. Marx’s Berliner allgemeine musikalische the thematic zone S in an auxiliary tonality (usually, Zeitung, and later formalized in [22] and [6], even if some but not always, the tonality of the dominant of I, de- underlying principles were already known before [19, 29]. noted by V); Somes authors conducted in-depth analyses of corpora with sonata forms, such as [12, 27] for Beethoven’s String • a development (D) characterized by tonal instabil- quartets or [32] for Beethoven’s Piano sonatas. ity, in which the existing themes are transformed and In the last decades, authors proposed systematic theo- ries on those forms [3, 4, 11, 21, 23, 28, 30]. The work c Louis Bigo, Mathieu Giraud, Richard Groult, Nicolas of Hepokoski and colleagues [13, 14], culminating in the Guiomard-Kagan, Florence Leve.´ Licensed under a Creative Commons book [15], will be used here as a reference. These works Attribution 4.0 International License (CC BY 4.0). Attribution: Louis formalized the notion of rotations organizing musical tech- Bigo, Mathieu Giraud, Richard Groult, Nicolas Guiomard-Kagan, Flo- rence Leve.´ “Sketching Sonata Form Structure in Selected Classical niques throughout the piece. String Quartets”, 18th International Society for Music Information Re- Music research on sonata forms is thus still active today, trieval Conference, Suzhou, China, 2017. two centuries after the climax of compositions in sonata 752 Proceedings of the 18th ISMIR Conference, Suzhou, China, October 23-27, 2017 753 Figure 1. Allegretto of the piano sonatina Op. 55, no. 2 by Kuhlau. HC/PAC/EEC/ESC describe cadences and structure endings using the notations from [15]. This movement has very short sections, a tiny development (Dev) that is almost only a retransition, and almost no transition between themes P and S. It nevertheless features the characteristic tonal path: S (and C) is in the dominant tonality (V, D major) during the exposition and comes back to the main tonality (I, G major) during the recapitulation. Theme S and conclusion C are exactly transposed between the exposition and the recapitulation. The theme P is both times in the main tonality, but lasts 8 measures in the exposition and 11 in the recapitulation. form. Such studies help to understand some principles of matic zones. The MC is often marked by a half-cadence, compositions and to have a new look on the history of mu- but also by a long preparation, a “triple hammer blow” and sic. Finally, sonata forms are one of the focus of lectures then a silence on all voices [14]. However these events are in music history, analysis or in composition. not always found – and such events can also appear outside of a MC. To our knowledge, not any study in MIR tried to 1.3 Sonata Forms and MIR detect MC in sonata forms. More generally, sketching an analysis of large-scale Several works in the MIR community target in sonata structures such as sonata forms is challenging for any an- forms, for example to test pattern extraction [25], tonal- alyst. A student in music analysis or a music theorist con- ity estimation [34], classification on n-grams, interval and siders different elements and, through diligent analytical metrical analyses [18]. However, there are very few works choices, summarize them into a coherent analysis. Our focusing on the sonata form structure. There will never computational strategy to analyze sonata forms in sym- be a “definitive analysis” of some piece in sonata form bolic scores takes inspiration from this approach. We pro- – even between musicians, one may choose to focus on pose to detect several analysis “features” using or extend- some aspects. Anyway, some analytical viewpoints on ing MIR techniques (Section 2) and then to combine them the sonata forms make consensus and can be the focus of to sketch the large-scale structure (Section 3). We test this MIR research. On audio signals, Jiang and Muller¨ com- strategy on a corpus of ten Haydn and Mozart string quar- puted correlations to detect exposition/recapitulation on tets and discuss the results (Sections 4 and 5). the first movements of 28 Beethoven piano sonatas with self-similarity matrices [17]. They also trace transpositions and harmonic changes during the different parts. Weiß and 2. ANALYSIS FEATURES Muller¨ propose a model of the “tonal complexity” and map The following paragraphs list analysis features on which it on sections of sonata forms [35]. we will build to sketch the structure of the sonata form. On symbolic data, we proposed in [7] a first approach Figures 2b and Figure 3 show these features on a first to detect the exposition/recapitulation based on pattern movement of a string quartet by Mozart. Such musical matching. Barate` and al. proposed a model of the sonata features are common in textbook or lecture descriptions of form strucure trough Petri Nets, but without any algo- the sonata form. Their selection was done according to rithm [2]. whether their presence or absence could be characteristic We argue that sonata forms are very stimulating exam- of one (or several) section(s) in a sonata form. ples for MIR research, going from simple cases (repeated The following paragraphs lists these features, noted pattern with a tonal path in a sonatina, as in Figure 1) to with boxes such as P . The detection of some of these fea- very elaborated constructions (such as Beethoven piano tures is taken from previous works [8]. Note that these sonatas) with many deviations from the norm [36]. The features are already relatively mid-level or high-level MIR key point of an analysis of sonata forms – a large-scale features, and their detection is often a challenge by it- tonal path – combines local-level features (themes, har- self that will not be detailed and evaluated here. Al- mony) with a piece-level analysis. though not perfect, these methods detect features that can An example of the complexity is the detection of Medial be combined as observable symbols produced by a Hidden Caesura (MC) that marks the break between the two the- Markov Model (Section 3). 754 Proceedings of the 18th ISMIR Conference, Suzhou, China, October 23-27, 2017 a) Reference analysis Tonality I V V vi ii I I I Structure P TR S C D R P' TR' S' C' ++MC ++EEC ++MC' ++ESC b) Analysis features P/S P S P' S' Tonality I V II V I vi ii I V I iivi I V I Pedals g, g, d'' g,, a' g' g, g, g' cz,, # # # Harmony 7 Breaks r r r r Cadences Harm.seq.