ACTAS DEL X ENCUENTRO DE CIENCIAS COGNITIVAS DE LA MÚSICA HYPOTHESES ON THE CHOREOGRAPHIC ROOTS OF THE MUSICAL METER A case study on Afro-Brazilian dance and music LUIZ NAVEDA AND MARC LEMAN GHENT UNIVERSITY Abstract A great part of the musical engagement is dependent on the human capacity to perceive and produce of temporal regularities in music. In Western music theory, these regularities are related to the concept of musical meter. A brief overview of the theories of musical meter reveals that a number of approaches are built upon abstract concepts of musical structure, axiomatic rules of preference or hypothetical models. In this paper, we argue that dance provides reliable explanations for a number of mechanisms behind the emergence of meter. We demonstrate our hypothesis by means of a case study on the analysis of dance and music recordings of Afro- Brazilian samba. The movement and audio data was processed by using TGA analysis (topological gesture analysis). The results show that the structure of musical meter is not only more elaborated in the dance gestures but also provides richer elements to support the concept of meter in music. We demonstrate that the structure of meter is readily available in the choreographic forms and delineated by biomechanical constraints of the dancer's body. We suggest that the structure of musical meter might have been formed as an entangled musical-choreographic form and was further fragmented in a disembodied view of musical knowledge. Resumen Gran parte del trabajo musical depende de la capacidad humana para percibir y producir regularidades temporales en la música. En la teoría de la música occidental, este aspecto se relaciona con el concepto de métrica musical. Un breve resumen de las teorías de la métrica musical revela que una serie de enfoques se basan en conceptos abstractos de la estructura musical, en reglas axiomáticas de preferencia o modelos hipotéticos. En este trabajo, sostenemos que la danza proporciona explicaciones fiables para una serie de mecanismos detrás del surgimiento de la métrica musical. Demostramos nuestra hipótesis mediante un estudio de caso sobre el análisis de las grabaciones de la danza y la música del samba Afro-brasileño. Los datos de movimiento y audio se procesaron mediante el análisis de TGA (análisis topológico del gesto). Los resultados muestran que la estructura del compás musical no sólo es más elaborada en los gestos de la danza sino que también proporciona elementos más ricos para apoyar el concepto de métrica en la música. Demostramos que la estructura de metro está disponible en las formas coreográficas y está delimitada por las limitaciones biomecánicas del cuerpo del bailarín. Sugerimos que la estructura del compás musical podría haber sido formada como una forma enredada de música y coreografía y se fragmentó en una visión descorporeizada de conocimientos musicales. Our frequent admonition - stop thinking and dance - isn't to say that the motion is unthinkable. It's to say that the body is capable of understanding more things at once than can be articulated in language. One has no choice but to think with the body. Browning (1995) Introduction The human capacity to perceive and engage in temporal regularities in music is a key musical ability without which the vast majority of music forms, traditional dances, rituals and other forms of musical engagement would not have evolved in the human culture. The concept of musical meter captures the structural properties formed by temporal regularities perceived in the auditory stream, from the viewpoint of the Western theory of music. However, scholars have long been Alejandro Pereira Ghiena, Paz Jacquier, Mónica Valles y Mauricio Martínez (Editores) Musicalidad Humana: Debates actuales en evolución, desarrollo y cognición e implicancias socio-culturales. Actas del X Encuentro de Ciencias Cognitivas de la Música, pp. 477-495. © 2011 - Sociedad Argentina para las Ciencias Cognitivas de la Música (SACCoM) - ISBN 978-987-27082-0-7 NAVEDA AND LEMAN struggling with gaps in representation, modeling and conceptualization of meter. From simple time prescriptions – such as the ones seen in a musical score – to computer algorithms for beat and meter detection – such as the ones used in computer processing in MIR applications1 – the formalization behind models of meter still requires more developments. Common sources of inconsistencies in these models include the inherent metrical ambiguity of music styles (McKinney & Moelants 2006), lack of isochrony in the compound metric levels (e.g., Blom & Kvifte 1986), cultural or personal preferences for certain tempos or metric structures (e.g., London 2009), and the perception/performance of several parallel metric structures (e.g., Parncutt 1994), among others. The attempts to find proper generalizations for the mechanisms that are behind the emergence of musical meter seem to have produced abstract2 models or parameterizations. These theoretical artifacts are then used to fill gaps between the theory and the diverse forms of the phenomenon of meter. Examples of these ‘abstract’ mechanisms and structures include representations such as metrical grids, metaphors of periodicity, mental models, oscillatory predispositions or simple axioms (some of these examples will be discussed in Section ‘Symmetry, periodicity and abstractions’). The application of theories of embodiment (e.g., Merleau-Ponty 1962; Varela, Thompson, & Rosch 1991) to musicology (e.g., Leman 2007; Toiviainen, Luck, & Thompson 2010; Van Noorden & Moelants 1999) and the contributions inherited from ethnomusicology (e.g., Blom & Kvifte 1986; Chernoff 1991; Clayton, Sager, & Will 2004) and cognitive sciences (e.g.,Trainor & Trehub 1992) demonstrated that some of the problems in explaining the emergence of meter could be solved by looking at the moving body and how it shapes musical behavior (in special, oscillatory movements). This shift towards a broader epistemological framework where musical engagement takes place and interacts with the human body (and not only a body that follows a mind) showed that certain aspects of rhythm and meter could be explained by the inherent biomechanics (see, for example, London, Gritten, & King 2006; Van Noorden & Moelants 1999) and morphology (Naveda & Leman 2009) of the musical movement3 and its cultural and social forms such as dance, social choreographies and spontaneous movement. Indeed, if one looks at the sociocultural displays in which music appears in most of the societies, it is difficult to ignore the recurrence of dance and music phenomena at the same time and spaces. In this paper, we argue that the structure of musical meter may have inherited more than phenomenological parallelisms with dance forms. We suggest that musical meter may have originally developed from interactions between music and dance, whose primary characteristics have been imprinted in both modalities. And intrinsically dependent music-dance structures. In the next sections, we outline a non-exhaustive review of the main theories of meter, our hypotheses and an experiment that aims at investigate how the musical meter is reflected on dance gestures. The experiment is realized in the context of Afro-Brazilian samba music and dance. Outline of the study In this study, we investigate how dance gestures inform about the structure musical meter, in the attempt to provide better insights on the theory of meter. In the Section ‘Background on meter’, we will delineate the questions and theories that form the background of this study. In the experimental part, described in the Section ‘Methodology’, we delineate our methods and explain how music and movement analysis were merged in the analysis of musical meter in the dance space. The methods were applied to a data set of 13 movement recordings realized professional dancers, specialized in Afro-Brazilian samba. Section ‘Results’ displays the results for all dancers, which focuses on the movement of hands, feet and how musical meter is represented in space. Section ’Discussion’ discusses the impact of the results against the theory of musical meter, which are summarized in the Section ‘Conclusion’. Background on meter Meter is a concept that seem not being easily detached from the surface of the sound in the auditory domain or, at least in the available symbolic and sensory descriptors of music. Symbolic information such as pitch and duration of musical events do not contain metrical structures per se. In fact, most of the metrical information in traditional Western notation is prescribed a priori and simplified as a system of isochronous bar and beat levels. Metrical structure is certainly more complex. State-of- the-art of the models for beat detection based on low-level features of musical audio are struggling to 1 Music information retrieval. 2 The use of the word abstract in this context means that the models or set of rules proposed in theories of musical meter that are weakly supported by causal explanations. 3 The terminology musical movement refers to any movement driven or accompanied by music. This definition includes spontaneous movement to music, dance, ancillary and expressive movements of musicians, among others. 478 HYPOTHESES ON THE CHOREOGRAPHIC ROOTS OF THE MUSICAL METER achieve acceptable recognition levels for beat and bar levels, even in an universe of Western popular songs4. Meter could then be seen as a ‘higher-level’ concept. This means that the structure of meter seem to emerge from more complex interactions between