Beat Hierarchy and Beat Patterns—From Aksak to Composite Meter (original) (raw)
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Rhythm: Africa and Beyond
This article studies the empirical structures and theoretical status of rhythmic feels in jembe music, which is a popular style of drum ensemble music from West Africa. The focus is on systematic variations of durations (Bengtsson 1975)—that is, cyclic patterns of non-isochronous pulse streaming at the metric level of beat subdivision. Taking for example a standard piece of jembe repertoire that is set in a 4-beat/12-subpulse metric cycle (often notated as 12/8), I show that the ternary beat subdivision forms a repeated sequence of unequal (short, flexible, and long) subpulses. This stable rhythmic feel pattern, SFL, is unmistakable and non-interchangeable with a second ternary pattern, which is characterized by long, flexible, flexible subpulses (LFF) and occurs in other pieces of jembe music. As predicted in Justin London’s “hypothesis of many meters” (London 2004), these timing patterns distinguish individual meters. I further analyze how schemes of binary and ternary beat subdiv...
Non-isochronous Metre in Music from Mali
The Oxford Handbook of Time in Music, 2022
The present chapter concerns the uneven subdivision of metric beats in various traditional forms of music from Mali. In this repertoire, beats are strictly isochronous, but subdivisions often seem to be governed by ratios that fall somewhere in between isochrony (1:1) and a shuffle rhythm (2:1). From the commonly accepted point of view which equates metric regularity with isochrony, such uneven beat subdivisions are generally regarded as expressive performance deviations from some underlying, structurally isochronous reference framework. Indeed, this concept of expressive microtiming variation or participatory discrepancy (Keil 1987) represents the standard interpretation of the well-researched timing of the 'swing eighths' in jazz performance (Benadon 2006; Butterfield 2011; Honing and de Haas 2008; Prögler 1995; Wesolowski 2015). By contrast, my long-term, participatory ethnographic experience with jembe-centred, dance-oriented drum ensemble music from southern Mali has convinced me that, in the context of this musical culture, uneven subdivisions, which are governed by ratios other than 1:1, may constitute temporal references structures in their own right. This chapter will (1) consider the roles that isochrony and non-isochrony play in various theories of rhythm and metre, (2) elaborate the hypothesis of non-isochronous subdivision-based metre, and (3) provide summaries of five empirical research projects that incrementally provide evidence for the hypothesis. Finally (4), I will summarize the empirical findings and discuss some of their implications for the psychology of rhythm perception, suggesting a strong role of culture and the specifics of cultural environments for perceptual capacities.
Feeling Beats and Experiencing Motion: A Construction-Based Theory of Meter (PhD Dissertation)
2019
Musical meter is often described as an objective grid-like system of time-points that is created by musical sounds. I define meter instead as any pattern of felt beats an individual listener chooses to hear, a physical and cognitive interpretation of the music that is (re-) created in the moment of listening. We construe meter through embodied metering practices: dance gestures, patterns of counting, or epistemologies of rhythmic motion. Many metering practices have conventional metering constructions, specific associations between sounding features, patterns of felt beats, and paths of motion through these beats. Drawing on concepts from cognitive science and performance studies, I explore how this embodied knowledge is constituted and applied in both planning of musical phrases by a performer, and in-time perception and cognition of musical rhythms by any listener or participant. Metering constructions and practices are often performed by and associated with certain communities and identities. I take a culturally-situated approach to meter and felt motion, studying traditions of embodied movement and bodily discipline including headbanging in heavy metal (Chapter 1), characteristic dance rhythm topics in non-dance concert music of the eighteenth century (Chapter 2), motivic manipulation and developing variation in late Romantic chamber music (Chapters 3 and 4), and prosody and speech gestures in operatic recitative (Chapter 5). Contrary to many existing theories of meter, I argue that our feelings of beat are not necessarily organized in cyclical grids, but are improvised on the spot by stitching together familiar motions. I also explore how movements often embody and perform aesthetic ideologies and cultural meanings, with these hermeneutic frameworks often shaping listeners’ choice of movements, their proprioception of their own movements, and their perception of the qualities of rhythm and motion in the music they are listening to.
Rhythmic Processes in Time-Space
Music and Space: Theoretical and Analytical Perspectives, 2021
This essay explores broad parameters of musical time-space formation and introduces an analytical representation-a pulse-stream graph-to illustrate how a unitary temporal pattern can give rise to the overall shape and form of a musical work or how multiple temporal patterns interact when unfolding in rhythmic polyphony. The time-space is stratified according to distinct cognitive processing of one of three types of memory (echoic, short-term, and long-term), requiring different analytical considerations depending on the timescale of the events under scrutiny (foregroud, middleground, and background). As one form of temporal continuity, rhythmic processes-closed, open, or flexible-outline different pathways through time. Analysis of György Ligeti's etude Entrelacs and Elliott Carter's work 90+ illustrate how compositional treatment of rhythmic processes and their interaction with other aspects of the musical work imply different sense of time, despite basing the work on conceptually identical long-range polyrhythms.
Rhythmic feel as meter: non-isochronous beat subdivision in jembe music from Mali
2010
[1] In various styles of music with a regular metric beat, the fast pulse subdividing the beat is non-isochronous. Ingmar Bengtsson found that a consistent alternation of long and short subpulse durations (LS) is characteristic of the rhythmic feel of Swedish polska, a form of Nordic folk dance music. The subdivision of Vienna waltz is structured by the repeated sequence of short, long, and medium (SLM) subpulses. Bengtsson stressed that such cyclic variation of subpulse durations is essential to the feeling of rhythmic drive. (2) [2] Non-isochronous beat subdivision is polymorphic and widespread in various musical traditions of the world. An SLL feel pattern (short, long, long) shapes the timing of insiraf, a rhythmic mode of classical Arab music from Algeria ). An MSML pattern (medium, short, medium, long) underlies and identifies the subdivision of samba music from Bahia in northeastern Brazil. From the musician's view, this pattern serves as a marker of their rhythmic dialect, which they address as suinge baiano (Bahian swing) and distinguish from the feels of other regional styles of samba . Of course, the LS pattern is typical not only of Swedish polska. It marks the swing feel of jazz, the notes inégales of French Baroque music, and is also found in jembe music, a popular form of drum ensemble music from West Africa. [3] The present article analyzes the structures and music-theoretical status of non-isochronous beat subdivision in the standard repertoire of jembe music from Bamako, Mali. LS is only one among various timing patterns that appear in jembe music and I will describe three further patterns: two ternary and one quaternary. The approach is empirical and quantitative: I measure the timing of ensemble music performances. My theoretical aim is to show that rhythmic feel-the consistent characterization of subpulses by stable timing patterns-is inherent in the repertoire and fundamental to the metric system ABSTRACT: This article studies the empirical structures and theoretical status of rhythmic feels in jembe music, which is a popular style of drum ensemble music from West Africa. The focus is on systematic variations of durations -that is, cyclic patterns of non-isochronous pulse streaming at the metric level of beat subdivision. Taking for example a standard piece of jembe repertoire that is set in a 4-beat/12-subpulse metric cycle (often notated as 12/8), I show that the ternary beat subdivision forms a repeated sequence of unequal (short, flexible, and long) subpulses. This stable rhythmic feel pattern, SFL, is unmistakable and non-interchangeable with a second ternary pattern, which is characterized by long, flexible, flexible subpulses (LFF) and occurs in other pieces of jembe music. As predicted in Justin London's "hypothesis of many meters" (London 2004), these timing patterns distinguish individual meters. I further analyze how schemes of binary and ternary beat subdivisions can be synchronized to operate in parallel. Such metric nesting is based on the patterned non-isochrony of rhythmic feels. Cyclic variation of subpulse durations, I argue, is inherent in the repertoire and fundamental to the metric system of jembe music.
2021
For a video presentation of the conclusions of the work see: https://www.youtube.com/watch?v=fN4fU4laue4 Three times in the history of Western Music - at the end of the 14th century, the end of the 16th century, and the beginning of the 20th century – has there been a flowering in the development of non-dyadic rational rhythmic hierarchies. Only in the last of these occurrences has this development persisted continuously to the present; each time before, rhythmic complexity collapsed into a system dominated by dyadic- and/or triadic-rational rhythmic hierarchies. By the 17th century, even triadic-rational rhythmic hierarchies had totally disappeared from musical discourse to be supplanted by our modern system of dyadic-rational time signatures. Even into the 21st century, dyadic-rational time signatures remain predominant, despite work by composers like Henry Cowell and Conlon Nancarrow, which suggested the possibility of a rhythmic paradigm shift during the early- and mid-20th century. Despite the persistent hold of dyadic-rational time signatures, developments in prescriptive rhythmic complexity during the 20th century have continued to the present, persisting over multiple generations of composers and forming distinct schools of musical discourse popular in contemporary classical music today. Among these composers are not only Charles Ives, Henry Cowell, and Conlon Nancarrow, but also Thomas Ades, Brian Ferneyhough, Michael Gordon, Karen Khachaturian, Milton Babbitt, Elliott Carter, and Jonathan Dawe among others. Within their oeuvre, each of these composers have encountered the need for a broader exploration, development, and notation of rhythmic structure beyond our current dyadic-rational system, allowing in their music pan-rational time signatures, irrational time-signatures, and/or dense and/or indivisible rhythmic hierarchies – all of these levels of rhythmic prescription either not seen since the 16th century or altogether never before seen in Western music. Given the present state of our system of music notation and rhythmic prescription within it, what are we doing and what can we do now in the 21st century with the rhythmic tools developed in the past one hundred years? By thoroughly understanding the history of prescriptive rhythmic experimentation in Western Music, we can possibly better understand why certain systems of rhythmic notation have persisted while others have been forgotten; through such better understanding of the history of rhythmic notation we might fashion a notational system today that overcomes our present limitations in rhythmic prescription better than previous failed models. To this end, I will trace the historical development of systems of rhythmic hierarchy from Medieval to Modern music, focusing on music with exceptional prescriptive, precise, mathematically defined rhythmic structures, excluding aleatoric and spatially based rhythmic notation. In doing this, we will gain a historical contextualization of the rise of pan-rational systems of rhythmic notation. Following this, we will survey a variety of modern compositional methods that expand standard prescriptive rhythmic notation, beginning with Charles Ives and Henry Cowell and ending with living composers like Thomas Ades and Michael Gordon. Last, this dissertation will address my own compositional work in the context of pan-rational systems of rhythmic hierarchies and propose a new addition to the lexicon of rhythmic notation that will emancipate the composer from traditional dyadically-rational rhythmic notation.
Investigating Musical Meter as Shape: Two Case Studies of Brazilian Samba and Norwegian Telespringar
The perception of musical meter is fundamental for rhythm production and perception in much music. Underlying structures such as pulse, meter, and metrical subdivisions are often described as successive points in time. This paper investigates whether experienced musical meter may not only include such points in time, but also trajectories between the points–that is, metrical shapes. Previous studies have pointed out that there seems to be a relationship between musical meter and periodic body motion like foot tapping, head nodding and dancing. This paper investigates musical meter in music styles with an intimate relationship with dance, and whether metrical points and trajectories can be understood by investigating performers' periodic body motion. Two motion capture studies form the empirical basis of this paper; first, a percussionist and a dancer performing Brazilian samba; second, a fiddler and two dancers performing Norwegian telespringar. The analysis showed that it seemed to be a relationship between the periodic fluctuation in audio amplitude and the performers' periodic foot motion on sixteenth note level in samba. Furthermore, motion analysis revealed similar periodic shapes in both percussionist and dancer foot motion. In telespringar there seemed to be a relationship between the metrical beat level and the fiddler's foot stamping. In addition, the beat duration pattern, as indicated by the fiddler's periodic foot stamping, seemed to correspond to the shape of the dancers' vertical body motion. The results support the view that there is a close relationship between musical meter and performers' periodic body motion. This suggest that the underlying meter may not only include metrical points in time, but that each metrical beat/subdivision duration has a corresponding metrical trajectory with a certain shape. If this is the case, then perceivers' and performers' implicit knowledge of the underlying reference structure in samba and telespringar might incorporate knowledge about the underlying metrical shape.
Rhythmic interpretation of the logaoedic metres,
The term logaoedic seems to have disappeared from recent studies on ancient music and philology, despite the fact that logaoedic metres are mentioned in the principal Greek texts on metrics such as Hephaestion’s Enchiridion de metris and Aristides Quintilianus’ De Musica. Also Latin grammarians such as Marius Victorinus, Atilius Fortunatianus, Marius Plotius Sacerdos and Caesius Bassus mention this phenomeon. Probably this is the result of a controversial discussion on an issue which has never been fully understood, in part because of the difficulties of interpretation that the ancient texts present and in part because the metric analysis of these metres can not be conducted in a satisfactory way without a rhythmic contextualization of the phenomenon. The aim of this article is to give a coherent rhythmic interpretation of the logaoedic metres, comparing the sources and presenting the rhythmic schemes of the examples cited in them.