In this chapter I shall turn to the concept of meter, and its role in shaping our musical perceptions. The first question to ask is why we have meter at all. I shall stress that meter has some special status among the various time spans of music, and in particular that its function is both established and constrained by our embodied perceptual and cognitive abilities. Later I will discuss some subtleties in the question of how we perceive meter in situated musical contexts, by examining its role in instances of West African music.

Rhythmic timescales. The extremely influential techniques of Schenkerian analysis (Schenker 1979) are characterized by concepts of hierarchy, progression, and recursion. Musical structure is understood on three levels: foreground, middle ground, and background. Analysis is seen as a process of isolating, identifying, connecting and integrating these three levels of musical perception, aiming for reduction of musical surface structures to a series of nested levels. The perspective is hierarchical in its layered organization and progressive in the implications between events within levels. The role of recursion is metaphoric, in that a large piece can be seen as a giant cadence, or composition as the large-scale embellishment of an underlying harmonic progression. The Ursatz, or underlying background structure, is seen as the point of analysis and the mark of a good composition. The theory presupposes that music's purpose is its background and not its foreground. This assumption seems to bias the very concept of analysis in favor of long-term form; ultimately, the entire theory legitimizes its own goals.

According to Lerdahl and Jackendoff (1983), who have a strong allegiance to the Schenkerian point of view, grouping structure in music is said to be recursive because it is supposed that there is a uniformity from level to level. That is, grouping structure can be elaborated iteratively and indefinitely by the same rules (ibid: 16). They suggest that "the elements of metrical structure are essentially the same whether at the level of the smallest note value or at a hypermeasure level (a level larger than the notated measure)." (ibid: 20) There are many objections to such a formulation. It must be granted that this is a theory of perception and cognition, not of composition; hence it does not presume that such uniformity exists in the music, but rather that in listening to music we tend to expect such regularities. However, an immediate problem with this kind of analysis is that it presupposes a kind of classic large-scale order or unity; notes hang together coherently as melodies, phrases answer other phrases, sections balance each other. The concept of coherence (often phrased by contemporary composers as "what works") is an old problematic, ascribable to many structuralist and pre-structuralist literary theories. It has been deconstructed by the observation that coherence or artistic unity is projected by some theory of coherence, and not by any intrinsic properties of the work itself (Street 1989). As another critique of the notion of recursive hierarchy in music, Narmour (1990) supposes instead that there can be multidirectional networks and communication between levels of the hierarchy.

In any case, if taken literally, the claim of recursive grouping hierarchies in the temporal domain must be rejected on simple cognitive grounds, because of the qualitative differences among the three kinds of memory, namely the echoic store, short-term or working memory, and long-term memory. As Brower (1993) has pointed out, echoic memory covers the immediate timescale of rhythmic activity ("foreground rhythmic structure"), whereas short-term memory covers meter and phrases ("middle-ground"), and long-term memory covers the timescale of musical sections and movements ("background"). The three different types of memory involve different kinds of processing. We entrain to a pulse based on the echoic storage of the previous pulse and some matched internal oscillator periodicity, we feel the relationships among strong and weak beats (accentual meter), we count times between phrases or bars (metric grouping), and we associate features of one section with memories of a previous section that is no longer represented in serial order. So for example, we can experience syncopation at the metric level, and so-called expansion and contraction at a higher level, but these are qualitatively not the same cognitive phenomenon. Hence it appears that the notion of recursion does not apply literally as we switch among these different timescales, because they operate in very different ways from a cognitive perspective.

The above arguments suggest that we tend to organize music in terms of certain ranges of musical times that are commensurate with the timescales of human activity, in keeping with the remarks of the previous chapter on embodiment. Among the pieces of the rhythmic puzzle that we discussed were three qualitatively distinct embodied regimes of temporal perception: the quick detail of speech and digital motion, the steady tactus-level pulse, and the phrasal breath. These distinctions, together with the arguments about grouping and memory discussed above, all enter into the following discussion of meter.

 

Pulse perception. One of the most crucial aspects of rhythm perception that has been established experimentally is the mind's role in entraining to a periodic input signal. This ability allows us to tap our foot to music. Given a periodic auditory pulse as input, we have a low tolerance for error in the signal; we easily detect any sudden deviation from periodicity above a small threshold. One might suppose that the mind would detect such errors in any of three ways: (i) compare each inter-onset interval (IOI) to each previous IOI, (ii) match the periodic signal to an internally generated periodic oscillator, or (iii) match each IOI to an internal ideal period.

Schulze (1978) carried out the following experiment to test each possibility. Subjects listened to a periodic series of tones with one of three possible kinds of small temporal perturbations, as shown below. From elementary theoretical considerations, it was possible to rank the errors detected by each method for three different experimental conditions. Estimates of the relative discrimination index for each of the methods (i)-(iii) are shown for each kind of perturbation. Each line represents one experimental configuration, in which an isochronous series of tones or clicks, separated by an inter-onset interval t , is modified by a perturbation D . In the experiment, the change occurred after a large number of unchanged intervals, to establish regularity. (Table adapted from Shulze 1978.)

[inline-center:image14-1.gif]

It turns out that the second alternative (ii) is correct. In other words, when we hear a regular rhythmic pulse, we don't match the intervals one by one, nor do we compare each interval to an internal ideal interval, but rather we co-perform this periodic pulse internally. This kind of internal, synchronized pulse generation is known as entrainment. A relatively simple phenomenon, entrainment is the essence of pulse perception. It has turned out to be a rather prodigious computational problem (Desain & Honing 1991).

Meter.
The next step up from entrainment is a more complex phenomenon known as meter perception. Much music of the world is organized metrically, that is, according to a periodic grouping of pulses; this grouping may or may not be explicit in the musical surface. Most generally, meter is a periodic grouping of a musical time unit; it can connote but does not strictly imply a hierarchy of weak and strong beats. Meter denotes a subharmonic (or grouping) of a pulse, and might also suggest a higher harmonic (or subdivision) of the same pulse. That is, it can simultaneously group and subdivide pulses into regular units. For example, the time signature 6/8 denotes a cycle of two pulses, each divided into three equal subunits. The best understanding of meter is as a periodic grouping of perceived pulses -- i.e. as a cognitive/perceptual phenomenon, not as an objective reality of the acoustic signal. However, this distinction is often elided, so we might speak of the meter of a piece of music. In doing so we would make some assumptions about the listener's and the musician's musical presuppositions. Studies of rhythm perception of both test patterns and musical performances show that meter itself is an ambiguous if not wholly imaginary property of the audio signal (Parncutt 1994). A given rhythm, whether intentionally musical or not, can evoke a number of contrasting pulse sensations and metric orientations in different listening subjects or in different trials with the same subject. In this regard, as we shall see below, West African and many African-American musics are no exception.

To circumvent this problem, one could create a distinction between the functions of meter in music production (as a generative principle) and in music perception (as an information-processing strategy). Or, more compellingly, one could avoid this distinction by defining meter as an internal periodic template that frames and temporally grounds both perceptions and actions. This latter definition is in keeping with a model proposed by Povel (1984). This model was proposed in response to experimental data involving both perception and imitation of temporal sequences, in which it was found that both musically trained and untrained subjects map temporal sequences onto an interval structure. In the model, the first step in temporal processing of music consists of a segmentation of the sequence into equal intervals (i.e., beats) bordered by events. In a second processing step, intervals smaller than the beat interval are expressed as a subdivision of the beat interval in which they occur. These beats and subdivisions serve to orient perception and action in a musical environment; meter may be seen thus as an attentive mechanism, as discussed below.

One small shortcoming of the above model, also admitted in a treatment by Lerdahl & Jackendoff (1983: 97), is that this definition of meter is challenged by asymmetric meters containing odd numbers of beats or an irregular pulse. In many cases (e.g. Eastern European, Greek, and Middle Eastern folk musics, South Indian classical music) one entrains to a series of long and short beats at the tactus level. These different kinds of pulses almost always occur in the duration ratios of 3:2 or 2:1, implying a common small temporal unit at a lower metric level. From these cases, it is apparent that a concept of metrical structure should not enforce regularity of pulse if it claims to apply universally, but instead should allow for a repeating group of irregular tactus-level pulses of either 2 or 3 constituent units.

Similarly, the accentual view of meter -- in which a metric template is seen as always reinforced by accentual and microtiming variations -- does not appear to carry over to many non-Western musics. One should not regard the global musical preponderance of "syncopation" (off-beat accents) as a vast set of exceptions to the "normal" accentual rules of meter, but rather as convincing counterexamples to such proposed accentual rules. Various signal-processing techniques have been developed to derive a pulse and a meter from musical recordings, but typically such attempts yield notoriously variable results for many such "syncopated" kinds of music such as jazz (e.g. Todd et al. 1998). This is because meter is not necessarily inherent in any audio signal. It is a perceptual and cognitive construction, derived from some perceived periodic patterning of perceived accents (including, paradoxically, accents imposed by the imagined meter itself) but also from some set of assumptions about meter.

Indeed, indicated meters appear in most Western sheet-music scores because of the composer's desire to exploit these assumptions, to allow the implications of a time signature to shape the perfomer's understanding and subsequent rendering of the piece. Aspects of meter can be conveyed in expressive musical performance. In Western tonal music, a given meter can suggest a certain template for phenomenal accent patterns and sub-tactus expressive timing variations. Meter provides a basic guideline for manipulating loudness, timbre, and timing in keeping with the composer's intention. Additionally, there exists a large vocabulary of diacritical marks to extend the connotations of meter. Due to all of this, we tend to speak of the meter of a piece objectively, because it is simply the time signature written to the left of the first bar of written music. This tendency is carried over erroneously to many ethnographic analyses of nonwritten musics, where the "meter" is simply that perceived by the transcriber. In a study of a foreign music, one should be aware of the cultural baggage attached to a musical concept like meter. There may be an analagous concept of orienting a periodic grouping of pulses, but it need not imply all the other attributes of meter that we recognize in Western music. Later I examine this possibility in the study of West African music.

Sometimes meter is also used to connote larger periodicities (as in "hypermeter"). Lerdahl and Jackendoff (1983) characterize metrical structure as a hierarchical nesting of beats to arbitrary degrees of recursive depth. This formulation covers too broad a range of timescales and presupposes temporal "unities" where they need not exist. In attempting to apply this theory to some rather simple musical examples (Lerdahl & Jackendoff 1983: 250-253), they encounter unexpected difficulties, and find that the supposition of large-scale periodicities beyond the barline level is much less robust and highly error-prone. It appears that meter functions most effectively as relatively small periodic groupings of the main beat, and quite variably at higher levels.

London (1997) has claimed that polymeter does not exist; that is, one cannot perceive two meters at once. Since meter exists only in the minds of the listeners and the performers, two meters thus cannot "exist" at once in the same mind. Instead one can hear ambiguous rhythms in which different metric candidates compete. The result, however, is not the simultaneous perception of two contrary meters but the canceling of the effects of one meter by the other. One can be aware of the possible presence of two different meters, and one can switch actively between perceiving them, as one can between the vase and the two faces in the classic visually ambiguous figure. One can also hear metrically vague music, in which no periodic grouping of pulses suggests itself. Certainly two people may simultaneously hear different meters in the same music. But one person cannot entrain simultaneously to two separate pulse groupings. In the classic figure-ground relationship, only one meter can function as the ground. This claim against polymeter seems to apply only to groupings of pulses in the vicinity of the tactus, however. One can be aware of multiple subdivisions of the tactus (as in some examples of Afro-Cuban rumba, where we perceive both quadruplet and triplet subdivisions in abundance [CD-28] ). [node:3798 teaser] Similarly, one can simultaneously hear different-length groups of measures (as in James Brown's "I Don't Want Nobody to Give Me Nothing" [CD-29] ,[node:3799 teaser]in which we easily apprehend that the vocals are in four-bar phrases and the horns and drums cycle a three-bar unit). Hence the claim against polymeter refers more to the level of entrainment than to perception in general - that is, to the act of imagining the movement associated with the rhythm, rather than the act of "hearing" the rhythm passively.

Our attentional capacities are sharply delineated by the timescale implied by meter, namely, that of the tactus. It is suggested by many (Gjerdingen 1989, Jones 1986, Jones & Boltz 1989, Jones & Yee 1993) that meter provides us with an attending mechanism -- a temporal template against which to process information in time. Meter is seen as an invariant of the musical environment, computed from recurrent temporal patterns. As an invariant, it gives us a baseline from which to discern musical variation (such as musical rhythm and expressive timing) more efficiently. This view is supported in experiments in which subjects have more difficulty reproducing rhythms that do not have an obvious common time unit than those that do (Jones 1986). Modelling metric oscillations with neural networks is quite straightforward. It seems plausible that a small signal from a modest, neurally based metric counter could be used to modulate the performance of a much larger neural network according to a given meter, yielding a form of metrically modulated attention (Gjerdingen 1989: 78).

In differentiation among various timescales of music, Jones (1993) and Jones & Boltz (1989) has described different music-listening strategies as different kinds of attention, namely future-oriented (long-term, memory-based) vs. analytic

(short-term, perception-based) attending. Actually, this distinction is more relational than absolute; there are intermediate regions between the two extremes. In any case, we can associate analytic attending with the timescale of musical meter.

These distinctions lead one to believe that, in its most useful form, meter measures a narrow range of rhythmic phenomena, limited roughly to what has been called the psychological present. Meter functions as an orienting principle among some small number of (often regular) tactus-level beats -- between two and eight, roughly. A metric grouping of beats stretches over a duration between approximately 800 ms and 5 s, which lasts longer than the duration of the echoic store (< 1 s) but shorter than the span of working memory (~ 30 s). Apparently, then, we must scale back our definition of meter itself to denote only groupings of the tactus. Hence hypermeter is not a true species of meter, nor is a smaller subdivision of the main beat ("micrometer"). One will find apparent exceptions to this rule in some adagios from the tonal-music literature, where a written measure might stretch over ten seconds, or in some allegros or prestos, where a written measure might last a half-second or less. Typically in such cases, however, the written meter and the perceived metric grouping are far from identical, the latter being both somewhat variable from one individual to the next, and somewhat constrained by our attentional capacities.

In light of these arguments against both polymeter and hypermeter, it becomes clear that the perceptual groupings of the musical tactus into twos, threes, fours, and so on (perhaps up to eights) retain special status among rhythmic perceptual phenomena. This unconscious periodic grouping of pulses as some kind of gestalt would saturate at "the magical number seven plus or minus two" (Miller 1956) at which point perception with such ease becomes impossible. At metric lengths beyond this, we require either a conscious counting principle to hold our place, or a grouping procedure for "chunking" the beats into larger units. In addition, familiarity is an issue with meter. The sound and feeling of a given meter needs to be experienced, or else it will not function in this unconscious way. This is why, for example, five-beat groupings seem alien to westerners but are quite common in Indian popular music. More remarks on cultural aspects of meter appear in a later section.

Models of meter perception. As mentioned above, meter perception has prompted a number of researchers in music cognition to develop models with varying degrees of success. Large (1994) has developed a compelling model for beat perception, which he has subsequently (1997) applied to meter perception. He modeled the phenomenon of beat perception as a pattern of coordination that arises between an internally generated periodic process (a self-sustaining oscillator) and a periodicity within a complex external rhythm (Large 1994, Large & Kolen 1994). The listener and musical input are treated as a single dynamical system consisting of the external (driving) rhythm and the internal (driven) oscillator; the attractor states of this dynamical system correspond to instances of entrainment. The internal oscillator's dynamics are assumed to adapt to the external periodicity, thereby modelling the robustness of ordinary beat perception to the subtle, systematic timing deviations that occur in human performance. Large (1997) has also developed the notion that networks of these oscillators can combine hierarchically to respond to multiple periodicities in the driving signal. The model allows hierarchies of entrainment, whereby a fundamental pulse frequency (the beat) and its subharmonics (slower periodicities) coordinate with distinct phase relationships. This is presented as a model for meter perception. While it provides some compelling results that are robust under expressive tempo variation, it appears that this model neglects crucial aspects of our perceptual apparatus that cause us to distinguish between pulse and meter. As discussed above, the notion of a tactus provides a primary pulse range that sits squarely in the echoic-memory regime, whereas the larger timescales associated with meter invoke a different variety of cognition (Brower 1993). In his model, by treating all periodicities as equivalent regardless of length, Large fails to ground his model in the embodied temporal processing abilities of human beings. Hence, while the model works very well with the expressive tempo variations of tonal music, it is not clear to what degree it represents the ways that we perceive and interpret such structures.

Another recent effort to construct a model for rhythm perception (Todd et al. 1998) stems instead from a strongly embodied sensorimotor theory. The authors have developed a model that takes into account the natural biomechanical frequencies of the body and the temporal characteristics of the auditory system, and treats beat induction as an active rather than a passive process. The computational implementation takes audio input and synchronizes a simulated locomotive action. When applied to something as culturally contingent as music, however, the implementation encounters problems getting the phase relationship right for the pulse of the audio signal, not to mention the meter. The model seems to err on the side of overemphasis on the sensory-motor (embodied) component, failing to account for the possibilities of supplementing or even overriding this component with learned input. The only learning discussed is that which tunes the sensory systems to their embodied dynamics and the motor control systems to the temporal-motional properties of the physical environment. However, as musical beings, we know that musical perception involves more than physical and raw sensory input. We cannot forget the role of culture in shaping our perception, and this includes rhythm perception, as I shall argue below.

Rhythm and Meter in West African Music

Studying what others have said about meter in the music of other cultures helps us understand the most basic, possibly cross-cultural functions of meter. In doing so, however, we have to unravel the cultural biases that all too often mark such cross-cultural studies. As a case study in the remainder of this chapter, I shall present my reactions to a wide variety of viewpoints from various ethnomusicologists, psychologists, and theorists about meter, pulse, and rhythmic grouping in West African music. In my opinion, many of these studies are characterized by two striking trends: a misapplication of music-theoretic and music-cognition models of rhythm and meter stemming from studies of Western tonal music on the one hand, and a well-meaning application of misunderstood African cultural and musical principles on the other. Although the models suggested by Lerdahl and Jackendoff (1983) and others go to great pains to keep meter and rhythmic grouping separate, the precedents set in African musicology by Western scholars tend to confuse the two. Furthermore, they tend either to ignore or to oversimplify descriptions provided by musicians and musicologists who come from West African cultures. Many highly influential treatments are fraught with misleading statements about such things as polymeter in African music. For example, Jones (1959) transcribed musical rhythms such that each phrase begins at the downbeat of a new meter, resulting in a jumble of meters of varying lengths and negligible perceptual salience. Below I attempt to address the contradictory viewpoints that works such as Jones's have engendered.

The Ghanaian percussionist C. K. Ladzekpo, a prominent performer and teacher of Anlo-Ewe dance-drumming in northern California, has written an extensive web document on the technique, practice, and cultural functions of this art form. He begins his section on rhythmic techniques thus:

In a complex interaction of beat schemes of varying rhythmic motions, the human mind normally seeks a focal point. Among the Anlo-Ewe, one of the integral beat schemes is dominant and the rest are perceived in cross rhythmic relationship to it. This dominant beat scheme is considered the main beat because of its strong accents in regular recurrence that pervade and regulate the entire fabric...
[I]n practice, the beat scheme of four units is the most commonly used. At any given tempo, the rhythmic motion of this beat scheme is the most moderate (not too slow or fast) and the most convenient as a focal point...

To better comprehend a main beat, it is structured so that it measures off equal increment of pulsations, the first of which normally bears an accent. These integral fractions or background pulsations are the major ornamental forces that give a main beat its distinct texture, flavor and character... The recurrent grouping of the main beats normally creates a fixed musical period or measure. While it is possible to create several measure schemes by varied groupings of the main beats, two types of such groupings are the most frequent in the development of Anlo-Ewe dance-drumming. The first most useful measure scheme consists of four main beats with each main beat measuring off three equal pulsations as its distinctive feature. The next most useful measure scheme consists of four main beats with each main beat flavored by measuring off four equal pulsations. These beat schemes are roughly equivalent to 12/8 time and 4/4 time in Western music.

In contrast to the Western measure concept of accenting the first beat of each measure, the Anlo-Ewe concept maintains regular accents on all the main beats. However, there is a tendency to end phrases as well as the entire composition on the accented pulsation of the first main beat implying further movement or flow. (Ladzekpo 1995)

Ladzekpo clearly states that the chief rhythmic organizing principle is an isochronous pulse in an appropriate tactus range, typically grouped into metric units of four pulses, and also subdivided into smaller isochronous subdivisions of three or four. The first of each such group of subdivisions is usually accented, but the first of each group of four pulses is no more accented than the other three. However, the first pulse of a group of four is understood as the end (as opposed to the beginning) of many musical phrases. The first pulse thus has privileged status among the four pulses and corresponds somewhat to the Western notion of a downbeat, although it functions slightly differently. In the original document, all of Ladzekpo's statements are supplementally depicted in Western musical notation to minimize cross-cultural ambiguity.

The strong accents to which he refers should not be taken to mean sonic accents. As noted in Pantaleoni (1972) in reference to the music of this same ethnic group, the gradations in volume accent in West African drumming do not necessarily correspond to those implied by a European time signature such as 12/8 or 4/4. In fact, the volume accents alone may rarely reinforce any unified meter at all, by Western standards. To the "experienced" listener in the dance-drumming environment, however, accents can also be of a phenomenal (sonic, visual, tactile) or purely cognitive (metric) nature. Not only do we have some metric sense that frames the rhythmic activity with conceptual accents; also, we see the dancers' grounded footwork and the musicians' subtle body language, and we feel the sticks beating the drums and the ground shaking. Such paramusical input is operative in any performed music, much as paralinguistic phenomena are in most linguistic communication (McNeil 1998); these aspects are consequences of situated cognition.

Much West African music is characterized by variable and repetitive rhythms played in conjunction with a basic timeline, such as a fixed pattern played on a bell. The bell part functions as a point of reference, a constantly repeating pattern that the other musicians use to orient themselves metrically. But one should be careful with the connotations of this last statement. Whatever parallel concept of meter exists in these cultures, it does not necessarily imply the same template of accents and stresses that a Western meter does. I am using meter in the sense offered in the previous section -- namely, as a perceived periodic grouping of tactus-level pulses. The extra connotations associated with Western meter, such as an accentual template and a basis for expressive tempo modulation, are not included in this general understanding of meter.

(To complicate the issue, the presence of African diasporic musics in the West, and their more and more frequent rendering in Western notation, has smoothed out the difference. For example, a piece of commercially available sheet music can bear next to the tempo marking a suggestion such as "swing,"

or "slow funk groove," or even "African 6/8 feel," thereby implying a rhythmic treatment that is decidedly non-European, that is indeed derived from African rhythms (Wilson 1974), and that is not implied by the time signature alone. Hence there has been a gradual expansion of the possibilities of written music to include non-Western elements, to the point that one cannotdraw a sharp boundary between Western notational concepts and non-Western musical practices.)

A guiding aesthetic principle in West African musics privileges rhythmic groupings that would challenge or "Signify on" the integrity of the pulse. It must be noted that an important function of the performance of drum music is the psychological balance achieved by internalizing seemingly conflicting rhythmic unities at the physical level (Ladzekpo 1995). Part of the crux of the activity of dance-drumming involves maintaining one's balance (i.e. one's sense of the steady isochronous pulse, metaphorically viewed as "purpose in life") in the midst of a torrent of interlocking cross-rhythms (metaphorically viewed as "obstacles") (Ladzekpo 1995). This does not necessarily imply that the intention of the composer/performer is to induce polymeter, nor does it imply the opposite. Rather, the musical construction is not framed in terms of meter, but in terms of crossed rhythmic groupings; these groupings can be serial or periodic or both, to use Parncutt's (1994) terminology. When two meters appear to the listener, it is because there are periodic groupings of short, serially organized rhythmic fragments or phrases, and their periodicity seems to imply a different meter from the primary one. In the sense described above, the music becomes metrically ambiguous. Most commonly it is some variety of triple meter that seems to appear over some variety of duple meter. But in context it is seen as a challenge, not an alternative, to the prevailing meter; frequently the latter is so obvious subjectively to the practitioner that it is not reinforced sonically very much at all. Waterman (1952) also emphasizes the importance of the subjective beat in African music, the underlying pulse that is not necessarily beaten out literally. He stresses that the appreciation of African music necessitates a "metronome sense." European music emphasizes the main beats, the upbeat and the downbeat. By contrast, African musicians assume implicitly that their audience is imagining these fundamental beats without difficulty; the audible musical material will fashion its rhythms around this mental beat, often using polyrhythms, cross-pulses, offbeat melodic accents, and much indirection and subtlety. Hence perceived groupings in the audio signal need not delineate the meter, and in fact frequently run counter to it.

So, where is meter in West African and related musics? If the Anlo-Ewe music described by Ladzekpo is any indication, meter is there, solidly, unproblematically, in the mind of the practitioner, and equally solidly in the mind of the acculturated listener, even if it is not obviously apparent in some objective rendering of the acoustic signal. One learns the main beat, its subdivisions, and its metric grouping; and then one learns the rhythm of the bell pattern, which simultaneously groups the main beats into larger units of four and subdivides them into smaller units of four or three. This simultaneous grouping and subdivision denoted by this referent rhythm suggests a way of orienting one's attention and physical entrainment to the musical signal; i.e., it connotes a set of assumptions in much the same way that a European time signature connotes a related but distinct set of assumptions. When learning to perform other rhythms in this music, one's attention is continually directed towards the concurrent bell pattern. This is done not because the asymmetric bell supplants the regular pulse, but because the bell gives the most consistent depiction of the pulse and its organization. Sonic accentual reinforcement is unnecessary and (uncoincidentally) is not a guiding aesthetic.

Thus the main beat and its metric grouping are articulated in a rather indirect fashion -- not with a continual parade of accentual reinforcement, but with suggestion and complexity. The meter is encoded in the rhythm itself. The way in which this is done is unambiguous but highly culturally specific. (In the audio examples that follow, a click track is heard alongside the written patterns, with the high click on the first beat of the written measure.) For example, the standard 12/8 bell pattern of the Anlo-Ewe people is heard phrased as [CD-30] [node:3784 teaser]

[inline-center:Image14.gif]

whereas the same bell pattern would be heard with a different starting point by the Yoruba people, as [CD-31] [node:3795 teaser]

[inline-center:Image15.gif]

and by yet another ethnic group as [CD-32] [node:3787 teaser]

[inline-center:Image16.gif]
Furthermore, the patterns are not necessarily grouped according to the barlines; for example, the Yoruba pattern is said to be grouped such that the final note is the so-called downbeat (Anku 1992), i.e. [CD-33] [node:3794 teaser]

[inline-center:Image17.gif]

where the parentheses delineate the grouping over the barline. (In the audio example, the grouping is delineated by a slight accent in intensity on the first note of each group.) Note that respective boundaries implied by grouping and meter do not reinforce each other in this case; this possibility is allowed for in the respective definitions of grouping and meter. This example shows that both the placement of the tactus and the grouping of elements varies from one community to the next with respect to a single rhythmic pattern.

Typically the constituent beats and subdivisions are not literally "counted" by the African practitioners. Hence literally there is no "1." Rhythms are frequently represented instead as linguistically derived mnemonics, an obviously favored technique in an oral culture. An example is the simple rhythm known in the West as "three over four" and represented by Ladzekpo as [CD-34] [node:3780 teaser]

[inline-center:Image18.gif]
This example is onomatopoeic, but there are many documented examples of rhythmic mnemonics with semantic meaning as well (Anku 1992).

(There has been a chicken-or-egg debate about the status of these linguistic phrases: are the rhythms derived from language, or are the phrases arbitrary mnemonic devices to represent the rhythms? Ladzekpo (1995) stresses the ubiquity of symbolic and metaphoric encodings in African music, which seems to support the former view. In any case, the fact that linguistic proverbs have been long associated with many rhythms in many African drum musics suggests that the music carries these meanings, whatever their etiology.)

The bell patterns mentioned above may be seen as musically encoded time signatures in a self-consistent musical language, implying a different set of basic assumptions than are used in the West. In many West African musical contexts, one learns the proper placement of rhythms not merely in relation to an underlying abstract meter but to the bell pattern itself; no explicit reference need be made to an underlying metric abstraction. An outcome of this approach is the organization of phrases relative to the so-called downbeat, referred to by Ghanaian musicologist W. Anku as the Regulative Time Point (RTP) (Anku 1992). Instead of referring to a specific subdivision of a specific beat in the metric hierarchy, a rhythmic phrase is said to have a specific relationship to the RTP. Improvisations based on this phrase will maintain this relationship, yielding the repeated use of what in Western terms might be called an anacrusis or "pick-up." In the figure below are some examples of rhythmic themes with different RTP relationships, i.e. different phase relationships to the underlying meter. The groupings are specified by the parentheses around each theme. A phrase with RTP n corresponds to the RTP placement on the nth relevant subdivision from the beginning of the phrase. For example, the bell pattern is designated as RTP 9 because the ninth eighth note of the phrase (beginning after the grouping parenthesis) is the RTP or downbeat, as indicated by the central hash mark.

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The examples are taken from Anku (1992), who describes these rhythmic phrases as structural sets because of the way they organize subsequent rhythmic material. The RTP corresponds to the downbeat in the indicated time signature. I have mixed representations here to ease understanding; Western meter is used to explain the West African RTP notion. (In the audio example [CD-35] , [node:3781 teaser] again you hear a metric click track to guide the ear, and again the groupings are delineated by a slight accent in intensity on the first note of each group. Once established, the bell pattern is sustained throughout, while themes 1, 2, and 3 are presented in succession.) Again, these phrases are often linguistically based, and thereby carry the encoded meaning of a proverb. The placement of the RTP in such a phrase may suggest the added element of linguistic emphasis (which in music we might call metrical accent), as in the difference between "I walked to the store" and "I walked to the store."

Hence, not only does the RTP relationship thoroughly specify when to begin a phrase in the metric cycle implied by the bell; more importantly, this relationship delineates the distribution of emphasis. This is similar but not identical to the accentual template implied in European music by a time signature, and in particular by the downbeat. However, the RTP relationship carries a stronger implication of repetition and cyclicality than is connoted by anacrusis and downbeat. A certain section of drum-ensemble music might be characterized by a certain RTP relationship, maintained each time the metric cycle comes around; the change to a new RTP relationship characterizes the transition to a new section. This treatment amounts to a different way of conceptualizing meter, in which no reference need be made to any mathematical abstraction or its accompanying accent pattern.

The crucial orienting role of the bell pattern and the complex interplay among the interlocking cyclic patterns on like-sounding instruments demands a high degree of skill in both auditory scene analysis (Bregman 1990) and selective attending (Jones 1993). These cognitive facilities are rarely highlighted in speaking of Western tonal music, which tends to be less stratified and less rhythmically dense at the tactus level. However, the centrality of streaming and attending in music perception and cognition should be apparent both generally and in the specific case of drum music. I return to the notion of streaming in the next chapter, where I point out how certain expressive rhythmic manipulation can enhance segregation of similar streams.

Meter perception and culture. Much has been written about African cultural concepts of time and how they might influence the approach to musical time. Ethnotheoretic discussions of how time is represented in the minds of African musicians (Merriam 1982, Stone 1985) have failed to appeal very extensively to African musicians themselves for information. Extramusical cultural investigations, usually in the form of literature searches, have given rise to rather extreme speculation about the "nature" of African time in the mind of "the African." While ostensibly aiming for cultural sensitivity, such studies have often applied oversimplified versions of selected cultural models rather abusively. A so-called "cyclic" mythology of life and death was seen to correspond to a beat cycle (Stone 1985) even though Western music also has beat cycles in the supposed absence of such a conception. Similarly, a cultural lack of ideal incremental measurement of time was seen as an argument against the existence of a steady underlying pulse (Merriam 1982) in a music that is quite unarguably pulse-based. These ethnomusicologists seemed determined to find essential differences between Western and non-Western ways of thinking, and to be able to display such differences in a pat description. In doing so they commit an epistemological error of presuming that such essential differences in worldview can be contained in one language but not in another. In other words, by assuming the role of impartial observer, they implicitly construct their own vantage point as a superior one for discerning such difference (Agawu 1992).

In this way they seemed to recapitulate the controversial stance of Whorf (1956), who asserted (despite a poverty of evidence) that the Hopi language contained such a radically incommensurate conceptualization of time from English that the Hopi themselves must experience a severely different reality from ours. (Whorf's well-meaning but flawed claims were later refuted in Malotki (1983)). The West African musicologist K. Agawu wrote, in direct response to such misinformed efforts in the study of African music, "[W]e have to be careful not to fall prey to simple dichotomies, especially those propped up by a vulgar essentialism." (Agawu 1992: 266) Elsewhere, he cautions:

What must finally be resisted is the impulse to construct an Africa that is always different from the West. No doubt some differences cannot be suppressed, but one may be surprised by the extent to which the need for, and circumstances of, music-making in Africa resemble conditions in other parts of the world, and bespeak a basic human need for artistic expression. (Agawu 1995: 4-5)

And again, on the "project of 'exoticizing'"

African music: "[S]uch relentless pursuit of difference must be resisted ... because it is likely to blind us to those areas in which difference actually occurs. For difference is perceivable only against a horizon of non-difference, and until we have constructed such a horizon, our efforts to understand African rhythm will continue to founder." (Agawu 1995: 193)

I do not mean to dispute concepts of mosaic time, nor to downplay the role of cyclical structures, nor to ignore the importance of learning the whole simultaneously with the parts, nor to dispel any other valid insights about African cultural models. Rather, in keeping with Agawu's admonitions, I only mean to be careful about how these ideas are described and employed, especially in regards to musical "time-reckoning." Just as we would not tolerate an assertion that all Western music is linear all the time from start to finish because all Western thought is linear and rational (nor could we really explain what such a claim is supposed to mean), so we cannot make such crude generalizations about the entirety of African music based on a vague and poorly explained cultural tendency.

While many rhetorical assertions are made that African musicians do not measure time or do not have a linear concept of time, nowhere are these claims proven in connection with music (nor is it very forcefully proven that all Western musicians do). A recent attempt to prove such a claim (Magill
& Pressing 1997) is by its own admission (Magill & Pressing 1997: 189; Pressing, private communication, 1998) scientifically inconclusive, although rhetorically quite assertive in its conclusion. The study is predicated upon a rather misleading dichotomy between "an asymmetric timeline-ground model, which represents a computational elaboration of traditional African understanding, and a pulse-ground model, which is based on Western ideas of regular meter" (Magill & Pressing 1997: 189). In other words, it is supposed that the "Western" concept of steady pulse does not exist in "traditional African understanding," and that African music's irregular "timeline" rhythm takes the place of pulse. The quote from Ladzekpo (1995) in the previous section suggests that no such dichotomy exists for him. Curiously, Ladzekpo and his brothers are cited as a reference in Magill & Pressing, as is a humorously long list of other Western and African "experts" (Magill & Pressing 1997: 190, 197), provided as if to demonstrate enough agreement as to render any challenge moot. When I pointed out Ladzekpo's description of the pulse as the cultural equivalent to a sense of "purpose in life," Pressing (private communication, 1998) claimed that Africans have a different way of explaining it to westerners that really does not correspond to their inner thoughts. To this I must respond, why the conspiracy?

In their rigorous statistical analysis of the bimanual tapping of authentic West African rhythms by an authentic Ghanaian percussionist N. K. Owusu, Magill & Pressing (1997) seem to have thrown the experiment off by asking their subject to refrain from playing in his usual way:

Mr. Owusu would often implement various flams in the course of a trial without conscious awareness. This apparently common stylistic device at first played havoc with the selection criteria, and as a result, it was necessary to remind him repeatedly at the beginning of each trial to avoid flamming... Mr. Owusu also showed a marked tendency toward acceleration over the course of a trial. This is not surprising as it is a common stylistic trait used in Asante drumming music; however, because it risks creating uninterpretable nonstationarity for long runs, he was also regularly reminded to maintain a steady tempo. (Magill & Pressing 1997: 204)

Pressing (private communication, 1998) reported that in fact Owusu would accelerate and decelerate over the course of a measure. I suspect that both the flams and the supposed tempo variation were actually a form of expressive timing against an isochronous pulse, as discussed in chapter 7. Furthermore I can imagine that such rhythmic expression was deeply intertwined in his performing practice, inseparable from the rhythms themselves, to the extent that forbidding him from playing this way created a highly irregular playing situation for him -- irregular enough that the results are necessarily inconclusive.

When learning West African music, one is instructed constantly to focus on one's relationship to the bell. But this should not be taken so literally as to ignore the pulse; for one is also continually reminded to remain grounded, which in my estimation is closer to staying with the (most often duple) pulse. This sense of pulse is highly contextual. It is undeniable that a given rhythm can be "pulsed" in a variety of ways; West African musicians are trained in the abilities to shift their metric perspective on a rhythm and to hear and generate cross-rhythms. But it is not necessarily the case that advanced West African musicians hear all possible metric groupings simultaneously to such a degree that any semblance of meter dissolves. There is nearly always one prevailing meter, against which all other metric possibilities provide a sense of contrast. In any case, despite frequent efforts to portray African music as "participatory" (Keil and Feld 1994), there is no question that West African musicians are highly specialized, possessing knowledge and understanding that goes far beyond that of the average West African person (Agawu 1995: 116). Hence it is not clear that the extreme competence of one highly trained individual may generalize to an entire subcontinent. Surely, "inner" musical time remains a mysterious and unexplained dimension of music cognition in general. But that does not imply, as some would have it in African music (Magill et al. 1997; Pressing, private communication, 1998), that there is no commonly agreed upon pulse or time unit among members of a musical ensemble or its listening audience, nor even that there is a deemphasized reliance upon such units.

Occasionally, attempts at understanding of cultural differences can turn out instead quite pejorative. When the same Ghanaian musicologist offered his voice to the fray (Agawu 1986) and suggested a balanced view in which we look at the music itself for partial answers it may contain, he was all but berated for confusing the theoretical discussion with his "indigenous" perspective (Stone 1986). The implication was not simply that every musicologist is contaminated by his or her cultural perspective, but rather that certain contaminants are more suspect than others. What this reveals, and what my present work attempts to address, is the prevalent tendency to treat non-European perspectives on music as extraneous, foreign, or "Other." Unquestionably, one should resist the assumption that because musicians are of a different culture, their cognitive processes are mysterious. It is possible to allow for difference without fetishizing it. Rather, the definitions and governing concepts of musicology and music perception must either expand to apply to the music of the world, or at least have their limitations and problematics acknowledged.

With Western tonal music, usually we defer to the authority of the composer by heeding the time signature indicated in the score rather than imagining our own. We ought to do the equivalent for the music in question here, for which typically no composer is credited. The equivalent authority would be the practitioner, the carrier of knowledge, as we would deem any musician in the ensemble, from the master drummer to the bell player. We could simply ask such a person where the beat is, when the cycle begins, and so forth; or we could ask more indirectly how one would dance or clap to the rhythm. The meter as imagined by the practitioner is apprehended by the listener from the music chiefly due to his or her familiarity with the material -- and specifically with its production, with its activity as dance-drumming. This does not necessarily imply training so much as it does acculturation.

When participating in the dance-drumming environment (which I have been fortunate to do in workshop contexts organized by Ladzekpo from 1994 to 1997), I usually cannot help but perceive the pulse, for it is quite readily reinforced by the sum total of the aural, visual, and physical/somatic input. And if my rhythmic footing is lost momentarily, I can always use the timeline, the bell pattern, to tell me which way is "up" -- or "where's 1," as it might be worded in conventional Western terms. But this is only possible because I have learned how to parse the bell pattern and accompanying rhythms and body language from a carrier of this tradition; I have been (however minimally) acculturated or attuned to the details of this musical activity.

I have also found myself in similar contexts to which I was not at all acculturated, as in a recent trip to Senegal in collaboration with some North American and British jazz and funk musicians, four Afro-Cuban percussionists, and five Senegalese drummers. We Westerners had great difficulties guessing which way the African musicians' rhythms were intended to be heard, as did they with ours. (As one might expect, this musical language barrier was clearly less extreme between the Senegalese and the Afro-Cubans.) At one point some of us were taken to the Senegalese group's local performance at a crossroads in Dakar. Though some of us had been exposed to other forms of West African music, we had extreme difficulty understanding how to perceive their particular music and dance, which to us was highly ambiguous, metrically and otherwise. We found ourselves watching for the incidental dancing and jumping of small children, our only perceptually "salient" orienting guideline.

What the above anecdote suggests is that in these cultures (and in all cultures, I would argue), meter perception is a practice -- an open-ended, intentional activity that is accomplished actively by the musical participants, while profoundly influenced by the perceivers' social context. (See Berger 1997 and Bourdieu 1977 for elaborations of this concept.) Meter perception is not simply a raw perceptual inevitability for which mathematical models of pulse salience and gestalt concepts of grouping will easily substitute. On the contrary, one requires crucial background knowledge to perceive the "correct" meter. Indeed, quite frequently an untrained listener from the West will perceive an "incorrect" meter in a piece of West African music by employing a standard minimum-syncopation principle. In the audio example [CD-36] , [node:3800 teaser] one might be tempted to hear a triple meter, but the high-pitched bell supplies the correct duple pulse.

Hence any model of rhythm perception and cognition must include stages at which incoming rhythms are compared to known rhythms, matched against known meters, and situated among broader expectations about musical events. It also must involve some degree of what may be called active perception, by which is meant the assessment of various alternative readings of the musical signal, and the switching among them, all carried out in time and continually revised and updated. In short, it must treat perception to some degree as a practice. Finally, it must replace the communicative model of musical discourse, i.e.

musician -> musical object -> listener

in which the musical signal simply carries information from the sound's creator to its perceiver, with a mutually constructive paradigm (Nattiez 1990),

musician -> musical object <- listener

in which both musician and listener are constructive, situated participants in a larger musical fact -- for example, in an intercultural encounter in which different musical presuppositions hold on either side. And in fact we might consider expanding this paradigm to account for the musician's and listener's respective cultures, and to allow for the ways in which the so-called musical object might also "construct" the musician and listener.

Summary

The point remains that a great many conflicting ideas have been bandied about regarding African rhythms, from Westerners in both ethnomusicology and cognitive psychology, and also from African musicologists. I would summarize my arguments as follows:

 


  • We need to keep our definitions consistent in order to avoid the confusion that occur so readily with terms such as grouping, rhythm, pulse, and meter, and in particular to avoid confusion between denotative and connotative meanings. As a general construct, meter most often denotes the smallest perceivable periodically repeating groupings of the perceived tactus-level temporal units. Allowance must be made for irregular pulse constructs as they occur in Mediterranean, Middle Eastern, and South Asian musics.

  • Meter need not denote a hierarchy of strong and weak beats; such a hierarchy is considered a secondary construct. However, the perceived meter is an abstract template that lies upon the musical material in a certain place; its particular relationship to the material is crucial. In other words, meter does include a phase relationship - that is, a concept of a regulative time point, which in the West we call the downbeat or the "one," but is conceived slightly differently elsewhere. So when we perceive meter, we mark one of the beats as the regulative point, where the metric cycle begins; this placement affects our perception of the rhythms that follow.

  • Meter perception also includes among its ingredients the perception of the pulse and its operational subdivisions.

  • We need to be aware of the nature-nurture questions entangled in terms like perception and cognition. Is meter perception a "natural" process, or does it involve some acculturation? Does meter just happen, or do we make it happen? If we make it happen, why do we know how to do so? Perception of meter is considered to be at least partially voluntary, in that a skilled musician or listener can hear a given rhythm in any number of meters. Meter perception is also strongly directed by learned schemas, and hence contains a culturally contingent component.

  • We need to be clear about distinctions between music theory and music practice, and about how well this distinction transfers across cultures. Does a theory equal a cognitive representation? Can volumes of prose make one understand what it's like to play African music as an African person in an African community?

It should be noted that some meter-like concept of small or large groupings of a pulse exists in a large number of musics of the world, including many European, African, South Asian, Southeast Asian, and East Asian musics. Sometimes this meter is reinforced visually, as in the conducted orchestral music of Europe, in the dancing that is inseparable from much West African drumming, and in the hand signals produced by the musicians and audience in South Indian classical music. Other times it is encoded musically, as in timeline-based and clave-based musics of the West African peoples and their diaspora, in the two-and-four hi-hat or backbeat of African-American jazz and popular musics, and in the accentual reinforcement of tonal music. Generally, the cultural elaboration of meter involves multisensory signals that must be decoded according to a body of culturally determined guidelines. Such guidelines may conflict with perceptual input, especially if we accept the reality of the intercultural encounter, and even more so if we grant that perception itself is in part a culturally determined practice. The "experienced listener" constructed in Lerdahl and Jackendoff (1983, p. 3) is indeed adept at such idiomatic decoding. Given the variety of types of musical organization, it is unlikely that a single, perceptually based model for beat and meter cognition would apply universally. However, given the cross-cultural existence of some concept of meter (as opposed to none), the tendency to organize tactus-level pulses into periodically recurring groups should considered as an important, possibly universal component of pulse-based music.

These points are mere tips of vast conceptual icebergs in musicology, anthropology, and psychology. Above all, this chapter is intended simply to caution against the dangerous cultural slippage that occurs when hypothesizing about both the cognitive universals and the cultural particulars of music. Like Agawu, I am calling for a restraint of the urge to revel in facile notions of difference.

Agawu's unique vantage point, that of a native West African raised on Northern Ewe music and culture and trained professionally in European music and musicology, allows him to make invaluable criticisms of the typical Western representations of Africa. His stance carries over quite effectively to the study of African-American cultures and musics. As a professional musician working in a number of African-American genres as well as a student of the cognitive science of music, I find myself in a similarly unique position, situated both to debunk some of the widespread problematics in the study of rhythm cognition and to suggest new alternatives. In my work I do not wish to represent African America as a frozen entity that allows easy description and that is free from interaction with mainstream European-American culture. Rather,I endeavor to show how the study of African and African-American musics can highlight previously unexamined aspects of rhythm cognition that are nonetheless globally relevant.

 

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