ABSTRACT

A striking feature of many non-we stern musics is the presence of non-isochronous beat patterns, such as the bell pattern found in many types of Sub-Saharan African drumming (a Short-Long, Short-Short-Long pattern, proportionally 2+2+3+2+3). Initially, this seems far more complex than typical western meters, meters whose beats are usually thought of as isochronous. However, studies of timing and dynamics have shown that western music almost always involves systematic deviations from isochrony in performance. In both western and non-we stern musics the resultant deviations from isochrony fulfill a common function: they establish higher-level periodicities, and thus allow the listener to extract a beat cycle, a dynamic two-leveled attentional pattern. This extraction does not depend on other cues from the musical surface (e.g., dynamic accent, melodic patterning, etc.); time-series information alone is sufficient. Musically, this means that while one has a sense of "beat" and "measure," one need not have a sense of accentual differentiation amongst those beats. This is precisely how Locke (1998) describes "African 4/4" in his description of Gahu, a traditional type of music and dance of the Ewe-speaking people of West Africa.

Other theories and models of dynamic attending have presumed accentual differentiation amongst the beats in a measure (Jones 1992, Large and Jones 1999, Large and Palmer 2002). While "knowing where the location of the downbeat" is obviously important for musical performers, this paper argues that accentual differentiation is not required for listeners to establish an effective attentional framework. Some anecdotal evidence that this can and does occur is presented.

1. Some Musical Examples

The first passage we will consider is the ubiquitous "bell pattern" found in many sub-Saharn African musics:

Click to hear the bell pattern

As Magill and Pressing (1997) noted "an oft-stated principle is that all parts [in an African drum ensemble] are designed to function in relation to the bell pattern" (p. 190), and they demonstrated (through the analysis of a complex set of covariances) that in the proper context this principle seemed to be true. Thus the bell pattern functions as the motor timing and attentional framework that guides the African musicians' perception and performance (see also Nketia 1963, Nketia 1974, Locke 1982, Locke 1998, Agawu 1987, Agawu 1995).

The bell pattern has a number of distinctive features. First, it involves a series of non-ischronous beats, here presented as (2+2+3+2+3) pattern. As was heard in the example, these uneven beats are undergirded by a running stream of more rapid articulations, as is typical in African ensemble drumming. These faster articulations give the long and short beats clear identities as 2s and 3s. Another feature of the bell pattern is its durational invariance; it is a kind of ostinato that is present from the beginning through the end of a particular performance. Given this invariance, one en regarded as both a "rhythm" and a "meter." This is markedly different from western musical practice, where rhythms (that is, durational sequences) may vary while meter (that is, counting frameworks) remain constant.

The next example is the opening theme from the second movement of Beethoven's Seventh symphony

Click to hear Beethoven's Seventh

In contrast to the bell pattern, here the beats are isochronous (note that some of the durations are beats, while the shorter durations are beat subdivisions). It is worth noting, however, that like the bell pattern, Beethoven's rhythmic figure is also durationally invariant; it too is a kind of ostinato. Indeed, a lot of western music, especially western popular music, involves similar sorts of repeated rhythmic patterns from beginning to end (especially in the accompaniment). A piece of music whose melody AND accompaniment involve constantly changing rhythmic figures is quite rare. In this sense, Western and African rhythmic practice may be more alike than has been previously stated or implied.

Therefore in both the bell pattern and Beethoven's 7th, a repeated pattern of durations marks a higher-level metric period:

Our third and final example, the "Ode to Joy" from Beethoven's 9th Symphony, is metrically trickier, because it has undifferntiated rhythmic values.

Click to hear "Ode to Joy"

In this performance the sense of 4-beat measures is clear, but how is this achieved? Pitch patterning alone is not enough, for this melody works in both 4/4 and 3/4:

Nor are there highly salient dynamic accents which mark each downbeat. Indeed, dynamic accent, while it can serve to mark metrical organization, is often equivocal with respect to meter. As Jonathan Kramer remarked: "A stress [dynamic] accent is incapable of affecting meter except in the most ambiguous of circumstances" (1986, p. 86; see also Rosenthal 1992, Drake and Palmer 1993). What seems to be most crucial in marking higher-level rhythmic and metric organization are timing cues, such that the surface durations are transformed, via expressive variations, into something like this:

Once we take expressive timings into account, similarities in the temporal organization of all three examples becomes apparent.  All three give the listener the beat period (or periods), to which most inter-onset intervals conform. In all three the emergent higher-level timing pattern also makes clear a higher-level metric period. It would thus seem possible for the listener to readily read-off the measure from these durational patterns.

But in many instances the first note of a sequence is not the first note of a measure, as when we have an anacrusis or pick-up note. Thus while the higher-level metric period is clear, its phase alignment with a particular note (that is to say, which note is the downbeat) is not:

Thust it would seem that these patterns, in and of themselves, are necessary but not sufficient to establish a sense of meter. That is, while one has sorted out the basic beat period (or periods), and how many beats are in each measure, one has not yet determined which beat is the downbeat.

2. Attentional approaches to meter

From the listener's perspective, meter is the dynamic, multi-leveled synchronization of the one's attentional energy or focus to regularly recurring musical events within a certain temporal range. Attention and attentional energy is a continuous aspect of our perception and cognition; it doesn't turn on and off at discrete moments, but waxes and wanes in time. Thus the synchronization that takes place is between peaks of one's attentional energy and the perceived and/or predicted onsets of salient musical events. This is the approach to meter developed by Mari Jones and her many co-authors (Jones, Kidd et al. 1981; Jones, Boltz et al. 1982; Jones 1986; Jones and Boltz 1989; Large and Jones 1999; Jones, Moynihan et al. 2001, See also Gjerdingen 1989).

It is a common presumption that more "important events" are given more attention than musically "less important" events. This is nicely illustrated by Large and Palmer (2002, their fig. 3):

Large and Palmer's figure represents a composite fluctuation in attentional energy, formed by the summation of two component attentional periodicities. The middle peak is the downbeat, and as such it receives more attentional energy than the other two beats in the measure. This figure indicates two things: (a) the temporal location of each attentional peak, and (b) the allocation of attentional energy at each location. But two questions came to mind. First, what, more generally, is an optimal arrangement for the distribution of attentional energy within a time-window of a certain temporal extent? Second, what makes one event "more important" than another?

3. Why are isochronous measures so common?

To address the first question, let us start by observing that in most music-theoretic approaches to meter, isochrony is often presumed to be necessary for metric well-formedness (Lerdahl and Jackendoff 1983, Temperly 2002). But why should metric well-formedness depend on isochrony (especially since we now have a great deal of evidence that shows that isochrony rarely occurs in human musical performance)? While one might attribute this to cultural bias on the part of theorists and researchers who are steeped in normative Western musical practice, there is perhaps a more basic reason for this presumption.

First, if we conceive of a measure as not an ordered string of beats, but as a recurring cycle, then a circular representation of such cycles makes clear what isochronous patterns entail: isochrony gives rise to symmetrical patterns of metric components relative to overall cycle:

Symmetry here is rotational symmetry, as each attentional peak is spaced evenly about the perimeter of the circle. What does this symmetry achieve? Answer: It insures a parsimonius spread of attentional energy within the measure. That is, within a time window of a certain scope (i.e., a range of 1.2 to about 4 seconds), one can expect a certain number of events (from 2 to 6), and then apportion one's attentional energies accordingly. While perfect attending would have our attention peaking at each and every salient event onset, since perfection is impossible, our best strategy is to cast a net of attention that will serve to catch most of the salient events that are apt to occur. For here is what would happen if we concentrated our attentional energy in one region of the time window:

This figure represents a rather longshot "bet" in apportioning our attention&endash;it is a good attentional strategy only if nothing that is particularly salient happens during the "empty" portions of this metric cycle.

Thus in an isochronous measure, we evenly divvy up the attentional window based on the number of events that tend to occur in that unit of time (N.B., from a rhythmic production/behavioral point of view, we establish a pattern of action based on the number of events we have to execute within a given time-span). While symmetry is good, in that it speads attention evenly throughout the measure, perfect symmetry is a problem. Recall our "Ode to Joy example." There it is the deviations from symmetry (that is, isochrony) that allow one of find the higher-order periodicity (which defines the metric cycle) in the first place. Moreover, there is some evidence that slight deviations from isochrony (that is, perfect symmetry) enhance beat tracking (Large and Palmer, 2002).

Meter may thus be regarded as an attentional trade off: while perfect symmetry might be the "best" distribution of attentional energy, perfect symmetry would remove any expressive cues to the organzation of the larger metric time-window. Therefore, in both "isochronous" and non-isochronous meters, deviations from perfect regularity are useful in that they allow the listener to extract higher-order periodicity while still establishing an effective distribution of attentional energy. In the case of non-isochronous meters, these cues are "engineered" into the beat cycle itself; in isochronous meters, they have to be added via expressive variation. An examination of the bell pattern shows how this is so:

The bell pattern, while non-isochronous, is maximally even: this arrangement is the best possible spread of 5 beats against the cycle of 12 more-rapid pulses that undergirds it. One must keep in mind that meter is almost always more than a pattern of IOIs of a particular scale or scoper; rather, meter involves the coordination of a number of related periodicities. Thus one cannot simply have a symmetrical arrangement of five evenly-spaced beats. Rather, here the placement of the five beat onsets (that is, the peaks of attentional energy that occur on the beat level of the metric hierarchy) must be coordinated with the onsets of lower-level articulations. In characterizing the attentional relationship(s) between beats and lower/smaller levels of meter, Large and Palmer's notion of summing lower and higher level periodicities makes good sense. My disagreement with them has to do with trying to distinguish, on the basis of any inherent attentional properties, amongst the beats themselves. In other words, is there an attentional need for a downbeat?

4. What makes one beat more important than another?

If one beat in a measure regulary marked moments of greater informational salience, then of course it would pay to give them more attention. But studies of various parameters (pitch contour, dynamic accent, harmonic change) are equivocal with respect to their metric and salience, though there is some evidence that timing information has a greater degree of metric salience . This is because musical practice itself is inconsistent. Significant harmonic changes may occur on the downbeat, or they may not (via various types of contrapuntal offsets, for example). Dynamic stress may occur on the downbeat, or it may not, or it may occur consistently off the beat (a rock and roll back-beat). Melodic contours events (peaks, valleys, large leaps) can occur anywhere within the measure.

Thus if one cannot differentiate beats in terms of their structural importance, is there any functional reason to differentiate amongst them in terms of attention? This is not to say that listeners do not need any sense of where the measure begins; clearly they must if they are to extract and maintain the higher-level metric period (more on this in a moment). But a pattern of metric attending which sets up a pattern more or less equivalent peaks of attentional energy within a given temporal window, without further differentiation amongst those peaks, may often be a good strategy for attending to the unfolding music, especially given that important events may occur on any beat in a measure (and will occur on different beats in different measures).

5. Do listeners notice downbeats?

There is some anecdotal evidence that listeners at times do not match their attending to the metric phase (while still maintaining a sense of the metric period). Locke (1998) describes the "Gahu" pattern (in West African Ewe drumming) which is based on a cycle of 16 subdivision units as an example of "African 4/4" in which "ALL STRESSES RECEIVE EQUAL ACCENT" (p. 19, emphasis in the original). Locke also describes this pattern as "a continually repeating phrase that can be reordered mentally into various rhythmic modes" (p. 23), and he terms this re-ordering a "gestalt flip" (ibid., p. 22).

Similar metric reorderings may occur in the experience Hindustani and Karnatak music. My colleagues in ethnomusicology (here my informants are Melinda Russell and Bruno Nettl) report that when an audience actively "counts tala" by marking beats and measures with characteristic finger and hand movement patterns, one can readily observe out-of phase counting amongst members of the audience. My informants also report that one can observe audience members elbowing each other when they notice that their neighbor is counting tala "incorrectly."

Finally, Jocelyn Neal (1997) has shown that in country line dancing in the USA, dancers regularly ignore downbeats in their choreographed and improvised step patterns. That is, there are often complex, extended step patterns that align and un-align with the musical downbeats. Neal reports that dancers furthermore often do not notice this lack of alignment.

6. Keeping the downbeat: conclusion

Having argued that (a) there may be no attentional reason to differentiate a downbeat within a cycle of beats, (b) that more often than not the musical surface does not provide consistent cues as to the structural importance of one particular beat within a cycle of beats, and (c) that there may be some evidence that listeners often "do their own thing", downbeat-wise, I do not want to go on to say that listeners do not hear downbeats.

Listeners do hear downbeats, in that they have a subjective sense of the head of the cycle. While in many cases this may well correspond to an ictus that is determined by stylistic convention and/or structural differentiation, in other cases (such as the Bell pattern) this sense of downbeat may be largely listener rather than stimulus driven. However, in both cases a clear sense of a cardinal location within the cycle is advantageous, in that it enhances the stability of the cycle as a whole. Moreover, we should recognize that the attentional process itself will create a sense of downbeat, as many studies of subjective rhythmization have shown.

A larger point is that, from an attentional perspective, isochronous patterns with expressive variation and non-isochronous patterns function in the more or less the same way. Both establish several levels of temporal invariance which may form the basis for the listener's own attentional framework. To put it in cultural terms, in both African and Western musics, one often has to deal with asymmetrical temporal patterns and create an effective metric framework with which to attend to them. While some approaches have emphasized the difference between African and Western music (see Temperly 2001, pp. 268-72 for a discussion of these sources), this paper has focused on their essential similarities.

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