ADDITIONAL BACKGROUND
The frame of reference for thinking about musical time in contemporary scholarship is dominated by the concept of time as a forward-moving arrow. The simplest expressions of this commonsensical view can be summarized in the notion that no matter what a composer might wish to be the case, there is little she can do about the fact that a listener will perceive her composition from beginning to end, in order...at first we will hear the beginning of the piece, later the middle, and finally the listener will hear a composition's final notes. Composition teachers often encourage their students to capitalize on this basic progression, by concentrating, early in a piece, on music that compels us to expect certain things about the middle; the composer is then endowed with a certain power to either confirm or contradict those expectations as a way of relating music's narrative structure to an expectant listener.
With this presumption in mind, and with our custom of thinking about how groups of events set up expectations about the future, it will strike many readers as wrong-headed to consider a rhythmic quality as a unique property of a single event, oriented toward its immediate past. But that is the central premise of what I am calling "hearing time freely": that by exploring temporal qualities as objects, rather than as processes, we will allow qualities of temporal relation and temporal difference to work independently of "trajectories," independently of "expectancy," so that time itself serves music in an articulate, variable way, that we are more likely to associate with pitch, timbre, and intensity.
This premise sets us off on a very particular path of inquiry: what are the factors that contribute to a single note's tendency to "feel" one way or another, rhythmically? The factors that seem most salient are the ones discussed in the previous section: "properties" (of a pair of timespans, defined by an irreducible ratio, and particularly giving a rhythmic quality to the 'third' event that closes-off the second timespan), "structures of exposure" (that determine which events 'lead up' to a third event, and impart a ratio's properties to the rhythmic quality of that event) and "orientations of experience" (that determine how a ratio functions in its more elaborate auditory scene). Together, these terms suggest and clarify what it would mean to resist hierarchical, expectant rhythmic experiences and replace them with heterarchical, freely-differential ones.
The Case for Expectancy
One of the primary forces behind the presumption that hierarchies are superior musical structures is the concept of expectancy. Expectancy—a perceiver’s expectation of events in the future, based on patterns in the past—is a process that can hypothetically govern a perceiver's relationship to patterns unfolding on the note-to-note surface of a composition, as well as on the formal relationships between larger ideas distributed over longer periods of time. When we imagine the role of expectancy in large structures, the process might be understood in much the same way as we understand the structure of a narrative plot: at the largest level of a story, characters normally experience a crisis, and something in their interactions with their surroundings produces an expected resolution, though we don't know at what point in time, or how the resolution will manifest. By contrast, at the local surface, the structure of 'expectancy' is a matter of a more constant and ongoing state of prediction, like that of steering an automobile: when the first part of a gentle curve requires a particular angle for the steering wheel, we allow that angle to persist as the basis for steering in the immediate future. The next part of the curve either confirms of denies the persistent basis, and the curve is negotiated through constant acts of correction. Musical experiences of rallentando or accelerando might resemble an adjustment to a steering wheel of metric expectancy; sudden tempo shifts disorient and excite us in much the way we might be stimulated by more radical maneuvers.
This short-term expectancy is often attributed to both proportional simplicity and metric hierarchy (Lerdahl and Jackendoff, 1983; Jones & Boltz, 1989; Desain 1992), but the two factors are not normally teased apart. In some theoretical approaches, the distinction of regular from irregular rhythm depends on whether events establish consonant metric patterns as cues for the expectation of a larger structure. Following Desain's (1992) study, a number of recent experiments have confirmed that expectancy is a distinct and important outcome of metric regularity (E. W. Large and M. R. Jones, 1999; Timmers, Ashley, Desain, & Heijink 2000). Christopher Hasty's (1997) concept of durational projection further extends this notion, beyond the obvious level of meter, and into middleground aspects of musical time.
Imagining Heterarchy
In these teleological models of rhythm, however, an opposing question arises: can there also be ‘individuated,’ or ‘metrically independent’ objects of temporal experience, that determine anything about the way we hear rhythm? This was the primary question in a series of experiments I conducted between 2003 and 2005, the results of which are reported and interpreted in my paper "Perceiving and distinguishing simple timespan ratios without metric reinforcement" (Carson 2007). Here, I demonstrated that pure timespan ratios can possess qualities of rhythmic experience, that listeners can distinguish, even when no metric context is provided for their appraisal.
Recall that an unmetered timespan ratio is made of only three events, bracketing two timespans; the percept of that ratio is absent until the second timespan has been completed, at the moment of the third event. The distinct quality of a timespan ratio—for example, its perceived simplicity or complexity— can thus only be observed as a property of a single timepoint. Since we are capable of distinguishing a "simple" additive timespan ratio from a complex one, hearing only three events and appraising their rhythmic quality at the moment of the third, then we will have to account for that distinction in an 'out-of-time' mode of perception. So it may be necessary to supplement our expectancy-based theories of rhythm with some notion of a reducible, retrospective, and "collapsible" temporality.
It is important to note that these two models of rhythm perception—“expectancy-producing” models and “individuating” or “qualitative” models—are interdependent. The philosopher Gilles Deleuze has clarified this interdependency in relation to a number of relational experiences of time, including developmental narratives in psychology and history, as well as aesthetic narratives in film and music. In an early thesis, Difference and Repetition (1994, originally 1968), Deleuze theorizes an interaction between “difference in itself” and “repetition for itself.” “Repetition for itself” describes objects that distribute on linear and metric continua; examples of this would include periodic features of time, like musical meter. Such repetitions transform our experience of “difference in itself”—for example, the qualitative distinction of ratio consonance—into integrated continuities; difference effectively becomes similarity (Deleuze 1994 [1968], 28-32, 70-71). Deleuze’s argument turns the contrast between continuity and difference back on itself, so that syntheses of these two models of thought can account for a variety of historical philosophies of meaning and identity (168-221). My immediate interest here is more modest, but nevertheless reaches toward the solution of a similar problem: how conceptual structures of repetition, like meter, affect the larger possibilities of difference perception in music. An important starting point in the investigation is the common-sense premise that expectancy is weakened by complex timespan ratios just as our experience of difference “in itself”—individuation of features out of time—is hypothetically strengthened.
The missing question in that intuitive relationship, however, is the problem of metric hierarchy. Metric hierarchy is the condition in which events separated by time are linked, or made equivalent, according to their positions in relation to repeated timespan proportions on more than one scale of periodicity. A few recent studies have begun to clarify this separation, by carefully distinguishing the perception of meter from the perception of rhythm. Repp, London, and Keller (2005) demonstrate that meter plays a significantly lesser role than timespan proportion in the accuracy of listeners' performance of 'uneven' rhythms (based on successions of timespans of lengths 2 and 3, at various tempi). Keller and Burnham (2005) show that "nonmetrical conditions" present a significant detriment to the task of distinguishing multipart or texturally complex rhythmic stimuli. In earlier investigations, the inference of a single timespan unit (Idson & Massaro 1976, Handel 1993), or of repeated larger timespans or timespan groups (Povel & Essens 1985, Desain 1992)—even when not always made explicit by events—yielded an important inferential 'clock,’ against which irregular or complex timespan pairs will produce perceptual dissonances. The scale at which similar event-groups repeat (such as the duration of a typical bar of metered music) can act as a comparative mechanism that trumps the question of proportionality: for example, the difference between the timespan ratios 4:5 and 4:4 (1:1) is much more salient when the ratio itself is a repeated sequential feature, as in an ostinato or ground bass, than when it occurs in an isolated circumstance. (Technically, the sequential repetition of a timespan ratio 4:5 produces a 9:9 (1:1) relationship, one structural level above the surface.)
How then, does the presence of simple or complex proportions, completely ungoverned by meter or repetition, influence our impressions of complex rhythmic textures? The question is important for at least two reasons. First, composers have long associated complex rhythmic proportions with complex musical experience. This association often motivates us to require performers to think outside of traditional metric hierarchies, where scores utilize nested tuplets, abstract metric modulations, or other non-standard rhythm notation, in order to reject or avoid binary and ternary timespan divisions. But empirical studies have not formalized the conditions under which such complexities of rhythm produce viscerally ambiguous or complex musical experiences.
Secondly, the question of how we perceive unreinforced temporal structures carries with it some more general implications for how listeners engage musical time. At least since Ernst Kurth's 1918 Grundlagen des linearen Kontrapunkts ("Foundations of Linear Counterpoint"), theorists have idealized a dynamically unfolding and diachronic aspect of our psychological engagement of musical form. Kurth argues (perhaps more from a sense of desire for potent metaphors than from any empirical observation) that the truly resonant and persistent features of musical expression are not the events themselves, but a mysterious additional force that acts upon them to "counteract the autonomous significance of the individual tone" or individuated structure (Kurth [1917] 1991, p 60). Like Kurth, Leonard Meyer holds that the musical composition is not a thing but "a process which gives rise to a dynamic experience" (1956, p 54). Meyer likewise advocates a model of music perception in which "we are constantly revising our opinions…in the light of present events" (1956, p 49), with continuously evolving predictions playing a dominating role in the apprehension of musical structure. The term expectancy comes to mind in these important precursors to Narmour’s “implication-realization” model. But psychological studies of rhythm have been much less likely to explore any of the ways in which synchronic time structures coalesce and persist in a rhythmic consciousness outside of musical time.
The distinction of synchronic and diachronic time-experience is remote from conventional music theory, because its implications—even in conventional uses of the terms—are unexpectedly complex. So it may not be too great a tangent to consider the connections between the musical distinction and the everyday meanings of the words. Anthropologists and historians have distinguished the terms in intuitively obvious ways: the term "synchronic" refers to an interconnected experience of time that might remind musicians of beat-classes or time-point classes in a system of repeated and functionally equivalent measures. (Beat 1 of bar 43 has a lot in common with beat 1 of bar 16, or beat 1 of any other bar; we can say that "they all perform the same role in the perception of time;" if they did not, there would be no reason to give them all the same name.) In cultural studies, synchronic temporality has been associated with the tendency of agrarian communities, for example, to structure their lives according to the passing of seasons; in studies of antiquity, the synchronic idea is applied to a notion of history or destiny that is stable, balanced, and cyclical. It might be said that a synchronic world view minimizes our ability to distinguish the idea of progress or teleology without envisioning an equal and opposite movement—in synchronic perspectives, all that initially seems accumulative, goal-oriented, or linear will be transformed to resemble the motion of a wheel, a pendulum, or a wave.
Diachronic perspectives are easy to imagine in opposition to this notion: the transitive property in philosophy, or math, for example, encourages us to imagine a trajectory of thought in which an accumulation of observations and basic facts leads a thinker toward larger truths. In proofs, we are not meant to worry that accumulating knowledge will necessarily result in later ignorance. On a more colloquial level, our views of everything from civil rights, medicine, exploration, information technology, are largely structured diachronically, in that the present is a line that divides the past from the future, and keeps them apart. The present is only moving in one direction. When civil or social justice is compromised, we usually describe the problem through an analogy with the past. By imagining that quackery and bigotry arises from a mindset "stuck in the 1950s" or "stuck in the middle ages", we imply not only that we've come a long way since then, but that there will be generally less bigotry in the future than there is now. The past may someday rear its ugly head again, but it will still be the past, and we know the general trend of things is inevitable. In place of the synchronic destiny that brings all lives, and all empires, to a close, while others rise (and fall) to take their place, we see a manifest destiny that urges us toward enlightenment, technological perfection, and an infinitely expanding future.
Of course the two perspectives ultimately coexist -- no futurist is without some imagination of a doomsday scenario, and no cyclical view of history is without an escape hatch into a completely unprecedented and transformed existence. But we can recognize these perspectives with varying strengths in varying situations, as in the examples above, and the modern condition appears uniquely bent on a diachronic world view. In a number of essays, Walter Benjamin critiqued teleological progressions of individual agency as a new symptom of post-industrial modernism. Nadia Sermetakis distills Benjamin’s project, showing that
Modernity portrays…itself as a self-originating continuum selectively appropriating the past [...]. Through the continuum, normative and perceptual grids are disseminated, which exclude whole spheres of historically discordant experience in favor of a dominant public memory of continuity and linearity.
Benjamin positions this “continuum” as a new condition of modern temporality. It masquerades as a perceptually basic and universal feature of experience, but it nevertheless processes and filters the thoughts of its perceiver in a historically specific way. Since the "spheres of...experience" that are excluded are conversely discontinuous, and non-linear, Sermetakis asks (along with Benjamin) us to question the primacy of the diachronic model, and critique it as an artificial amendment to more synchronic norms of human thought.
In my ears, neither of these models of time experience accounts adequately for even the most basic hearing of musical rhythm. Not only is it possible to hear time in free ambivalence between the present, past and future, but for some kinds of musical experience, it is actually necessary – and at least two kinds of temporal ambivalence seem to be required. The first is one in which time relationships can have qualities that inscribe the surface of a composition without folding/falling back into a relentless developmental arrow. The second is one in which time can be perceived as a pure intensity of experience, freely differentiated from its temporal mode of production (and is this not how we experience everything else?) In the discussions that follow from here, I will focus mostly on the first of these two questions, but I hope that the second will remain a conceptual possibility lingering in the environment.