Hearing rhythmic gestures:

Hearing rhythmic gestures:
Moving bodies and embodied minds

Justin London

(Carleton College, U.S.A.)

www.people.carleton.edu/~jlondon

1. Introduction

What I am going to talk about today are the speed limits for musical rhythm--when is a rhythm “too fast” and when is a rhythm “too slow” and see how those speed limits compare with the limits for other rhythmic activities of a non-musical sort. Here is an illustration of what I mean, a little game of "name that tune."

Excerpt ONE, Excerpt TWO, and Excerpt THREE

NOTE: Click on each link to hear examples; as these examples are very short, and timing is critical, if your browser is set to "play sounds as it loads" you may wish to rewind and then listen again to hear each demonstration properly. When you are done listening, use the "back" button to return to this page, and the rest of the text.

To state the obvious, the first example was too fast, the second, too slow, but the third was just right (or just right if you like John Eliot Gardiner’s performance). In the first, too-fast rendition, the notes came at such a furious rate that you couldn’t make out the tune. In the second, you couldn’t directly make out the tune, but some of you (perhaps most of you) may have been able to figure it out by catching each note in your mind’s ear and then reconstructing them in your imagination. But in the third--the real performance--you were able to grasp the tune and its identity simply and directly. For it was in that performance that we were able to hear the melody as a coherent rhythm, that is to say, as a musical gesture. So, where exactly are the boundaries between "too fast" and "too slow," and how do they constrain or otherwise affect our sense of rhythmic shape and gesture? That is what I will be talking about today.

I will start with the shortest of temporal intervals--durations that are definitely too short (which is to say, too fast), and present several examples of these ultra-short intervals. In slowing them down bit by bit I hope to demonstrate to you just where the speed limit is for musical rhythm (that is, the maximum speed limit). I'll do the same for the minimum--how slow can you go?.

I will then talk about some important temporal distinctions within those speed limits, a limit on our ability to hear a beat or pulse, and our strong preference for beats within a fairly narrow range of tempo.

I will then take a few moments to illustrate the interactive nature of our rhythmic perception and cognition, showing how we actively structure sound patterns into musical shapes, and at times even fill in missing elements in rhythmic patterns.

Having talked about musical rhythm, I will then move on to other rhythmic behaviors, behaviors that are in some sense "prior" to our perception and production of music. So I will talk about the speed limits and preferred rates for walking, running, and clapping. It will be shown--or rather, it will be riculously obvious--that these activities are subject to the same speed limits as music, and so I will then discuss reasons for why this is so.

Then finally, I will conclude with some rampant speculation on the nature of musical gesture, and what qualities are necessary for a musical gesture (or a non-musical gesture, for that matter), to be truly "musical."

2. The Long and Short of Musical Rhythm

As my opening examples demonstrated, we cannot grasp the shape of a melody or rhythm if it is too fast or if it is too slow, even though we can, in some sense, make sense of the sounds (noting their contour, some aspects of speed and motion, timbre, and so forth). Our ability to hear coordinated rhythmic movement seems to be subject to more general perceptual and cognitive limits. Those limits--the speed limits for musical rhythm--are a maximum of 600 events per minute, or a minimum of 30 events per minute

Now, a brief remark about our unit(s) of measurement. Musicians are accustomed to thinking about tempo in terms of beats per minute, but psychologists who study music perception are not. Rather, they typically measure the duration of the inter-onset interval (IOI) between events, either the onsets of tones, or between very short clicks, and so forth. So one can also talk of these speed limits as a range between 100ms (a tenth of a second), and the longest, two seconds. These are durations, and durations are not the same thing as the interval between beats; this is, of course, the very distinction between rhythm and meter. Nonetheless, both isolated durations and periodic stimuli are subject to these same perceptual speed limits, though they are manifested in different ways in different temporal contexts.

Now these speed limits have long been known by musicians. Here is nice summary, taken from Peter Westergaard's theory textbook

The Range of Useful Tempos

(after Westergaard 1975, p. 274)

Beats/minute	IOI (ms)	Tempo comment
30	2000	too slow to be useful
42	1414	very slow
60	1000	moderately slow
80	700	moderate
120	500	moderately fast
168	350	very fast
240	250	too fast to be useful

As you can see, Westergaard recognizes the minimum speed--the slow end--but doesn't quite go up to the maximum of 600bpm. Westergaard has a good reason for this, as we shall soon see.

2.1 From Too Short to Very, Very Short

To understand these speed limits, let me start at the shortest of all durations: zero. If two sound events occur at the same time, we only hear one thing. But if their onsets are separated by only a little bit--as little as 2 ms--we notice a change in the sound (this was confirmed by Exner in 1875). Here is a demonstration: you will hear a series of four sounds--two clicks that occur at the same time, then separated by 1, 3, and 5ms. The series is played twice.

Click Pairs at 0, 1, 3, and 5ms

There is a noticeable change in the quality of sound--instead of a sharp, crisp click, one hears something that sounds, to my ear, remarkably like two stones being hit together.

In this example each sound was produced by a pair of clicks, and they were the same frequency (made of sine tones at 3000hz, a duration of 1ms with a bell-shaped envelope). One could also use two different clicks, but at these very short intervals, one cannot determine their order. Hirsh (1959) found that we need at least 20 ms separation between click or tone onsets to do this. My next demonstration uses a pair of comprised of frequency-differentiated clicks, one high and one low. First you will hear HiLo, then LoHi. There is a 30ms separation between the component clicks of each pair.

HiLo -> LoHi Click Pairs

I hope you can hear a different sense of the "snap" produced by the different click pairs. It may be difficult to hear these brief sounds due to room acoustics, as well as due to individual differences in discrimination abilities (as they say, "your mileage may vary"). But what one can hear in this instance is a difference in the timbre of each click pair, just as we heard a timbral difference between click pairs separated by less than 2ms versus those separated by more than 2 ms.

We are still a long ways away from the domain of musical rhythm. For of course there is a difference between discriminating amongst these different onset separations versus hearing two separate sounds. For in the examples I've just played, we don't hear two clicks--we just hear different sorts of individual clicks. In order to hear two separate events, they must be at least 50 ms apart (as measured from event onset to event onset). Here are a series of pairs of clicks, separated at 30, 40, 50, and then 60 ms.

Click Pairs separated by 30, 40, 50, and 60ms

Now, at last, we hear two distinct clicks. But we are still not within the realm of musical rhythm. In the range of 50-100ms, we can hear individuated events, but they still lack rhythmic definition. That is, we cannot make reliable judgments of length (which of successive intervals are longer or shorter) or even quantity (how many rapid tones or clicks does one hear). 100ms is the magic number. When the shortest durational elements in a pattern are longer than 100ms, we can begin to discern rhythmic shapes and rhythmic groups.

Here is a demonstration of the 100ms threshold, and how durations longer than 100ms afford rhythmic perception. You will hear a series of clicks--a click train, if you will. Each train consists of six clicks, the first five of which are evenly spaced. The last click comes either early or late. The listening task with these examples is two-fold. First, can you notice that the last inter-click interval differs from those that preceded it(?). Second, when you hear a pair of such click trains, are you able to tell if they are different, and how they are different(?) (that is, whether the stimuli were ordered "early-late" or "late-early").

Click Train faster than 100ms

What you just heard involved a baseline interval of 70ms; the first series was "early" (by 15ms) and the second late (by 15ms). I hope you were not able to tell the difference--indeed, you may have had trouble discerning six clicks. Now I will slow things down a bit:

Click Train Slower than 100ms

Here the baseline interval was 120ms, and the last click's position was altered by 20ms (keeping the difference roughly proportional to the baseline). Here, I hope you COULD tell the difference, as the stimuli were ordered Late-Early.

So we have crossed the 100ms threshold, and once we do, we are able to hear individual event onsets, and notice differences in the temporal interval from onset to onset. And the reason why is fairly simple: your brain can only work so fast. In order to compare and discriminate between two temporal intervals, or notice a perturbation in a continuous series of temporal stimuli, the "standard" interval has to be heard, encoded, put into memory, then retrieved from memory so that it can be compared to the target interval. To perform these task requires higher-level processing in the brain, beyond the inner ear and the primary auditory cortex, and such processing takes time (see Roederer, 1995).

2.2 How slow can you go

From too fast, let us look at the other end of the rhythmic spectrum--where is too slow? Simply slowing a series of pulses down more than 40-30 bpm will demonstrate the upper limit for beat coherence--you will be able to subjectively feel a lack of connected motion from pulse to pulse. A move of objective measure comes from studies of synchronized tapping. If you ask someone to simply tap along to a metronome, she will typically anticipate the metronome tick by a short bit (so-called "negative asynchrony error"). If the metronome slows down beyond 30bpm, this anticipation disappears. Instead, the tapping response occurs shortly after each tick--in short, the test becomes a measure of reaction time, and at this pace it does not matter if the ticks are regularly spaced or random--the synchronization (or rather, lack thereof) is the same.

Here is another way of demonstrating the two-second limit:

"Shave and a Haircut"--Normal Tempo; "Shave and a Haircut"--Slower Tempo

This is a common rhythmic figure, sometimes known (at least in the US) as "Shave and a Haircut--Two Bits" (it's an old moniker for this figure, since it has been along time since one could get a haircut, let alone a shave, for fifty cents). First you heard it at a moderately quick tempo, and then much slower. Even at the slow tempo, however, the figure remains complete--that is, it is heard as one figure and not two successive figures--even when the interval is stretched a bit. But when the interval between the "shave and a haircut" and "two bits" is stretched beyond 2 seconds, the figure falls apart.

"Shave and a Haircut"--Too Slow

That is, the "two bits" no longer create a sense of closure that is connected with the opening "shave and a haircut." Instead, one hears two separate figures.

2.3 Two Other thresholds

100ms and 2 seconds stake out t a very wide range, encompassing several orders of temporal magnitude (one way of thinking about it is there are approximately four "octaves" of musical rhythm)--not all durations and periodicities within this range are alike. Here is a slide which summarize the temporal "landscape" for musical rhythm:

A table of musical and perceptual periodicities

Period/Rate

Musical Phenomena

Perceptual Phenomena

50ms/

1200 bpm

· Trills, Glissandi, Drumrolls

· Event separation threshold (Steudel 1933)

100ms/

600 bpm

· Shortest durations in rhythmic figures (Friberg and Sundström, 1999)

· Shortest possible metric subdivisions (London 2002)

· Limit on subjective rhythmization (Bolton 1894)

· Streaming threshold for pitch patterns (Miller and Heise 1950, Van Noorden 1975, Bregman 1990)

· Threshold for reliable durational discrimination (Hirsh, Monohan, et al 1990)

· Cortical processing of sound patterns (Roederer 1995)

· Synchronization Threshold (Repp 2002)

200-250ms/

300-240 bpm

· Fastest beats (Westergaard 1975)

· Limit of subdivision benefit (Repp 2002)

· Upper limit for melody recognition (Warren 1993)

· Upper end of range of pulse salience (Parncutt 1994)

· Holistic vs. Analytic Processing
(Michon 1964)

· Cutoff for backward masking
(Massaro 1970);

· Limit for short-term memory
(Crowder 1993)

· Shift in nature of JND for duration (Friberg and Sundberg 1995)

600-700ms/

100-86 bpm

· Tempo giusto

· Center of range of maximal pulse salience (Parncutt 1994)

· Indifference interval (Wundt 1911)

· Spontaneous tempo (Fraisse 1982)

· Minimal degree of tempo drift (Madison 2000)

1500-2000ms/

40-30 bpm

· Slowest Beats--lower limit of the "range of useful tempos" (Westergaard 1975, Warren 1993)

· Shift from anticipatory attending to reaction time (Woodrow 1932)

· Upper limit on subjective rhythmization (Bolton 1894; Fraisse 1982)

5-6 seconds

· Longest measures/hyper-
measures (London 2002)

· Limit of psychological present (James 1890, Pöppel 1972, Michon 1978, Fraisse 1984)

Recall Westergard's claim that 240 beats per minute (250ms periodicity) was "too fast to be useful." This is true if we consider this as a limit for Tempo (which is what Westergard is claiming), that is, the fastest rate at which we can discern a beat or pulse. For while we can hear durations in the 100-200ms range as rhythmic elements, they are too short/too rapid to serve as beats--but they can serve (and do serve) as subdivisions of the beat. This is what Parncutt (1994) found as the limit for the range of pulse salience, and what Warren (1993) found as a limit for melody recognition--that is, within the range of 200ms to 2000ms for note-to-note onset, listeners could identify familiar tunes, but they could not if they were presented faster or slower.

The 200-250ms threshold crops up in many studies of temporal and music perception:

Holistic vs. Analytic Processing (Michon 1964)
Influence of backward masking (Massaro 1970);
Limit for short-term memory (Crowder 1993)
Shift in nature of JND for duration (Friberg and Sundberg 1995);
Limit of subdivision benefit (Repp 2002)

There is a second threshold, and for most adults it is around 100 BPM (600ms).

For most adults it is around 100 beats/minute (a 600ms periodicity). Studies which have demonstrated the salience of this figure include:

Indifference interval (Wundt 1911)
Spontaneous tempo (Fraisse 1982)
Minimal degree of tempo drift (Madison 2000)
Center/Anchor of range of "maximal pulse salience" (Parncutt 1994)

Thus, there really is a "tempo giusto," or tactus--an innate tempo which we prefer, and which we gravitate towards. But it is not based on breathing rate, or heartbeats, or other metabolic periodicities (as musicians have proposed in the past). Rather, it seems to be related to timing preferences that have a neurobiological origin, rooted in the kinematic aspects of our perception and motor control (more on this in a bit).

What makes the notion of a "tempo giusto" interesting (as well as messy, and harder to study) is the fact that most musical passages involve several concurrent levels of rhythmic structure, and so while the 600ms may be most salience, there are almost always longer and slower periodicities present in the musical "signal" (if you will). Hence the differing impressions of speed (and I hasten to add, different gestural qualities) in the previous demonstration derive from the composite effect of the rates of the subdivisions, beats, and downbeats.

3. Musical Rhythms--Hence Musical Gestures--are Interactive

Listening to music is an interactive process. While composers and performers create the patterns of sound that we listen to, their efforts do not complete the musical work. Musical patterns--melodies, rhythms, gestures--are not simply "out there" to be aurally observed. Rather, in virtue of our perception, cognition, and memory, we actively contribute to the creation and shaping of musical structure.

3.1 The effect of preferred tempo on grouping and meter

Here is an example of how our temporal preferences affect how and what we hear. I've composed a melody (a rather boring melody) which I will play at two different tempos. This melody consists of a melodic figure in even notes cycling over and over again (think of it as really bad minimalism).

Melody in Quadruplets; Melody in Triplets

Now, what I hope you heard was, in the first instance hearing the melody in quadruplets, and then when it slowed down, triplets. In both, the beats were around 500ms, and in the first, the subdivisions were about 125ms, and in the second 167ms (that is, SDs were faster than 200ms in both cases). These were both deadpan performances--there weren't any particular cues, other than the pitch contours themselves, as to how the sounds should be grouped, where one should hear accents, and so forth. Indeed, I was careful to compose the melodic figure so that it was neutral with respect to triplet versus quadruplet patterning. The fact that our sense of meter and grouping shifted with changes in tempo demonstrates the "subjective" aspect of our rhythmization.

3.2 Interpolating beats and fighting rhythmic noise

Another demonstration of active listening involves our ability to interpolate missing elements in a rhythmic pattern, sometimes known as filling in the missing beats. Here is an example:

Stop-Time Loop

This is an example of the "stop time" figure that is commonly found in blues and rhythm-and-blues songs. The figure articulates beats 4 and 1--it moves from upbeat to downbeat, but then does not articulate beats two and three of the 4/4 measure. When you heard it, it wasn't just that you knew they were missing, but that you tapped your toes, swayed your heads, and at some level felt and "heard" the missing metric articulations. Indeed, for most listeners this response is visceral and automatic.

That was a sound example I constructed by cleaning up and looping the introductory riff from "Hootchie Cootchie Man" by Muddy Waters. Here is the real thing:

"Hootchie-Cootchie" excerpt

Note that buried in the mix you can hear the kick drum softly filling in the missing beats (and more). What is also of interest is that the figure in the guitar, drums, and harmonica is so rhythmically strong, you are able to keep the beat even though Muddy Water's singing strongly contradicts your sense of pulse--if you were to hear it apart from the backing band, you would be hard pressed to find a beat in it.

Not only, then, do we add rhythmic structure in contexts where the surface pattern is ambiguous (as in the two-tempo demonstration) or when we have to fill in an "empty" rhythm or measure; we also are able to interpolate elements and/or construe a rhythmic pattern even when the musical surface gives us contrary rhythmic cues. Syncopation is the obvious case here, when we maintain a beat against a rhythmic offset--and of course, the particular gestural quality of syncopation depends on our holding onto the beats which the rhythms then syncopate against. Keeping the beat against the rhythmic "noise" of Muddy Waters' text declamation involves a similar interaction between the listener and the music.

My larger point is, I hope, clear: musical gestures aren't just "out there" to be observed by listeners. Completion of rhythmic figures (that is, of a gesture), as well as our sense of a gesture's form and shape depend on our active and interactive engagement with the sonic surface.

4. Periodicities Preferences in Other Motor Behaviors

There are many ways in which our bodily motions and gestures involve periodic movement--we wave our arms back and forth, we nod our heads up and down. And indeed, some types of movement--walking, running, hand clapping--are by definition periodic. Just as we've looked at the speed limits and preferred rates for musical rhythms, now let's take a look at the speed limits and typical rates for some of these rhythmic behaviors.

4.1 Walking and Running

Let us start, obviously, with walking and running. While there are number of variables in the study of walking and running gaits (the length of the stride, the size of the foot, force of the heel strike, the angle of the foot and the angle of the knee, angle and velocity of arm swinging, and so on and so forth), I will, for obvious reasons, focus on the stride rate or cadence--the number of steps per minute.

ASIDE: We need to keep clear the distinction between steps (which occur between the initial contact of one foot to the initial contact of the opposite foot) versus strides (which involve successive points of initial contact of the same foot). A stride is two steps, a complete cycle of all of the movements involved in walking or running.

4.1.1 What are the speed limits for walking?

For both men and women, the range is between 60 and 132 steps per minute, and for both men and women the median rate is 117 steps per minute (512 ms, or close to 120 beats per minute--a classic march tempo).

	Males	Females
Step Length	79	66
Stride Length	158	132
Steps/minute	117 (60-132)	117 (60-132)
Speed	1.54 m/s	1.31 m/s

What is perhaps most interesting here is that the mean stride rate for both men and women is the same (117 steps per minute, slightly more than one half-second per step). Now men are generally larger than women, especially in terms of height, and for walking, inseam and foot size. And as a result, the stride length for men is indeed longer. But the stride rate is the same. Men walk faster than women not because their stride is faster, but because their strides are longer.

ASIDE: How fast do we march? If a march is at 120 beats per minute (one step per beat), then the step rate is a bit faster than the mean--120 (which is one half-second/500 ms per step). The standard pace is 8 steps for every five yards (5 yards = 4.55 meters). If each step covers .569 meters, then marching speed is about 1.14 meters per second--in other words, a march is slower than median walking pace. Now when we speak of marching, there is that sense of inevitability about it--perhaps due to associations with armies marching into battle--motionwise, a sense of great intertia. But this may be more due to our sense of mass (literally, a mass gathering of people moving together) rather than velocity at which the mass is moving.

4.1.2What are the speed limits for Running?

To start, let me remind you of the distinction between a walk and a run: when walking, one foot is on the ground at all times, and at some points in the walking cycle, both feet are on the ground. In a run, however, at some points in the gait cycle, both feet are in the air. In both walking and running, however, we speak of the stance versus swing phases for each foot. Here is a comparative diagram:

In a sprint, most of the time you are in the air. As you can see for each stride you are in the stance phase 20% of the time, and in the swing phase 80% of the time. Given that each stride in a sprint takes about 500ms, the stance phase occupies 100ms of each stride.

The transition from a walk to a run is of special interest--and it is tricky to pin down, since the timing of this transition depends on both the stride length and the stride rate. Steindler (1955) reports that the borderline is around 180 steps per minute (320 ms--male subjects, presumably, with an 82cm stride length). Note that this is slightly above double the rate for preferred tempo (two times 320 = 640ms), and that when the stride rate gets a bit faster--at 600ms--one is in a stable run.

Indeed, what these numbers also suggest to me is that what a run requires is the emergence of a coupled set of stable rhythmic levels--that is, rather than "thinking in steps," the body "thinks in strides." Moreover, it strikes me as highly significant that the running gait stabilizes at an inter-stride interval of around 600ms, the very same rate which anchors the range of maximum pulse salience.

The fastest runners get their maximum speed by optimizing an increased stride rate with an increased stride length. The maximum stride rate for trained runners is about 2 strides (4 steps) per second, or 250 ms per step (a tempo of 240 beats per minute). Untrained runners may employ a slightly higher stride rate (2.3 strides per second, or 220 ms per step--a temp of 273 beats per minute), but do not lengthen their stride (and as a result, they do not run as fast).

4.1.3 Comparisons between walking, running, and musical rhythms

Let's now compare some of the walking and running data with our magic numbers for musical rhythm and meter:

Periodicity	Musical Significance	Gait Significance
100ms/ 600 bpm	Minimum duration for an element in a rhythmic pattern	minimum time for stance phase in a rapid sprint
200-250ms/ 300-240 bpm	Fastest possible beats; durational threshold for various judgment tasks	Fastest step rate in a sprint;
600-700ms/ 100-90 bpm	Indifference interval; attractor tempo in the range of maximal pulse salience	Stride rate in stable run
1.5-2 sec. 40-30 bpm	Slowest possible beats	Slowest walking rate

I find at least two things noteworthy here:

(a) the relationship between stride rate in running and preferred tempo (both at around 600ms)--that is, a periodicity that anchors our sense of musical time plays an important role in creating a running stride. But as I previously mentioned, a running stride involves a pair of steps. But if there is a correspondence between "running" and a musical sense of speed, then, like running, musical patterns must involve several levels--a pair of rapid "beats" that form a higher metrical level.

(b) The typical walking period involves a step rate of 500 ms (120 beats per minute). 120 bpm is a march tempo (well known to American musicians who have marched in parades and at sporting events--two steps per second, with the entire parade show choreographed to a precise number of steps/seconds). Yet we don't think of marches as "Andante"--as a moderate walking tempo (or rather, a march is a brisk walk). I am not quite sure what to make of this . . .

4.2 Hand Clapping and Rhythmic Applause

How fast can you clap your hands? In a footnote to his 1987 paper "The Sound of Two Hands Clapping" (The sound of two hands clapping: An exploratory study. Journal of the Acoustical Society of America, 81, 1100-1109), Bruno Repp measured the maximum rate at which participants could clap their hands. Top speeds ranged from 123 to 184 ms per clap with an average of 152 ms. The average comfortable clapping rate had IOIs of 250 ms, with a range from 196 to 366 ms. It is interesting that the most comfortable clapping rate is about twice as fast as the "tempo guisto."

But there's more. In a recent article in Nature, Néda, Ravasz, et al. reported on the self-organization of rhythmic clapping in audiences. As they describe it, "initial incoherent applause is followed by a relatively sudden synchronization process, after which everybody claps simultaneously and periodically. What is interesting is that when synchronization occurs, the clapping period doubles. Here is their histogram which describes the unsynchronized (black, on the right) versus synchronized (red, on the left) periods of a controlled experimental study of clapping.

Note that the peak of the unsynchronized clapping behavior is rather wide--a wider spread of clapping rates than was found in Repp's study--but most prefer to clap in the 4-5 claps per second range (a 250 to 200 ms periodicity). This falls off rather steeply on the right, with no one clapping faster than 6 times per second (167 ms period). The synchronized clapping, as one would obviously expect, displays a narrower range of variation, with a sharp rise to a peak at slightly less than 2 claps per second.

The relationship to musical periodicities would seem to be (a) that synchronized clapping tends toward the 600ms periodicity in the center of the range of maximal pulse salience, and (b) that non-synchronized, vigorous clapping tends not to be much faster than the 200ms periodicity--that is, not faster than the fastest rate at which we can discern a pulse.

4.3 Parallels Between Musical and Kinematic Rhythms

Now, many researchers have investigated the nature of kinematic rhythm and its relationship to musical rhythms. In some instances, such as the studies here which relate ritards to the ways in which runners slow down or to physical processes naturally tend to run out, specific musical behaviors are related to more general principles of kinematics and/or Newtonian mechanics.

More generally, researchers in human movement have noted that in many cases typical periods are independent of modality of response--preferred tempos, for example, are the same whether subjects tap their fingers, their foot, or swing their legs. This is taken as evidence that these preferred rates and rate limits must derive from a centralized timekeeper. That time-keeper (or time-keepers, as the case may be) works in the context of a brain-body system, one in which the brain is designed--so to speak--to control a body of a given/typical size and shape, which muscles of a certain power and flexibility, with certain kinds of feedback (tactile, visual, proprioceptic). So one reason we have the kinds of rate limits that we do is precisely because they relate to the kinds of bodies (physically speaking) that we have.

Well, if there is a centralized timekeeper for kinematic movements--that is to say, for rhythmic behaviors--then it seems plausible that musical behaviors (which is to say, rhythmic behaviors of another sort) would make use of the same timekeeping mechanism(s). Hence we should not be surprised that rhythmic behaviors of all sorts, both musical and non-musical, fall within the same range and are subject to the same kinds of temporal preferences.

There is one more point worth observing here. The speed limits and preferences for kinematic movement and for musical rhythm are also those which allow for--indeed, optimize--synchronized behavior, our ability to move in time with others. The importance of synchronization for a group of musicians is, of course, obvious. But this synchronization is also just as important for the listener, as we are able to hear "in time" with the music--that is to say, with the musical behavior of the musicians.

I've now broached another broad topic, one that I can only mention in passing, and that is music-making is a form of social behavior, one which involves coordinated attention (and often movement) amongst all of the participants at a musical event. A number of authors, such as Bjorn Merker and William McNeill have explored the deep-seated biological and sociological bases for temporally coordinated social behaviors, and the role that music plays in engendering such behaviors. Suffice to say, our perceptual-temporal speed limits, and our proclivity to synchronize our attention and behavior to periodic stimuli within those limits, may be a defining characteristic of our human nature.

5. A Tenuous Conclusion

To finish my talk I will now climb out on a limb with respect to the limits of musical rhythm and hence the limits of musical gesture. Let me say that I am not sure I really buy this argument myself, but when Anthony Gritten invited to come speak, I began to think about the relation of my research to the notion of "musical gesture."

My concluding argument is, in a nutshell, that not all musical gestures are really "musical." It goes something like this:

1. "Musical" = "Rhythmic"

2. "Rhythmic" = "Having a discernable temporal pattern"

3. A Discernable Temporal Pattern (DTP) entails

(a) component durations fall within the 100ms to 2 second range

(b) component durations are organized into a sequence which affords (or has the
potential to afford) a sense of pulse

4. IF there is a DTP →
THEN there is a sense of virtual motion,

AND IF there is a sense of virtual motion →
THEN there is a sense of gesture

5. BUT IF musical sound events are
< 100ms or > 2 seconds in duration →
THEN then there cannot be a DTP,

AND IF there is not a DTP →

THEN there is not a sense of virtual motion,

AND IF there is not a sense of virtual motion →

THEN there is not a "musical" gesture

The first three points are definitions. For some process or series of events to be characterized, either directly or metaphorically, as "musical" it must be "rhythmic." This means that it involves not single sounds, but a series of sounds, and that they have a discernable temporal pattern.

Now, what does "having a discernable temporal pattern" entail? It would seem that to be discernable, the pattern has to be comprised of durations that we are capable of grasping and relating to each other--and this means that durations must fall within the range of our perceptual and cognitive faculties--that is, within the range of 100ms to 2 seconds.

So much for discernable. What about pattern? Here I would say that the durations (of which we need at least two) need to occur in a sequence which affords (or at least has the potential to afford) the listener a sense of pulse and/or metre. While this [DEMONSTRATE BY TAPPING ON THE PODIUM] is obviously pattern, even a single snippet [DEMONSTRATE] has rhythmic qualities, as we can imagine its repetition (indeed, may feel it viscerally--consider the opening of "Hootchie Cootchie Man").

On now to the argument proper. First, there is a link between a DTP, a sense of virtual motion, and a sense of "musical gesture." When we have a DTP, it engages our sensory-motor faculties. As Neil Todd has argued, it is this engagement which gives rise to our sense of rhythm-as-motion. This perceived motion, importantly, is one which affords our sympathetic movement, as we can imagine ourselves (as well as, perhaps, others) moving in a similar manner.

And so we have gestures. For of course, a gesture is a movement of our body. But the range of musical rhythm is not just a range of possible bodily motions--we can, to be sure, twitch faster, or forcibly walk slower. And we might well call spastic or herky-jerky motions "gestures"--but we would not call them rhythmic gestures, and hence, we would not perceive in them musical qualities. While we can observe such movements, we cannot sympathetically move with them.

And hence my tenuous conclusion: obviously, not all musical sounds afford a discernable rhythmic pattern (very long, sustained notes, such as pedal tones; very rapid glissandi, trills, tremolos; passages in 20th-century compositions which eschew a regular sense of beat or pulse, and so forth). While we can hear these musical sounds (of course), we can't move with them. And if we can't move with them, they are, un-rhythmical. If they are un-rhythmical, then they are un-musical--and hence, in some very deep sense, not "musical gestures."

Thank you very much.

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