the psychology of music || structure and interpretation of rhythm in music

9 Structure and Interpretation ofRhythm in Music

Henkjan Honing

Cognitive Science Center Amsterdam, Universiteit van Amsterdam,The Netherlands

I. Introduction

The aim of this chapter is to give an overview of research relating to the temporal

aspects of music perception and cognition. This topic has quite a history as a

research topic, having been covered extensively by Paul Fraisse in the first edition

and Eric Clarke in the second edition of this volume (Fraisse, 1982; Clarke, 1999).

However, this chapter focuses primarily on the developments in the past 10 years.

More precisely, it gives an overview of rhythm, meter, timing, and tempo from

both music theoretical and cognitive perspectives, focusing on perceptual aspects

of rhythm. For an overview of performance aspects, see Palmer (Chapter 10, this

volume); for developmental aspects, see Trainor and Hannon (Chapter 11, this

volume); for neuroscience aspects, see Peretz (Chapter 13, this volume) and Wan

and Schlaug (Chapter 14, this volume).

The production and perception of rhythm and timing is addressed only spar-

ingly in music theory. Existing theories of rhythmic structure are restricted to

music as notated in a score, and, as a result, tend to refrain from making state-

ments about music as it is performed by musicians, and perceived and appreciated

by listeners. This might explain a commonly heard complaint on the relative

impoverishment of rhythmic theory (Cooper & Meyer, 1960; Kramer, 1988;

London, 2001). However, the arrival of new technologies (most notably that of

MIDI1 and of the personal computer), as well as a wider use of experimental meth-

ods in music research, has resulted in a considerable increase in the number of

empirically oriented investigations into rhythm, encompassing research into the

nature and properties of music as an acoustical, psychological, and cognitive phe-

nomenon (Bregman, 1990; Clarke & Cook, 2004; Honing, 2006b; Huron, 1999;

Parncutt, 2007). This has led to an important shift from studying the music

1 Commercial standard introduced in the 1980s for the exchange of information between electronic

instruments and computers.

The Psychology of Music. DOI: http://dx.doi.org/10.1016/B978-0-12-381460-9.00009-2

© 2013 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/B978-0-12-381460-9.00009-2

theoretical aspects of music, that is, as notated in the score (e.g., Cooper & Meyer,

1960; Lerdahl & Jackendoff, 1983), to studying the cognitive aspects of music,

that is, as performed and perceived (e.g., Clarke, 1999; Gabrielsson, 1999;

Longuet-Higgins, 1987). This shift is partly based on the realization that there are

important differences between what is notated in a score, what can be measured in

a sound signal, and what is perceived by the listener (Figure 1). For instance,

a meter, while often made explicit by a time signature in the score, cannot be

(a) Audio (measured )

(b) Performance (measured )

(c) Grouping (perceived )

(d)4 3 1

Rhythm (perceived )

(e) Meter (perceived )

(f) Tempo (perceived )

(g) Timing (perceived ) 0

d →

s →

s →

t →

t →

1

f →

0

a → Figure 1 Decomposition of a

rhythmic signal in directly

measurable and perceived

components (a denotes

amplitude, t denotes time,

s position in the score, f tempo

factor, and d timing

deviation).

370 Henkjan Honing

directly measured in a sounding rhythm. It is actually induced in the listener: the

listener constructs a metrical interpretation while listening to music. Further

aspects of rhythm, such as timing and tempo, are also clearly of a perceptual

nature—next to being an intrinsic aspect of performance—and cannot directly,

at least not without a model, be measured in a rhythmic signal. Hence the fields of

perception and cognition play an important role in the study of musical rhythm.

In addition, in the past few decades, a change can be observed from studying

rhythm and timing from a psychophysical perspective (studying the relation

between stimulus and sensation) using relatively simple stimulus materials

(cf. Handel, 1989), to studies in which the ecological validity of the materials used,

the task, and the effect of musical context have all been taken into account

(Clarke & Cook, 2004; Honing & Ladinig, 2008; Honing & Reips, 2008). In its

entirety, this has resulted in a substantial body of work, of which this chapter can

present only a small selection focusing on the cognitive science of rhythm and

timing. An extensive bibliography on rhythm-related studies of the past 10 years

will complement this selection.

And last, a strong connection with other structural aspects of music (see e.g.,

Chapters 6, 7, and 8, this volume), as well as the intimate relation between music

perception and performance, should be borne in mind (see Chapters 10 and 14, this

volume; Sadakata, Desain, & Honing, 2006).

II. Overview: Decomposing the Rhythmic Signal

In order to give some structure to the notion of rhythm, one possible way of

decomposing rhythm will be proposed here, primarily as a way to introduce the

concepts used in rhythm perception research.

A rhythm can be considered as consisting of several components, such as

rhythmic pattern, meter, tempo, and timing. Most listeners are able to derive these

different types of information from the acoustic signal when listening to music

(see Figure 1).

A first component is the perceived rhythmic category, referred to as a rhythmic

pattern. This is a pattern of durations that can be represented on a discrete,

symbolic scale (see Figure 1d). This concept differs from the notion of a performed

or expressively timed rhythm that is measured on a continuous scale (see

Figure 1b). A rhythmic pattern is comparable to rhythm as it is notated in a musical

score. In music theory, when referring to rhythm, this rhythmic pattern is meant

(Cooper & Meyer, 1960). Rhythmic pattern is also related to the process of catego-

rization as studied in music cognition (Desain & Honing, 1991), the process of

deriving rhythmic categories from a continuous rhythmic signal.

A second component of a rhythmic signal is the metrical structure that a listener

might assign to it. A rhythm is often interpreted in a metrical framework, be it a

regular pulse (or beat) or a hierarchically organized interpretation of two or more

levels of beat (see Figure 1e). Beat is related to the notion of tactus, as it has been

3719. Structure and Interpretation of Rhythm in Music

discussed in music theory (Lerdahl & Jackendoff, 1983), and to the cognitive pro-

cess of beat induction (how listeners arrive at a sensation of regular pulse when lis-

tening to a varying rhythm), as it is studied in music cognition (Honing, 2012;

Parncutt, 1994; Povel & Essens, 1985). Although some theories suggest that

rhythm exists solely under metric interpretation (Longuet-Higgins, 1994), one

could also consider the figural aspects of rhythm: rhythm as a sequential pattern of

durational accents that can be grouped at the surface level (Handel, 1993). These

groups can again be hierarchically ordered (see Figure 1c), commonly referred to

as grouping (Lerdahl & Jackendoff, 1983) or rhythmical structure.

A third component of a rhythmic signal is tempo: the impression of the speed or

rate (and changes thereof) of the sounding pattern (Michon, 1967; see Figure 1f ).

Although it is still unclear what exactly constitutes the perception of tempo,

it seems to be related—at least in metrical music—to the cognitive notion of beat

or tactus: the speed at which the pulse of the music passes at a moderate rate,

that is, between 500 and 700 ms (Fraisse, 1982; London, 2004/2012). In music the-

ory, the notion of tempo is only sparsely addressed (Epstein, 1994).

A fourth component is expressive timing that carries the nuances in a rhythm

that can make it sound, for example, “mechanical,” “laid-back,” or “rushed” (see

Figure 1g). This is apparently caused by the fact that some notes are played

somewhat earlier or later than expected. Timing is thus not relevant to music the-

ory, but of considerable interest to music cognition research. For example, why is

a rhythm with a slightly shorter note not simply perceived as a different rhythm?

And how do all these components (i.e., rhythmic pattern, meter, timing, tempo,

etc.) interact to shape our perception of a rhythm?

In the remainder of the chapter, these four rhythmic components are discussed,

along with the perceptual and cognitive processes that can be associated with

rhythm. However, to visualize rhythm and timing in a general way, first a graphic

representation is introduced that allows the abstract space of all possible rhythms,

timed in all possible ways, to be visualized.

III. Structure and Interpretation: Visualizing Rhythm Space

A common method in the study of rhythm and timing in music is to analyze a

number of typical examples from the music literature (Epstein, 1994; Kramer,

1988; Lerdahl & Jackendoff, 1983). This approach, however, may cause difficulties

in that the insights obtained may be dependent on the specific choice of examples,

idiosyncrasies, or musical style. For some of the topics addressed in this chapter,

we will therefore use a visualization that captures the space of all rhythms. This is

an abstract mathematical notion that captures all possible rhythms in all possible

interpretations (Desain & Honing, 2003; Honing, 2002).

To be able to visualize this abstract rhythm space, we restrict ourselves to four-

note rhythms with three interonset intervals (IOIs). These IOIs can be projected in

a three-dimensional rhythm space in which each axis represents the length of one

372 Henkjan Honing

time interval (Figure 2). Every point in that space represents a rhythm of three

intervals of a certain duration (a rhythmic signal; cf. Figure 1b). The total duration

of a four-note rhythm is shorter if the point is close to the origin and longer if it is

moved farther away from the origin.

When we reduce the space to all rhythms of a certain total duration (e.g.,

all rhythms with a total duration of 1 s), this can be depicted as a triangular

cross-section of the rhythm space (indicated in gray in Figure 2). We call this

triangle a chronotopological map (“chronos”5 time, “topos”5 place) or, alter-

natively, a rhythm chart (Figure 3).

To give an example of how to read this chart, consider rhythm A (see left side

of Figure 3). This rhythm consists of four onsets (at 0.0, 0.25, 0.75 and 1.0 s),

can be represented with the IOIs 0.25, 0.50, and 0.25 s, and is a single point in the

1

1

0

1

Inte

rval

1 (s

) →

Interval 3 (s)

→

Interval 2 (s) →

Figure 2 Rhythm space. A cross-section (in the shape of a

triangle) indicates all rhythms of equal length, in this case,

all rhythms with a length of 1 s.

0

0.25 0.50– 0.25–

.25 .50 .75 1

0

0.25 – 0.25 0.50–

time (s) →.25 .50 .75 1

(a)

(b)

Figure 3 Two sample rhythms (left) and their location in a chronotopological map or

rhythm chart (right).


triangle. To locate it in the rhythm chart shown on the right side of Figure 3,

first find the value of the first interval on the relevant axis, and follow the line to

the inside of the triangle, in the direction parallel to the side of the triangle.

Then do the same for the other two intervals, and the point where the three arrows

converge indicates the position of rhythm A in rhythm space.

This chronotopological map (Figure 3, right) contains not only frequently occur-

ring rhythms from music all over the world, but also very unusual ones. There are

no exceptions; all possible rhythms consisting of three IOIs, and all possible ways

of timing them, are included. We will use such a map in discussing the four com-

ponents of rhythm mentioned before (rhythm, meter, timing, and tempo) and the

interplay between them.

IV. Rhythmic Pattern: Representation

Technically, any series of sounds or events that has duration can be called a

‘‘rhythm’’; the greater the number of component durations and the variety of

their sequential organization, the more complex the rhythm (London, 2001).

Taxonomies of rhythmic patterns go back to Aristoxenus (cf. Cooper & Meyer,

1960; for more recent attempts to quantify rhythmic complexity, see Pressing,

1999; Shmulevich & Povel, 2000; Thul & Toussaint, 2008). In Western music

notation, rhythm is often notated proportionally (Figure 4). This can be called a

proportional or relative representation, because it indicates how the durational

intervals between the notes relate (e.g., in Figure 4, the second IOI is twice as

long as the first one).

However this notation is a music theoretical concept, and above all a practical

means for musicians to write down and remember rhythmic patterns. In itself,

it doesn’t say anything about the tempo (the speed at which it’s played) or the

timing (whether a particular note is played too early or too late) of a particular

rhythm. For example, if you were to ask a percussionist to play the rhythm

depicted in Figure 4, then it might look like the following series of measure-

ments: 0.23�0.58�0.29 sec. This is called an absolute representation, “absolute”

because from this series of measurements, the rhythm can be reproduced exactly

(for instance with a computer). It turns out that, even if a musician attempts to

play exactly in time with a metronome (i.e., a “deadpan” performance), some-

thing of his or her original timing and phrasing will still remain (Clarke, 1987).

The converse is also true: even if the rhythm sounds precisely as marked in the

score, then that doesn’t mean that it has been performed exactly as notated (see

Section V and Figure 9).

Figure 4 A proportional representation of rhythm as is common in

Western music notation.

374 Henkjan Honing

We can now ask ourselves: when will a rhythmic signal (cf. Figure 1b) be heard

as rhythm X, and when as rhythm Y, because, for instance, it is performed with

some expressive timing? As a listener, how does one differentiate between rhythm

and timing? To be able to answer these questions, we will now discuss categorization:

the cognitive process by which we recognize, classify, or divide objects in the

world around us (Harnad, 2005).

V. Rhythmic Pattern and Timing: Categorization

How do listeners distill a discrete, symbolic rhythmic pattern (cf. Figure 1d) from a

series of continuous intervals, that is, the rhythmic signal (cf. Figure 1b)? Fraisse

(1982) stressed the importance of low integer ratios (like 1:1 and 1:2) in the percep-

tion of rhythm, ratios toward which noninteger rhythms will migrate. Other authors

(Nakajima, 1987) suggested that categorization can be expressed as a psychophysi-

cal function, mapping continuous intervals into discrete categories, independent of

context. Still others (Clarke, 1987) investigated whether this categorization might in

fact be a result of categorical perception (Harnad, 1987). However, the implication

of true categorical perception is that expressive timing would be barely detectable,

which clearly is not the case. Timing is actually one of the most compelling aspects

of music (Ashley, 2002; Hudson, 1994). Hence, categorization is not simply a map-

ping from a continuous variable to a discrete one—losing important continuous

information in the process. In fact, both types of information, the rhythmic pattern

and expressive timing, are available at the same time, with the categorization func-

tioning as a reference relative to which timing deviations are perceived (Clarke,

2000; Desain & Honing, 2003; Sadakata et al., 2006).

As an example of this process, consider the rhythm shown in Figure 5 (the

downward arrow depicting rhythm perception). Next to the recognition of the

rhythmic categories (represented by integers in Figure 5, bottom), a listener also

perceives the expressive timing of the performed rhythm. Even untrained listeners

can appreciate the exaggerated “against the beat” quality of the triplets (Honing &

Haas, 2008) and the natural slowing down at the end of the group of sixteenth notes

(Palmer, 1997).

Categorization in rhythm perception has commonly been studied by presenting

interpolations between different rhythmic patterns to listeners in both an identifica-

tion task (probing the recognition of categories) and a discrimination task (testing

for increased sensitivity near category boundaries). As such, it applies the paradigm

developed for categorical perception (Harnad, 1987) as used, for instance, in the

domains of speech (Repp, 1984), color perception (Saunders & van Brakel, 1997),

and the perception of melodic intervals (Burns & Ward, 1978).

Clarke (1987) describes an experiment in which a short musical sequence was

presented in two different metrical contexts (a duple and a triple meter), with the

two notes at the end of the sequence systematically being varied between the ratios

1:1 and 1:2 (Figure 6). The participants performed an identification task in which


they had to identify the rhythm as belonging to type 1:1 or type 1:2 and a discrimi-

nation task in which they judged whether a pair of rhythms was same or different.

The resulting identification function showed a strong change in slope at the

category boundary between the two rhythms, and the discrimination function has a

strong peak in the same position, which is conventionally taken as clear evidence

for categorical perception. At the same time, however, the judgments were influ-

enced by the metrical context, showing that the category boundary is not fixed and

can be shifted by metrical context.

Schulze (1989) did a follow-up study addressing some of the methodological pro-

blems of Clarke’s study (Figure 7), the main point being that the forced-choice para-

digm used in the identification task steered the participant’s responses toward the

available categories. Schulze therefore used a somewhat different experimental

setup, in which he trained two participants with a set of interpolated rhythms and

asked them to give a graded identification response (i.e., as many response catego-

ries as stimulus types). The discrimination function was derived indirectly from

these responses. He showed that categorical rhythm perception is open to perceptual

Figure 6 Stimuli used in Clarke

(1987).

Figure 5 Example of two representations of time that are present in music: (top) a

performed rhythm in continuous time, and (bottom) the perceived rhythmic categories in

discrete, symbolic time. (A sound example is available at http://www.hum.uva.nl/mmm

/categorization/.)

376 Henkjan Honing

http://www.hum.uva.nl/mmm/categorization/

http://www.hum.uva.nl/mmm/categorization/

learning: the participants were able to distinguish more categories after an intensive

training period before the experimental trials.

By contrast, Desain, Honing, and their colleagues undertook a series of empiri-

cal studies (e.g., Desain & Honing, 2003) in which a considerably larger set of tem-

poral patterns were used as stimuli: 66 four-note rhythms with a fixed total

duration of 1 s, systematically sampled over the whole rhythm space (see left side

of Figure 8).2 The results of a first experiment, in which participants were asked to

notate this set of 66 rhythms (an identification task), are summarized in the right

side of Figure 8. The thick lines demarcate the observed boundaries between the

different rhythm categories.

One can see, in Figure 8, that not all categories are of the same shape and size

(as would be predicted by a straightforward rounding-off algorithm, as used by

some music notation software). Some rhythms allow for considerable timing vari-

ation, without the risk of being perceived as another rhythm (e.g., the rhythmic

categories 1:2:1 and 1:1:2). Other rhythms allow for little variation in the timing

(e.g., 2:3:1 and 3:1:4). If timing variation is applied to these rhythms, they are

quickly perceived as an altogether different rhythm. One should note, however,

that Figure 8 depicts quite a reduction of the responses (for a complete, color

.5 .25

D

BA

C

← Interval 2 (s)

Inte

rval

1 (s

) →

Inte

rval

1 (s

) →

Interval 3 (s) →

Interval 3 (s) →

.5

.75

.25.75

.5

1 0.75 0.50 0.25 01

0.75

0.500.50

0.25

0

0.25

01

0.75

.250

← Interval 2 (s)

Rhythm

A 3:1:2B 4:1:3C 2:1:3D 3:1:4

Figure 7 Stimuli and results of Schulze (1989) depicted as a chronotopological map

(zooming-in on a small part of the rhythm space, indicated by the diagram at the left). The

gray lines indicate the perceived category boundaries. The gray area is the hypothetical

shape of the rhythmic category A. The dots identify the (interpolated) rhythms, crosses mark

the mechanical ones (i.e., A, B, C and D).

2 Desain and Honing (2003) reported only on two of the experiments. The full results, including those

that show the effect of overall tempo and dynamic accent, are available online at http://www.hum.uva

.nl/mmm/categorization.


http://www.hum.uva.nl/mmm/categorization

http://www.hum.uva.nl/mmm/categorization

visualization, see Desain & Honing, 2003 or the URL mentioned in footnote 2).

Each islet in Figure 8 (right) is, in fact, a mountain, the summit of which indi-

cates the rhythm notated by the majority of listeners: the “modal” or most fre-

quently identified rhythm (Figure 9).

Interestingly, this modal rhythm never overlaps with the metronomic version,

but with a rhythm that incorporates some timing variation. For instance, the major-

ity of listeners perceived the category 1:1:1, the most frequently selected notation

for a rhythm that was timed as 0.33�0.31�0.36 s; a minority of listeners notated

1:1:1 for the rhythm 0.33�0.33�0.33 (the metronomic rhythm as indicated by the

score). Apparently, if the rhythm 1:1:1 is phrased with a small ritardando, then it

sounds more like the notated rhythm than if a computer had played the rhythm

exactly as notated. This suggests that the rhythmic categories are not simply

Figure 9 Mechanical versions of

characteristic rhythms and their

most frequently identified

interpretation (modal ).

Figure 8 (Left) The sampling of the rhythm space as used in the experiments mentioned in

the text, and (right) the results with lines marking the category boundaries (Experiment 1

from Desain & Honing, 2003).

378 Henkjan Honing

integer-related rhythms such as notated in a score (see Repp, London, & Keller,

2010 for a replication of this effect for two-interval rhythms).

Furthermore, as was already noted by Clarke (1987), this categorization process

remains open to top-down cognitive influences, either influenced by the preceding

musical context (veridical expectation) or influenced by expectations as a result of

earlier exposure to music (schematic expectation; Bharucha, 1994; Huron, 2006).

When the same rhythms as used in the experiment depicted in Figure 8 are presented

in a duple or a triple meter context (i.e., primed with a beat that is subdivided either

in two or in three), the perceived categories change dramatically (Figure 10). For

example, when the rhythm 0.26�0.42�0.32 (marked with an asterisk in Figure 10)

was preceded by a rhythmic context that induced a duple meter, it was heard by

most of the participants as 1:2:1 (category marked 2 in the left side of Figure 10).

However, when the same rhythm was preceded by a rhythmic context that induced a

triple meter, then the majority of participants heard that as 1:3:2 (category marked 9

in the right side of Figure 10).3

It is puzzling, however, that although meter was shown to exert a strong influence

on the recognition of rhythm (Clarke, 1987; Desain & Honing, 2003), existing

computational models of meter can explain this phenomenon only to a small extent

(Desain & Honing, 2001). This can be considered as additional empirical support for

the idea that there is more to rhythm than meter alone, as has been emphasized in

several musicological and music theoretical studies (Honing, 2002; London, 2001).

Figure 10 The effect of duple (left) and triple (right) meter on rhythmic categorization

(Experiment 2 from Desain & Honing, 2003).

3 This empirical fact is problematic for theories that are based on musical score representations (such as

Lerdahl & Jackendoff, 1983): It reveals a circularity in which the leaves (or notes) of an analytic tree

(e.g., a metrical analysis) are a result of a structural interpretation to which these leaves (or notes) are,

in fact, the input. The paradox can only be resolved when one makes a distinction between the continu-

ous rhythmic signal (cf. Figure 1b) and the perceived rhythmic categories (cf. Figure 1d).


Overall, this research suggests that expressive timing cannot simply be defined

as a deviation from what is notated in the score (Todd, 1992). Based on the empiri-

cal results presented earlier, a more realistic interpretation might be that it is the most

frequently heard performance of a rhythm—rather than the canonical or integer-

related version of it, as notated in a score—that might function as a reference or cate-

gory. Or, in other words, expressive timing is best defined as a deviation from the

most frequently heard version of a rhythm, which depends on memory.

Nevertheless, the research just described also has its limitations. One of these is

related to the identification task used: the participants were asked to notate care-

fully what they had heard. This is a task that assumes specialized skills and restricts

the group of potential participants considerably, and as such, the generality of the

results. One possible alternative is to use a discrimination task instead, which

makes the task doable for most listeners and can form an alternative technique for

constructing the rhythmic charts shown earlier.

What we can conclude however, is that the ability to hear nuances in the timing

of a piece of music is an outcome of a cognitive process of categorization which,

in turn, is dependent on memory (Snyder, 2001), expectation (Huron, 2006), and

the ways in which we have been exposed to music in the course of our lives

(Honing, 2011a). A listener does not perceive rhythm as an abstract unity, as is

notated in a score, nor as a continuum in the way that physicists describe time.

We actually tend to hear rhythm and timing in what one might call “clumps”: the

islets that can be seen on the chronotopological maps shown earlier.

VI. Metrical Structure

A. Syncopation

The second component of rhythm I will discuss here is metrical structure. I will use

the terms pulse (or beat) to refer to a highly salient, periodic layer of articulation in

the musical texture (normally with a period between 400 and 800 ms) and meter to

refer to the emergent (or induced) temporal structure of at least two levels of pulse.

An important distinction to be made is that between rhythmic pattern and metri-

cal structure. Although some music theorists question and deemphasize this distinc-

tion (Hasty, 1997), the general consensus is that rhythm and meter are in fact two

very separate notions (London, 2001). While rhythm can be characterized as the

varying pattern of durations that is perceived to be present in the music, meter

involves our perception and, more importantly, (embodied) anticipation of such

rhythmic patterns. Meter is, as such, a cognitive phenomenon (London, 2012;

Longuet-Higgins, 1994).

The interaction of rhythm and meter, and the role that cognition plays in its per-

ception and appreciation can be illustrated with the phenomenon of syncopation.

It is often described, rather informally, as “an accent that has been moved for-

ward,” or as “a technique often used by composers to avoid regularity in rhythm by

displacing an emphasis in that rhythm.” (Oxford Music Online, 2011). To illustrate

380 Henkjan Honing

this, consider the two rhythms depicted in Figure 11. Which of these is a synco-

pated rhythm?

A formally trained musician will easily point out the left example, guided by the

slur marking a syncopation. However, as performed by a drum computer, these

notated rhythms will sound identical. The reader here is influenced by the notation.

When we listen to a rhythm (even if it is simply a series of isochronous clicks, like

a clock), we tend to interpret it in a metrical fashion (Brochard, Abecasis, Potter,

Ragot, & Drake, 2003) and hear it as syncopated, or not, depending on the metric

interpretation. A time signature in the notation is no guarantee that a listener will

perceive the meter as such. This is illustrated by the example in Figure 12.

Western listeners tend to project a duple meter while listening to a rhythm

(Drake & Bertrand, 2001) and hence perceive a syncopation (depicted on the left

of Figure 12). However, if a listener were to expect, for example, a compound

meter (as on the right of Figure 12), then the syncopation will disappear altogether.

An important insight here is that the perception of rhythm should be seen as an

interaction between the music—the sounding rhythm—and the listener—who

projects a certain meter onto it (Fitch & Rosenfeld, 2007; Honing, 2011b; Longuet-

Higgins & Lee, 1984). We can therefore use the presence (or absence) of a

perceived syncopation as evidence for the presence (or absence) of a strong metric

expectation, which provides a method to probe metrical expectation in listeners

(see Section VI,B).

B. Beat Induction as a Fundamental Cognitive Skill

Beat induction4 is the cognitive skill that allows us to hear a regular pulse in music

and enables our synchronization with it. Perceiving this regularity in music allows

us to dance and make music together. As such, it can be considered a fundamental

human trait that, arguably, played a decisive role in the origin of music (Honing &

Ploeger, in press). Furthermore, it might be considered a spontaneously developing

and domain-specific skill, as projecting or perceiving a regular pulse seems to be

absent in spoken language (e.g., Patel, 2008).

Beat induction has been a topic of many music perception studies, mostly

concerned with the theoretical and psychological aspects of this cognitive skill

(Desain & Honing, 1999; Large & Jones, 1999; Parncutt, 1994; Povel & Essens,

Figure 11 Which rhythm is syncopated?

4 The term beat induction is preferred here over beat perception (and synchronization) to emphasize that

a beat does not always need to be physically present in order to be ‘perceived’ (cf. Figure 12).

Furthermore, it stresses that beat induction is not a passive, perceptual process but an active one in

which a rhythm evokes a particular regular pattern in the listener. How far this process is open to learn-

ing, and whether there might be a cognitive and neurological difference between beat induction and

meter induction, is a topic of current research (Honing, 2012).


1985). More recently, the phenomenon has attracted the interest of developmental

psychologists (Hannon & Trehub, 2005), cognitive biologists (Fitch, 2006), evolu-

tionary psychologists (Honing & Ploeger, in press), and neuroscientists (Grahn &

Brett, 2007; Grube, Cooper, Chinnery, & Griffiths, 2010) as a skill that is funda-

mental to music processing that can be argued to be an innate (or spontaneously

developing), domain-specific and species-specific skill.

However, with regard to the first issue, scientists are still divided whether this

ability develops spontaneously (emphasizing a biological basis) or whether it is

learned (emphasizing a cultural basis). Some authors consider a sensitivity to the

beat to be acquired during the first year of life, suggesting that the ways in which

babies are rocked and bounced in time to music by their parents is the most impor-

tant factor in developing a sense for metrical structure (cf. Trehub & Hannon,

2006). By contrast, more recent studies emphasize a biological basis, suggesting

beat induction to be specifically tuned to music; studies have shown that beat

induction is already functional in young infants (Zentner & Eerola, 2010) as well

as 2- to 3-day-old newborns (Winkler, Haden, Ladinig, Sziller, & Honing, 2009).

These recent empirical findings can be taken as support for a genetic predisposition

for beat induction, rather than it being a result of learning (Honing, Ladinig,

Winkler, & Haden, 2009).

Furthermore, developmental studies suggest that infants are not only sensitive to

a regular pulse, but also to meter (two or more levels of pulse; Hannon & Johnson,

2005). Thus it is possible that humans possess some processing predisposition to

extract hierarchically structured regularities from complex rhythmic patterns

Figure 12 Two possible notations (labeled as ‘Score’) of the same rhythm (labeled as

‘Rhythm’). In the left example a metrical tree represents a duple meter, in the right example

it represents a compound meter (labeled as ‘Listener’). The numbers at the leaves of the

metrical tree represent the theoretical metric salience (the depth of the tree at that position in

the rhythm). A negative difference between the metric salience of a certain note N and the

succeeding rest R indicates a syncopation (Longuet-Higgins & Lee, 1984). The more

negative this difference, the more syncopated the note N or ‘louder’ the rest R.

382 Henkjan Honing

(Ladinig, Honing, Haden, & Winkler, 2009). Research with newborns provides the

context within which to understand more about these fundamental capacities

(Honing, 2012; Winkler et al., 2009).

VII. Tempo and Timing: Perceptual Invariance

The two components of rhythm that are studied in the domain of music cognition,

but rarely in music theory, are tempo and timing. Timing plays an important role in

the performance, perception, and appreciation of almost all types of music. It has

been studied extensively in both music perception and performance research (for

the latter, see Palmer, Chapter 10, this volume). The most important outcome of

this research is that a significant component of the timing patterns found in music

performance—commonly referred to as expressive timing—can be explained in

terms of musical structure, such as the recurrent patterns associated with the metrical

structure that are used in jazz swing (Ashley, 2002; Honing & Haas, 2008) or the

typical slowing down at the end of phrases in classical music from the Romantic

period (Honing, 2003; Palmer, 1997). These timing patterns help in communicating

the temporal structure (such as rhythm and phrase structure) to the listener.

Furthermore, timing is adapted with regard to the global tempo: at different tempi,

other structural levels of the music are emphasized and the expressive timing is

adapted accordingly (Clarke, 1995, 1999). One might wonder, however, whether tim-

ing would remain perceptually invariant over tempo, as has been found in other cog-

nitive domains, including speech (Perkell & Klatt, 1986), motor behavior (Heuer,

1991), and object motion (Shepard, 2001).

Perceptual invariance has been the topic of several studies in music perception

(Handel, 1992; Hulse, Takeuchi, & Braaten, 1992; Repp, 1995). A well-known and

relatively uncontroversial example is melody (Dowling & Harwood, 1986). When a

melody is transposed to a different register, it not only maintains its frequency

ratios in performance, but it is also perceived as the same melody (i.e., melody

remains perceptually invariant under transposition). With respect to other aspects

of music, such as rhythm, there is less agreement in the literature.

Whereas one might expect rhythm to scale proportionally with tempo in pro-

duction and to be perceptually invariant under tempo transformation, a number of

studies have shown that this is not always the case (Handel, 1992; Monahan &

Hirsh, 1990). With respect to rhythmic pattern, listeners often do not recognize

proportionally scaled rhythms as being identical (Handel, 1993). With respect to

timing, rhythms are timed differently at different tempi (Repp, Windsor, &

Desain, 2002).

With regard to expressive timing, the literature has been divided over whether it

is relationally invariant over tempo (Desain & Honing, 1994; Repp, 1994).

Although earlier perceptual studies present rather inconclusive evidence (Repp,

1994, 1995), more recently the idea that musical performances might be understood

in terms of a tempo curve—a mental representation of timing abstracted from the

rhythmic material and overall tempo, that can be represented as a continuous shape


or function (Desain & Honing, 1993; Honing, 2003)—has been critiqued as a

musical (Honing, 2003), perceptual (Honing, 2006a) and cognitive construct

(Honing, 2001, 2005). The alternative view proposes a richer memory representa-

tion of timing than what can be captured by an unstructured tempo curve; such

curves form the basis of several models of musical time (Epstein, 1994; Feldman,

Epstein & Richards 1992; Friberg & Sundberg, 1999; Kronman & Sundberg,

1987; Longuet-Higgins & Lisle, 1989; Sundberg & Verillo, 1980; Todd, 1992;

Todd, 1985). These recent results have led to a tempo-specific timing hypothesis

that has been shown to be valid in the perception of baroque and classical music

(Honing, 2006a) as well as in jazz performance (Honing & Haas, 2008).

However, one might hypothesize that the absence of relational invariance in the

perceptual studies mentioned is merely a result of expert knowledge, as the parti-

cipants were mostly musicians who were very familiar with a particular musical

repertoire.

To test this, Honing and Ladinig (2009) studied the influence of exposure ver-

sus expertise in making expressive timing judgments. This was done using an

online listening experiment in which listeners with different musical preferences

(exposure) and music education (expertise) were asked to compare two perfor-

mances of the same composition (15 pairs, grouped in three musical genres),

one of which was tempo-transformed (manipulating the expressive timing). The

study showed that these judgments are not primarily influenced by expertise (e.g.,

years of formal training) but mainly by exposure to a certain musical idiom.

The interplay of familiarity with a particular genre (exposure) and the level of

formal musical training (expertise) had a significant effect on discriminating a

real from a manipulated performance. In short: both in perception and in produc-

tion, timing seems to be tempo-specific.

VIII. Rhythm and Movement: Embodied Cognition

The majority of the research discussed earlier, however, focuses on rhythm cogni-

tion as a perceptual phenomenon. Therefore, in this final section, some of the more

recent work on embodied cognition is discussed.

The relation between musical rhythm and motion has been studied in a large

body of theoretical and empirical work. Early examples, from the 1920s, include

work by Alexander Truslit and Gustav Becking (see Shove & Repp, 1995, for an

overview). More recently, a number of authors (Todd, Cousins, & Lee, 2007;

Trainor, Gao, Lei, Lehtovaara & Harris, 2009) have presented evidence suggesting

a direct link between musical rhythm and movement. The link is “direct” in the

sense that it is argued that rhythm perception is influenced (or even determined) by

our physiology and body metrics, from the functioning of our vestibular system to

leg length and body size. Although there is apparently no relation between body

build and walking speed (Macdougall & Moore, 2005), some theories suggest a

direct connection between body build and preferred tempo (Todd et al., 2007).

384 Henkjan Honing

The latter theory makes the peculiar prediction that body length will have an effect

on rhythm perception: longer people will prefer slower musical tempi, and shorter

people will prefer faster ones (cf. Repp, 2007).

In a rather different approach, Phillips-Silver and Trainor (2005) conducted a

developmental study that showed that body movement (rather than body size) can

influence rhythm perception. They asked mothers to rock their 7-month-old chil-

dren in time to a rhythm that could be heard in two different ways: in time (as in

a march) or in time (as in a waltz). Half of the babies were swung backward and

forward on every second beat of the bar; the other half, on every third beat.

The researchers showed that the babies in the first group preferred rhythms with

accents on every second beat ( time), whereas the group that was rocked to a

three-beat tune had a preference for rhythms with an accent on every third beat

( time). Thus, in a surprisingly simple experiment, they demonstrated that move-

ment indeed influences the perception of rhythm.

In short, there have been a number of studies that have investigated the ways in

which physiological phenomena (e.g., heart rate, spontaneous tapping rate, walking

speed) might influence or even determine rhythm perception (Leman, 2007;

Phillips-Silver & Trainor, 2008). It is important to acknowledge that these embod-

ied explanations of rhythm perception, however simple they might seem, form a

significant addition to the “mentalist” or cognitive perspective that I have largely

adopted in this chapter.

Acknowledgments

Preparation of this chapter was supported by the Hendrik Muller chair designated on behalf

of the Royal Netherlands Academy of Arts and Sciences (KNAW), and was written while I

was a member of the Research Priority Area “Brain & Cognition” at the University of

Amsterdam. I gratefully acknowledge the constructive criticisms and detailed comments of

Eric F. Clarke, Justin London, and Caroline Palmer, and the aid of Fleur Bouwer and Sandra

Wallner in preparing this manuscript.

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404 Henkjan Honing


the psychology of music || structure and interpretation of rhythm in music

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