Although each chapter in this book has a distinct focus, there are many concepts that recur. This is especially true for Chapters 2–12, which explore various aspects of Western music. The present chapter introduces some of these recurrent ideas for readers less familiar with rhythmic terms and surveys significant recent theoretical contributions to the study of rhythm in Western music. The interested reader can find more comprehensive overviews of rhythmic theory in two essays by William E. Caplin and Justin London in The Cambridge History of Western Music Theory.1
As noted in the Introduction, the present volume takes the term rhythm to refer to the temporal organization of music. Writers on time in Western music, however, frequently use the term rhythm in a more circumscribed manner to refer specifically to the durations of sound events. A repeating sequence of durations might be referred to as a rhythmic pattern, for instance. In this sense, rhythm is a property of a wide range of styles from Medieval plainchant to common-practice tonal music to the plethora of compositional languages present in the past hundred years. Within most Western music since the late Medieval period, there is also a sense that the individual rhythmic events occur in relation to a regular underlying pulse, typically referred to as the beat. And, moreover, those beats are not perceived to be of equal strength but have a recurrent pattern of strong and weak beats called meter. Meter is a feature of some music from the late Medieval period, is found in virtually all music from the Renaissance to the start of the twentieth century, and is present in most – but by no means all – music from the past hundred years. Meter offers a way of measuring musical time that is distinct from chronometric time; its patterned regularity, or periodicity, provides a framework that coordinates individual sound events, or rhythm.
The origin of rhythm, in the sense of durations of sound events, is clear enough: sounds begin and end, and this physical property is directly observable in the same way that pitch (frequency) and volume (amplitude) are. Meter, on the other hand, cannot be ascribed to a discrete component of sound. Yet, for the most part, listeners immediately respond to meter, such as by coordinating a pattern of dance steps or clapping on particular – rather than all – beats. What are the musical features that allow listeners to infer meter from the aural input? This is a complex question that music psychologists and music theorists have wrestled with, but it is the latter body of scholarship on which I draw below.
Meter and Metric Dissonance
A detailed and highly influential treatment of the musical factors that create meter is found in Fred Lerdahl and Ray Jackendoff’s A Generative Theory of Tonal Music.2 Lerdahl and Jackendoff present a series of preference rules. These include preferences for similar musical content to receive parallel metric placement and for the onset of long events to fall on stronger beats. Long events refer not only to extended rhythmic durations but also to a variety of other parameters, such as the length of a dynamic level, pattern of articulation, or harmony. For common-practice Western art music and genres such as jazz and rock, changes of harmony are often the most significant factor in the projection of strong beats. In addition, the pitch onsets within the bass line itself, at least in many styles, tend to occur on strong beats.
As a demonstration of meter in common-practice tonal music, consider an excerpt from a string quartet by Haydn (shown in Example 1.1) and try to auralize it without paying attention to the notated 
meter and the barlines. In the first seven measures, observe the placement of long durations (half notes and dotted half notes) in the second violin and viola. Although moving in consistent quarter notes, the cello also outlines a three-beat pattern owing to the lower register of every third pitch. Moreover, when the lowest note departs from the pitch C and the harmony moves to predominant and then dominant, these changes coordinate with the established triple meter.
Now consider the music that begins in the excerpt’s eighth measure. The repeated melodic-rhythm pattern in the first violin outlines a two-beat pattern. The sudden shift to this contrasting thematic material, reinforced by the forzando marking, suggests a strong-weak (rather than weak-strong) identity for these two-beat units, as does the placement of long durations in the second violin. For two measures, the music projects a duple grouping of beats, namely, 
meter. One could argue that a composer writing after 1900 might have notated a change from meter to meter for these two measures, and that the aural effect here is a change in meter completely akin to that which can occur between the large sections of a common-practice tonal work, such as a ternary or rondo form. The prevalent view, however, is that the established metric context informs our understanding of short passages that project a different meter. In other words, the duple grouping of beats in these two measures is not heard as fully stable but rather as an unstable intrusion that subsequently resolves. The phenomenon of duple grouping of beats, usually across a two-measure span, within a triple-meter context is frequently encountered, and is referred to as hemiola. In Baroque music it even has a typical formal function as preparation for a cadential arrival. I will return to the formal function of the hemiolic measures in the Haydn excerpt below, but for now it suffices to observe that the harmonic changes in the excerpt’s last two measures re-establish triple meter and bring the phrase to a satisfactory tonal – and metric – conclusion.
During the past two decades, many authors have applied the terminology of consonance and dissonance familiar from theories of pitch organization to the domain of meter. The most extensive development of this analogy is found in Harald Krebs’s book on the music of Robert Schumann.3 Krebs outlines two types of metric dissonance: grouping dissonance and displacement dissonance. In a grouping dissonance, one or more layers in the music projects a grouping of beats that is non-congruent with that of the prevailing meter. The hemiola described above is the simplest instance of grouping dissonance, as it involves a switching between triple and duple grouping at the level of the beat. More complex grouping dissonances might involve a switching between quadruple and triple grouping, for instance. The number of textural layers involved in the grouping dissonance, as well as the particular musical parameters that cause it to arise, give grouping dissonances a variety of intensities.
Displacement dissonance involves one or more textural layers that shift the strong beat from its expected location. For instance, in a triple meter dynamic accents or placement of harmonic changes might make the second or third beat of the notated meter – the prevailing metric consonance – sound as the strong beat in the meter. As with grouping dissonance, displacement dissonance can involve the entire musical texture or only particular layers and can thereby seem to be stronger or weaker. Consider the initial pair of phrases from the first movement of Haydn’s Symphony No. 104, shown in piano reduction in Example 1.2.
1.2 Haydn, Symphony in D Major, No. 104, I, mm. 17–33 (piano reduction)
At the start of the excerpt, strong beats in the meter are articulated through the placement of long durations in the melody and the harmonic changes at the moments corresponding to the downbeats of the first, third, and fourth measures. The lack of rhythms faster than the eighth note suggests the beat is the notated half note (as does Haydn’s cut-time, or 2/2, meter signature to the reader of the score). The metric organization is duple with no ambiguity as to the location of the strong beats. In the fifth measure, the alto voice (played by the second violins) has a series of half-note durations displaced by a quarter note from the strong beats. Compared to the grouping dissonance in the string quartet excerpt, the displacement dissonance here is much weaker and in no way makes the location of the strong beats unclear. (And for a listener thoroughly familiar with eighteenth-century style, the sense of displacement dissonance is very minimal since the dislocation of this layer arises through the contrapuntal technique of the suspension.) Many writers would simply refer to this alto line as syncopated, although the term syncopation can also be used for the singular placement of the onset of a long duration on a weak beat. In the excerpt’s second phrase (shown on the second line of Example 1.2), the fifth and sixth measures exhibit a somewhat stronger displacement dissonance owing to the participation of two voices (played by the second violins and cellos) and the placement of these voices in the bottom of the texture.
Hypermeter
To this point, I have written almost exclusively about the level of meter referred to as the beat or tactus, that is, the level to which most listeners would respond bodily through finger- or toe-tapping and to which most conductors would coordinate their gestures. Yet, at least in music of the eighteenth and nineteenth centuries, the sense of strong and weak ascribed to beats within a meter also operates on larger (i.e., slower) levels of the metric hierarchy. The annotations on Example 1.2 include Arabic numerals, and these represent a type of meter. A widespread, but not pervasive, view among music analysts is that all of the measures marked “1” have a strength, or metric accent, analogous to the first beat in 
meter.4 This strength is articulated by changes in melodic design and harmony. Meter above the level of the notated meter is referred to as hypermeter, the unit corresponding to a complete cycle of hyperbeats as a hypermeasure, and the first beat of a hypermeasure as a hyperdownbeat.
Hypermeter is less consistently periodic than is meter. One scenario where hypermetric irregularity frequently occurs is when a cadential arrival simultaneously functions as the beginning of the next phrase. In Example 1.2, the first phrase spans eight measures, concluding on the dominant harmony. The second phrase, which is parallel in construction, heads to a cadence on tonic harmony in its eighth measure. However, the arrival is marked by the sudden onset of a new dynamic and the entrance of the winds, brass, and timpani. The melodic idea that begins at this point initiates the next phrase, meaning that the measure has a dual function in the passage’s phrase organization. Hypermetrically, a measure that was initially weak (a fourth hyperbeat) is reinterpreted as strong (a hyperdownbeat); this is shown by the 4 = 1 annotation.5 Phrase overlap, or elision, can occur without hypermetric reinterpretation, and hypermetric irregularities can arise in other situations.
Let’s return to the string quartet excerpt in Example 1.1 and consider its hypermetric structure; the reading shown, with which I concur, is adapted from William Rothstein’s book Phrase Rhythm in Tonal Music.6 The Arabic numerals convey quadruple hypermeter, stemming from melodic parallelism (compare measures 1 and 5 of the excerpt). The hemiolic passage begins where the fourth hyperbeat of the second hypermeasure is expected, and it also replaces the expected cadential arrival on tonic harmony. From the perspective of phrase structure, the hemiolic measures expand the phrase by delaying the cadence; adopting Rothstein’s terminology, they can be understood as a parenthetical insertion in the phrase structure owing to the degree of contrast they exhibit with the surrounding music. The theoretical question that arises is whether they cause hypermeter to be inoperative or whether they suspend hypermeter temporarily. In the view of Rothstein and many other authors, a parenthetical insertion does not preclude the continuation of hypermeter; in fact, some analysts contend that lengthier parenthetical insertions can even have their own independent surface hypermeter while the underlying hypermeter is held in abeyance until the end of the parenthetical insertion. This view stretches the extent to which periodicity can be withheld without losing the temporal foundation of hypermeter. It asserts that hypermeter is more dependent upon the influence of phrase organization and the distinct qualia of hyperbeats than upon the measuring of duration.
The idea that hypermeter can exist in the absence of strict periodicity has led theorists to debate the extent to which meter is operative at levels above the notated measure. For Lerdahl and Jackendoff, meter is a “relatively local phenomenon” that, in tonal music, often extends “from one to three levels … larger than the level notated by barlines, corresponding to regularities of two, four, and even eight measures.”7 Theorists influenced by the hierarchical understanding of pitch organization posited by Heinrich Schenker, such as Carl Schachter, William Rothstein, and Frank Samarotto, typically view meter as still operative on slightly deeper levels (i.e., levels corresponding to sixteen or thirty-two measures). Of course, the number of hypermetric levels present depends somewhat on the nature of the music; a piece with exceedingly regular phrase structure or harmonic rhythm – such as a waltz or march – is more readily interpreted in this manner. In other cases, a greater degree of abstraction is required, as higher levels of meter are correlated with significant tonal arrivals and assumed models of underlying periodic phrase structure beneath surface-levels expansion (or, less frequently, contractions). Very few authors posit the existence of hypermeter at the larger levels of form (i.e., beyond thirty-two measures) owing to the extreme deviations from periodic beats, but one notable instance is Jonathan Kramer in his book The Time of Music.8
Positing multiple levels of hypermeter asserts that meter has a quality not unlike the physical property of inertia, that is, once established meter has considerable inherent stability and independence from the individualities of the musical foreground. In other words, when events that induce the perception of metric accents occur at unexpected moments, the ongoing meter and hypermeters have a resilience that allows them to continue. Some recent authors have questioned this separation of meter from the details of the musical surface, either on phenomenological or cognitive grounds, or both. Informed by research in music cognition, Justin London suggests that meter has a “temporal envelope” whose “upper limit is around 5 to 6 seconds.”9 London demonstrates how the constraints on human temporal perception can explain the prevalence of certain meters at various tempi, as the shortness of subdivisions of beats and the length of hyperbeats move toward perceptual thresholds. The latter perhaps explains the rarity of triple hypermeters, besides an aesthetic preference for the symmetry and balance of duple construction.10 From a phenomenological perspective, Christopher Hasty has offered the strongest critique of what I have called metric inertia, arguing for the role of rhythmic durations in creating “projected potentials” that are realized or denied depending on whether an immediately successive event begins at the expected moment in time.11 Hasty’s approach invites close hearing of the music and demands constant renewal of meter through the durations of events and their identities as beginnings, continuations, or anacruses. For Hasty, meter is not fundamentally about levels of beats in proportional relationships but about different configurations of rhythmic events whose particularities can make two passages with the same notated meter have quite different temporal characteristics, and in Hasty’s view these features are metric, as opposed to rhythmic.
Given the competing claims in contemporary music theory about the nature of hypermeter, one might wonder about the validity of the concept and whether there is any evidence that composers of common-practice tonal music were sensitive to hypermetric considerations. There are clear indications that some composers were cognizant of hypermeter, at least for one or two levels above the notated meter. Explicit notation of hypermeter is exceedingly rare, but there are examples. The most famous occurs in the scherzo of Beethoven’s Ninth Symphony where he writes ritmo di tre battute and ritmo di quattro battute to show shifts between triple and quadruple hypermeter. A less well-known instance is found in the Mephisto Waltz No. 1 where Liszt uses Arabic numerals to indicate quadruple hypermeter in a manner exactly parallel to the analytic annotations on the examples above, as shown in Example 1.3.12 Moreover, Liszt notates a measure of rest before the music begins. Somewhat more commonly encountered is a notated measure of rest at the end of a movement or work to complete a hypermeasure; an early instance of this happens at the end of the first movement of Beethoven’s Piano Sonata in A Major, Op. 2, No. 2.
1.3 Liszt, Mephisto Waltz, No. 1, mm. 1–9
Perhaps the strongest support for the idea of hypermeter comes from pieces in fast tempi where the notated downbeats are perceived as beats. In these instances, the perceived meter is not the notated one but rather a hypermeter; given that there is some subjectivity involved in deciding which level of meter corresponds to the heard meter, most analysts simply employ the terms meter and hypermeter with respect to notation. Many nineteenth-century scherzo movements are notated in meter but proceed at a sufficiently fast tempo where the downbeats of consecutive measures are perceived as beats in a larger, usually quadruple, meter. The scherzo from Beethoven’s Ninth Symphony mentioned above is exceptional in that this larger meter shifts back and forth between triple and quadruple organization; typically, the larger meter remains quadruple throughout, albeit sometimes with playful moments of dislocation when the hyperdownbeat shifts (generally by two notated measures), as in the scherzo from Beethoven’s Seventh Symphony. Outside of the scherzo repertoire, a clear instance where the notated meter is not the perceived meter occurs in the first movement of Beethoven’s Fifth Symphony, shown in reduction in Example 1.4. Instead of coordinating their gestures with the notated 2/4 meter, conductors uniformly show a larger quadruple pattern that spans four notated measures. This leads to a moment of metric crisis in the development section when Beethoven fragments the thematic material until the winds and brass play isolated chords in rapid alternation with ones sounded by the strings, and the clarity of four-measure units dissolves.
1.4 Beethoven, Symphony No. 5, I, mm. 6–21
Meter in Post-tonal Music
In music written since 1900, metric structure has become much more varied, not unlike the broadening in pitch organization beyond common-practice tonality. The degree of metric periodicity found in music throughout the eighteenth and nineteenth centuries waned, except in many genres of popular music, where – due, at least in part, to the connection to dance – metric periodicity remains present. In fact, popular genres are distinguished as much by their characteristic beat, or groove, as by features of melodic, harmonic, or formal organization. Often these characteristic elements are recurrent rhythmic patterns or established norms for using particular instruments to articulate meter, as in the rock drum kit.
While some genres of Western popular music, such as progressive rock, moved away from multiple levels of duple (and less frequently triple) meter, it was in the art-music tradition where the most consistent break from metric periodicity occurred. The present chapter cannot survey all of the rhythmic innovations of the past century; rather, it outlines some of the most significant ones and their implications for thinking about rhythm.
Throughout the eighteenth and nineteenth centuries, meter consists of equally spaced beats that are organized in a duple or triple grouping, depending on whether one or two weak beats fall between adjacent strong beats. Except for unmeasured pieces, such as some Baroque keyboard preludes, there are very few exceptions to the principle of equally spaced, or isochronous, beats. The most famous exception is the second movement of Tchaikovsky’s Symphony No. 6 (“Pathétique”), composed in 1893, where instead of a triple-meter scherzo (or waltz) a lively movement in 5/4 meter occurs. Quintuple meter consists of both duple and triple grouping of beats, either consistently (as recurring 2+3 or 3+2), or with variable patterning of the duple and triple groupings. In either case, a larger periodicity results, and the sense of meter remains clearly intact. Very occasional instances of septuple meter can be found before the twentieth century, yet in these instances composers stuck to the convention of notated duple and triple measures. Two examples occur in the music of Brahms: his piano variations on a Hungarian song (Op. 21, No. 2) and the slow movement of his Piano Trio in C Minor, Op. 101; in the former work, a consistent alternation of notated and measures occurs, while in the later one each notated measure is followed by a pair of measures. In the piano variations the folk inspiration of the asymmetrical meter is explicit, but in the piano trio movement the transparent melody-and-accompaniment texture, slow harmonic rhythmic, and simple harmonies invoke folk music (as depicted by nineteenth-century composers).
The folk impetus behind asymmetrical meters remains explicit in much of the music of the early twentieth century, most notably that of Bartók and Stravinsky. While much of Bartók’s music features consistent use of an asymmetrical meter such as 
or 
, some of his works and many of Stravinsky’s present a more trenchant challenge to the sense of meter through the use of rapid changes of notated meter, often referred to as mixed meter (e.g., a succession of four measures with 
, , , and notated meters). Most often, mixed-meter passages maintain a consistent beat or subdivision – usually the eighth note – and the way those beats group into a meter or the subdivisions group into beats changes unpredictably. Frequently, such passages are based around a short melodic cell that recurs in slightly varied forms that render it longer or shorter, and the onset of each of its iterations is generally an important reference point for feeling the temporal organization. Passages with such a high degree of metric irregularity raise several theoretical questions: How much deviation from periodic accentuation can a listener relate to a periodic underlying metric grid? At what point does the notated meter become best conceived as an element of the score that communicates compositional organization and helps performers synchronize with one another but does not have much connection with listener perception? When does a sense of beat and meter dissolve into a tracking of periodic pulses? Music theorists have offered a variety of perspectives on these questions; perhaps most influential is Hasty’s Meter as Rhythm, which has broad applicability even in music with little periodicity due to its continual engagement with local durations and their potential for replication. Hasty’s approach compels the analyst to engage temporally with music, however complex its rhythmic design, as seen in his discussion of music by Anton Webern, Elliott Carter, and Stefan Wolpe.
Besides a greater range of possibilities within the domain of rhythm, art music of the past century has also seen changing relationships between rhythm and other musical parameters. Returning once again to Stravinsky, I would point out that passages with mixed meter and additive rhythmic construction are not his only rhythmic innovations. Equally new are passages built upon three or more independent rhythmic layers, each repetitive, sometimes composed of an exactly repeating ostinato and sometimes an irregularly recurring figure. A clear example is the first of Stravinsky’s Three Pieces for String Quartet where the cello and viola have an ostinato that repeats after seven quarter notes, violin I has an ostinato that repeats after twenty-three quarter notes, and violin II has an irregularly recurring four-note interjection. Similar layered textures occur in Stravinsky’s Rite of Spring, composed at nearly the same time, often building to a thick texture involving the entire orchestra. In such passages, one layer is often sufficiently prominent to exert its metric identity on the texture as a whole, but the distinction between the rhythmic profile of individual lines and the effect of the overall musical texture begins to breakdown. This permeability between the parameters of rhythm and texture became of considerable interest to composers in the middle of the twentieth century, such as in the ensemble and orchestral works of György Ligeti in the 1960s and 1970s.
In eighteenth- and nineteenth-century music, rhythmic-metric design and pitch structure are closely intertwined but have different organizational principles. Composers of the twentieth century experimented with importing techniques familiar from the domain of pitch into the realm of rhythm, such as mid-century approaches known as integral, or multi-parametric, serialism. The transformations of transposition, retrograde, inversion, and retrograde inversion applied to twelve-tone pitch rows by Schoenberg were adapted to rhythm, albeit in different ways, by composers including Pierre Boulez, Karlheinz Stockhausen, and Milton Babbitt.
Meter and Meaning
Music exists in time, and rhythm is therefore an inherent property, however it is organized and perceived. Rhythm also plays an important role in the communication of expressive meaning in a wide range of music. For instance, fast rhythms might convey excitement or agitation, a rhythmic pattern might reflect some aspect of the lyrics in a texted work, or a rhythmic figure might reference a musical topic. Or rhythm might produce a visceral response such as when the bass groove re-enters at a beat drop in electronic dance music. In closing, I will explore a few more abstract ways that rhythmic design can create meaning.
In my research on the music of Brahms, I have observed several instances where thematic material undergoes rhythmic transformation during the course of a movement or work, typically leading from a less stable initial state to a more stable one.13 This might involve a theme whose metric or hypermetric structure is initially unclear or incorporates metrically dissonant elements and that later recurs in a more stable or metrically consonant version. This type of large-scale thematic process is not unique to Brahms’s music, although it occurs with greater frequency than in the music of many other composers. Moreover, I have suggested that large-scale changes in metric or hypermetric structure can have significant meaning even when they occur in the absence of shared thematic content.14 Similarly, through his use of “metrical maps,” Krebs tracks changes in the types of metric dissonances in pieces, and has coined terms to reflect intensification and de-intensification (e.g., tightening and loosening; surfacing and submerging).15 These global processes, although less celebrated than tonal procedures such as modulation, can shape the overall expressive impact of a work. In the music of the past century, and especially as composers have written more about their own practices, certain rhythmic techniques have been developed for particular expressive purposes, such as Messiaen’s deployment of repeating rhythms and symmetrical rhythms to project qualities of timelessness and contemplation. The following chapters offer perspectives on the possibilities for rhythm to convey meaning in addition to its role as a structural component of musical design.
Introduction
Music is an essentially temporal experience, and the temporal structures by which music unfolds are critical to listeners’ aesthetic, emotional, and behavioral responses. Music is perceived at multiple related timescales, from notes to measures to phrases. In our usage, rhythm refers to the absolute timing of individual notes or sounds, beat refers to the perceived regular pulse that listeners tend to feel and synchronize their movements with, and meter is the repeating cycle of beats, often a pattern of variable salience (composed of stronger and weaker beats). The beat tends to be steady or theoretically isochronous (evenly spaced), although human performance of music inevitably adds temporal variability, via both musical intention (e.g., rubato, expressively stretching and compressing the beat rate) and natural performance dynamics (e.g., due to the limits of temporal precision of human movements). Importantly, beat and meter perception can differ between listeners, relating to factors such as musical context, expertise, cultural experience, or cognitive processes such as attention.
In this chapter we discuss perceptual, cognitive, and neural aspects of musical rhythm: the relationships between rhythmic stimuli and beat and meter perception, the influence of a listener’s attention and experience, and the interesting correspondences between musical rhythm and movement. We also discuss the instantiation of musical rhythm in the brains of listeners, and what we may learn from rhythm perception across non-human species.
Perception of Rhythm, Beat, and Meter
The perception of beats tends to arise in humans when they hear musical rhythms, usually as one level, termed the tactus, in a hierarchical metric structure.1 Beats arise at specific, regularly spaced positions in a rhythm, and tone onsets “on the beat” are perceived as more salient than onsets of surrounding tones. Once the perception of ongoing beats is established, beats can be perceived even when no tone onset occurs, as well as in silence. Povel and Essens demonstrate that certain temporal grouping structures influence the perceived salience of individual notes in a rhythm, guiding beat and meter perception.2 They show that when notes are isolated – the second in a group of two, or the first or last in groups of three or more – they are perceived as more salient, or subjectively accented. When subjectively accented notes occur at regular intervals, beats are perceived at the rate and cyclic positions that align with the most subjective accents. This model is limited to assessing perception for isolated rhythms out of the musical context, rather than capturing the ongoing and dynamic perception that occurs for real music, but it is an important empirical demonstration of how hearing rhythm leads to perceiving beat and metric structure.
A critical aspect of beat and meter perception is that they are not direct products of a rhythmic stimulus, but are active psychological phenomena, and, as such, they depend on internal processes in the listener’s mind and brain.3 One demonstration of the internal contributions to rhythm perception is that humans tend to perceive an isochronous stream of identical sounds as having alternating strong and weak notes – the “tick tock” phenomenon.4 As a rhythmic stimulus becomes more complex than isochrony (e.g., musical rhythms, which tend to have inter-onset intervals that vary in duration), the subjectivity of perception also becomes more evident and more complex, and the malleability and heterogeneity of perception across listeners becomes evident. That is, despite listening to the same rhythmic stimulus, different listeners may experience different beat and meter perception, in relation to multiple interacting factors, such as their cognitive state during listening (e.g., whether or not they are attending to the rhythm), their familiarity (i.e., cultural experience) with rhythms, and whether or not they have musical training.
The flexible nature of rhythm perception – that perception is not strictly a product of the rhythmic stimulus – has been shown in brain responses of listeners. The “tick tock” perception of a metronomic sequence has been found to relate to neural responses occurring after individual sounds: responses to odd-numbered sounds were stronger than those to even-numbered sounds.5 Another study had listeners impose a march or waltz metric structure on a metronomic sequence by imagining an emphasis on either every second or every third note. The results showed distinct signals in the electroencephalogram (EEG) of listeners corresponding to not only the rate of the metronome but also to the rate of the imagined metric emphasis.6 Other researchers had listeners imagine an emphasis on one of two notes in a repeating rhythm consisting of two notes and a rest, all having the same durational value. Brain responses in listeners increased in strength due to the imagined emphasis.7 These studies show neural activity corresponding to perception that is generated internally, rather than strictly by the stimulus, although they do not indicate how, or by what mechanisms, these internal contributions to perception occur.
Rhythm and Movement
From a biological perspective, perhaps the most notable thing about musical rhythm is that it elicits movement from human listeners. Moving to musical rhythm is one of the most convincingly universal aspects of music. This movement tends to be synchronized to the regularities in the rhythms and is enjoyable, perhaps explaining why humans have been spontaneously synchronizing movements to music since the time of our ancient ancestors.8 In most cultures, music and dance evolved together, and even today, there are cultures that do not have separate words for music and dance.9 Moving to music occurs spontaneously, without training, at a young age. For example, infants make a greater number of rhythmic movements when they hear music, or even steady drumbeats, although these movements are not synchronized to the beat.10 Synchronization ability emerges in some children by age three or four, and later for many other children.11
Musical Features That Influence Movement
In the scientific study of music perception, the term groove has been used to refer to the quality of music that makes an individual listener want to move.12 Music that is rated as high in groove elicits more spontaneous movements than music that is low in groove, even when listeners are instructed to remain still.13 Some acoustic and musical factors are known to influence groove: a strong repetitive beat and a high density of sound events between beats are associated with more groove.14 Other factors that influence groove include emotional responses to the music, preferred tempo, enjoyment, and familiarity.15 Groove and enjoyment ratings tend to be correlated.16 Groove has also been related to neural activity: rhythms that were rated as having more groove tended to elicit greater neural entrainment (see below), although this relationship was only observed for rhythms that were human-performed rather than computer-synthesized.17
The way individuals move to music reflects their perception of its hierarchical metric structure.18 Vertical torso movements and side-to-side arm movements tend to occur at the beat rate, whereas other movements, such as shoulder rotation and side-to-side body sway, occur at slower metric rates (every two or four beats).19 The energy to move a body part depends on size and distance from the center of mass; thus, it is natural to select slower metric levels for body parts that require more energy.20
Music also affects non-dancing movements such as walking.21 For example, even when walking in synchrony to music that is at the same tempo, walking speed fluctuates, influenced by other musical features such as loudness or pitch patterns.22 Perceived groove, and to a lesser extent, familiarity, also increases walking speed.23 Although spontaneous synchronization to music can occur during certain activities, such as running24 or dancing, it does not necessarily occur during walking. For example, when walking to music on a treadmill, only participants who were explicitly instructed to synchronize actually did so.25 Similarly, another study found that participants walking to music outside did not spontaneously synchronize.26
Movement and Its Relationship to Rhythm Perception
Moving to rhythm can alter how that rhythm is perceived. In one influential study, two groups of seven-month-old infants were bounced to the same rhythm, but one group was bounced every second beat, and the other group was bounced every third beat.27 After the bouncing, infants could choose to listen to different versions of the rhythm by triggering different speakers with their gaze: rhythms listened to longer were considered preferred. Infants preferred rhythm versions that were accented consistently with how they had been bounced: infants bounced every two beats preferred rhythms with accents every two beats, and infants bounced every three beats preferred rhythms accented every three beats. In another study, when adults bent at the knee to every second or every third beat while hearing the same ambiguous unaccented rhythm, they later reported that an accented rhythm that matched their bounce rate was more familiar.28 Thus, the perception of metric structure is altered by how our bodies have moved to that rhythm.
Simply tapping along with a beat in rhythm can influence how quickly and accurately the beat is perceived. Tapping along at the beginning is most helpful for rhythms in which the beat is not obvious.29 The tapping-induced improvement may result from greater attention to the beat caused by tapping, or from the extra feedback about the beat timing provided by the taps. Tapping along with the beat can improve perception even after tapping has stopped. In one study, participants tapped with an isochronous sequence, and then judged whether a final tone was “in time” with the previous part of the sequence or not.30 Tapping to the initial sequence led to better accuracy than did listening alone, even when tapping stopped before the final tone. Tapping aided percussionists more than musical novices when making the judgments.31 Thus, overall, tapping aids beat perception and timing accuracy, but musical experts have greater tapping-induced timing benefits.
Interestingly, some rhythmic features of music overlap with rhythmic features of movement. For example, when music slows down, the deceleration dynamics are similar to those observed when runners slow to a stop.32 In addition, one of the most popular tempos in a database of contemporary Western music is very similar to the preferred walking rate of most humans: around 2 hertz (Hz), or 120 beats per minute.33
Musical Rhythm in the Brain
Neuroscientific studies of musical rhythm aim to understand the links between the human experience of musical rhythm and the functions and activity of the brain. While neural correlates of rhythm have led to fascinating findings, it is notable that we lack a truly robust and reliable brain marker of beat perception – a neural signal that, when detected, indicates the listener is perceiving a beat. Rather than a measure of brain activity that can tell us exactly what is happening in the mind of the listener, two of the most prominent branches of research in the neuroscience of rhythm inform us about both how musical rhythm exerts its effects on human listeners, and about fundamental mechanisms in brain function. These are the involvement of the brain’s motor system and of neural oscillations.
Musical Rhythm and the Brain’s Motor System
Perhaps unsurprisingly, given the strong behavioral relationships between music and movement, there is strong evidence that rhythm and beat perception cause activity in the brain’s motor system. Motor areas, including premotor cortex and the cerebellum, respond during passive listening to music, according to a recent analysis of forty-two functional magnetic resonance imaging (fMRI) studies.34 As discussed below, rhythmic aspects of the music, rather than melodic or timbral aspects, appear to drive these motor responses.
Links between music and movement may arise in part through very basic brain mechanisms. For example, simply hearing a tone can change the excitability (how likely a neuron is to fire) of motor neurons in the spine.35 Musical rhythms also change the excitability of the motor system. One study found greater motor system excitability for rhythms with a strong beat than a weak beat,36 and another study found greater motor excitability for high groove music compared to low groove music, although only in musicians, not in non-musicians.37
Higher-level motor areas also respond to rhythm. Hearing musical rhythm, even when no movement is made, activates brain areas that control movement, including the supplementary motor area, premotor cortex, cerebellum, and basal ganglia.38 Certain motor areas, such as the supplementary motor area and basal ganglia, appear to respond more to regular rhythms that give rise to a clear sense of the beat compared to rhythms that do not.39 Other motor areas, such as the cerebellum, respond more to irregular rhythms that do not induce a beat.40 Research with different neurological patient populations supports this dissociation: basal ganglia function is compromised in patients with Parkinson’s disease, and they also have a deficit in detecting changes in beat-based rhythms, but not non-beat-based rhythms.41 In contrast, patients with cerebellar degeneration have deficits in tasks using non-beat-based rhythms, but not beat-based rhythms.42 Finally, consistent with a role in beat perception, basal ganglia activity does not correlate with the speed of the beat that is perceived,43 and instead is most active for sequences with rates around 500–700 milliseconds (ms),44 the range in which beat perception is also maximal.45 Therefore, the basal ganglia are most responsive to regularity at the rate that best induces a sense of the beat. Overall, these studies support the idea that different motor areas underlie perception of rhythms, and especially rhythms that elicit beat perception.
An important part of understanding the neural mechanisms of rhythm and beat perception is not just which brain areas are active, but how these different brain areas communicate with each other. Communication can be indexed by “functional connectivity,” which measures correlations in activity between two brain areas over time. When correlations between two brain areas increase, communication is thought to be greater. Connectivity between brain areas changes based on the type of rhythm being listened to. When listening to beat-based rhythms, compared to non-beat-based rhythms, the connectivity increases between the basal ganglia and cortical motor areas (supplementary motor cortex, premotor cortex), as well as between the basal ganglia and auditory cortical areas.46 Thus, rhythm and beat perception increase communication within motor networks, and between auditory and motor networks. This may be because we automatically try to link our auditory perception of the rhythm with a potential motor response, even when we have no intention of actually moving.47
Thus, auditory and motor areas are important to perceiving a rhythm and feeling the beat. Feeling the beat (compared to hearing rhythms without a beat) increases activity in a subset of these motor areas, including the basal ganglia and supplementary motor area. Motor and auditory areas also exhibit greater functional connectivity during perception of the beat. A potential mechanism for this connectivity may be through oscillatory responses, which are not directly measurable with fMRI, but can be measured with EEG or magnetoencephalography (MEG).
Musical Rhythm and Neural Oscillations
Neural interactions between auditory and motor areas during beat perception may be accomplished by oscillations. Neural oscillations are fluctuations in the excitability of neural populations, and are a fundamental brain mechanism that allows neural activity within and across brain regions to synchronize, coordinating their processing. Neural oscillations occur at different rates, or frequency bands. Two frequency bands have been associated with rhythm perception: the delta band (1–3 Hz), which spans the rates at which the beat is perceived48 and is associated with temporal prediction,49 and the beta band (15–30 Hz), which is associated with the motor system50 and also with temporal prediction.51 Delta- and beta-band neural oscillations appear to support important functions during rhythm perception; moreover, the two bands appear to interact during perception of rhythms, possibly in service of temporal predictions and/or communication between auditory and motor systems.52
Neural oscillations synchronize, or entrain, with auditory rhythms. For example, beat-rate oscillations (which are usually in the delta band) appear to entrain to the perceived beat during rhythm perception.53 Entrainment of delta-band oscillations in musicians have also been associated with groove in human-performed (but not computer-synthesized) musical rhythms54 and with cross-cultural differences during musical rhythm perception.55 Musicians have greater beta-band entrainment during music perception than do non-musicians.56 Entrainment of neural oscillations to the beat causes greater neural responsiveness for stimuli on the beat than off the beat, which may be the mechanism underlying improved perception of on-beat compared to off-beat sounds.57
Oscillations in the beta band are associated with motor functions, and modulations of the strength of beta oscillations have also been associated with beat perception.58 For example, an above-mentioned study measured oscillatory neural responses evoked by a repeating rhythmic pattern consisting of two tones followed by a rest.59 While undergoing MEG to measure neural oscillatory responses, listeners imposed a mental accent on either the first or second tone. Beta-band responses were stronger for the tone that was mentally accented, corresponding to the perceived beat, despite both tones being acoustically identical. In isochronous auditory sequences, beta power peaks just prior to the onset of each tone, but not when the sequence timing is random and unpredictable,60 suggesting that beta-band activity may index the expectation of a regular beat. Consistent with the fMRI studies described above, beta power in these studies appears to originate from both auditory and motor brain areas, including premotor cortex, supplementary motor area, and cerebellum.
Other Influences on Rhythm and Beat Perception
Rhythm perception can change with the listener’s cognitive state, depending on, for example, whether or not they are attending to the rhythm, and different listeners can perceive the same rhythm differently, depending on cultural experience or musical training.
Attention
Attention is one cognitive mechanism by which listeners’ internal states contribute to perception of musical rhythms. An overarching theory, Dynamic Attending Theory, posits that rhythm perception is mediated by fluctuations in attention that synchronize with (or entrain to) the metrically salient positions in the rhythm – aligning closely to the theory that beat and meter perception arise from the interactions between neural oscillations.61 Evidence that dynamic attention underlies perception of rhythm comes in the form of greater perceptual sensitivity to events that occur in temporal positions that are strongly predicted by the temporal structure of the preceding sequence, such as “on-beat” tones.62
Attention is also related to the hierarchical aspect of musical rhythm perception: listeners can focus attention on a rhythmic stimulus or can rather perceive a rhythm more passively, and attention can alter perception. Attention seems required to perceive the beat when it is indicated only by temporal structure, particularly for complex rhythms,63 whereas volume changes that mark the beat in a rhythm can induce beat perception without a listener attending.64 One neural study of attention and rhythm perception compared brain responses to individual tones that perturbed either the rhythmic or metric structure of a perceived rhythm. Brain responses occurring approximately 100–150 ms after the perturbation were observed after rhythmic perturbations regardless of whether or not listeners were attending to the rhythm, whereas they occurred for metric perturbations only when listeners were attending to the rhythm.65 This indicates that perceiving metric structure may require more cognitive engagement, enabled by attention, than perceiving the rhythm itself. Another study used a similar method and found that brain responses were sensitive to metric structure only when listeners were attending to the rhythm, but responses were sensitive to the beat regardless of attention.66
Cultural Experience of the Listener
Musical rhythms differ across cultures, as has been widely documented in the field of ethnomusicology. Besides cultural differences in rhythmic structures, ethnomusicologists have also documented cultural differences in the perception of rhythm, and recent attention to cultural variability from a cognitive science perspective has empirically validated the influence of culture on rhythm perception. Cultural differences in rhythm perception have been shown in children as young as four months old. One study showed that American infants prefer rhythms with a regular meter to those with an irregular meter, while Turkish infants did not have the same bias, presumably related to their exposure to the irregular meters found in Turkish music.67 Another study found that Japanese and American participants differed in their perception of how sequences of alternating short and long tones were grouped. American listeners had a strong tendency to group the pattern as “short–long,” while Japanese listeners did not have a tendency for one grouping over the other, and were much more likely than American listeners to identify the sequence as “long–short.”68 Comparing two cultures directly, another study found that North American and East African listeners had greater accuracy in tapping the beat to rhythms if the rhythms were based on culturally familiar musical rhythms, and that East African participants tended to use a greater range of metric levels as the tapped beat compared to North Americans.69 Moreover, these two cultural groups were found to have different patterns of neural entrainment to rhythms – East Africans tended to have greater entrainment to the fastest metric beat rate and North Americans to the slowest.70
A recent line of research has used a novel, iterative rhythm reproduction paradigm to demonstrate that cultures vary in the underlying perceptual biases that listeners bring to rhythm perception. Listeners hear and then synchronize their tapping with repeating, rhythmic, three-interval sequences. Their taps are converted to a sound sequence that they hear and synchronize their tapping to again, and this process is repeated five times. Over time, the participants’ tapping stabilizes, with fairly accurate synchronization, and the intervals that are produced at this stage are thought to reveal perceptual biases of the listener – the time intervals that are most expected, familiar, and easy to tap. This paradigm has demonstrated cultural differences, for example that American and native Amazonian (Tsimané) listeners differ in their rhythm perception biases.71 Some stable patterns were the same for Westerners and Tsimané (e.g., 1:1:1), but there were other patterns stable for Tsimané and not Westerners (e.g., 1:2:2), and for Westerners but not Tsimané (3:3:2).
Musical Training of the Listener
Unsurprisingly, musical training is associated with better ability to perceive and produce rhythms, and to synchronize to the beat of rhythms or rhythms themselves.72 However, neuroimaging studies show mixed findings with respect to brain activity related to musical training and rhythm perception. Studies have found that while performing a rhythm discrimination task, musicians have greater activity in motor regions of the brain compared to nonmusicians, despite not having superior performance on the discrimination task,73 as well as greater communication between auditory and motor brain regions when listening to rhythms during a rating task.74 However, another study found that active motor regions during a rhythm synchronization task did not differ in their degree of activation between musicians and nonmusicians but, rather, other frontal brain regions associated with more general cognitive function were more active for musicians.75 A different study found that some motor regions are less active in people with more musical training.76 A series of studies on differences in brain structure between early- and late-trained musicians (those beginning training before and after seven years of age, respectively) showed that early-trained musicians performed better on a rhythmic synchronization task,77 had greater connectivity in the corpus callosum – the primary white matter tract connecting right and left hemispheres78 – and greater gray matter volume in the premotor cortex.79
Rhythm Perception in Non-human Species
One topic of recent interest is whether non-human animals have beat perception and synchronization abilities.80 This interest was spurred by Snowball, a dancing cockatiel that bobs its head to certain music.81 Snowball, however, only synchronizes for brief “bouts,” and only when the tempo is close to its preferred rate. Moreover, visual cues (e.g., from Snowball’s handler) enhance performance. In terms of other species, there is some evidence that budgerigars, bonobos, chimpanzees, and elephants may be able to synchronize to simple stimuli, such as isochronous metronome tones.82 The most convincing non-human example of synchronization comes from a head-bobbing California sea lion named Ronan. Ronan synchronizes head-bobs not only with isochronous metronome tones, but also to music, even music she has never heard before.83 Interestingly, Ronan can re-synchronize quickly when the rhythm contains an error, such as a sudden timeshift to an earlier or later phase of the beat, and the timecourse of her correction for the error looks similar to humans.84
Evolutionarily, non-human primates are closer to humans than sea lions or songbirds. However, they don’t appear to spontaneously synchronize to auditory or musical sequences, although other timing abilities are similar to humans. For example, when reproducing single time intervals, rhesus macaques and humans are equally accurate. However, humans are more accurate when synchronizing with metronome sequences and also when continuing movements at the same rate after the metronome tones stop.85 Moreover, during synchronization, macaques often tap just after tone onset, whereas humans tend to tap with, or even slightly ahead of, metronome tones. Macaques are not entirely insensitive to auditory regularities, however. For example, macaques showed behavioral evidence of awareness (changes of gaze and facial expressions) when timing was altered in isochronous, but not irregular sequences.86 Similarly, unexpected tone omissions from isochronous sequences elicited mismatch negativity (MMN) brain responses in EEG, similar to humans. However, humans also showed larger MMN responses when the omissions were “on” rather than “off” the beat, whereas the macaques’ responses did not show this distinction, suggesting they were not perceiving the beat. Overall, therefore, monkeys appear to be able to perceive regularity, particularly in simple isochronous sequences, but are less able to perceive beats in more complex rhythms, and less accurate when synchronizing movements.87
There are currently two main theories of the underlying neural requirements for beat perception across species. The vocal learning hypothesis suggests that beat perception occurs in species that are vocal learners, which alter their vocalizations in response to environmental input. Vocal learning is mediated by neural connections between auditory input and vocal motor output centers, and this circuitry is proposed to underlie the capacity for beat perception.88 Parrots are vocal learners,89 as are humans, bats, cetaceans, seals, elephants, songbirds, and hummingbirds. The second theory suggests that the degree of neural structural connection between auditory and motor areas in a species correlates with rhythmic and beat perception abilities.90 Rhesus macaques have limited auditory-motor connections and have basic timing skills such as producing single time intervals,91 whereas chimpanzees have more auditory-motor connections and have shown some capacity for spontaneous synchronization.92 However, neither of the theories explains the existence of beat perception in animals that are neither primates nor vocal learners, such as Ronan the sea lion.93
Conclusion
Cognitive and neuroscientific research informs us of fundamental aspects about the perception of musical rhythm. Musical rhythm’s unique characteristics – that it elicits perception of a steady beat and hierarchical metric structure, that it elicits movement and pleasure from human listeners, that it is both universal and culturally specific, and that it is essentially uniquely human – relate to the cognitive and neural processing of these particular sound sequences. Perceiving rhythmic sounds in a musical way (e.g., beat and meter perception) is an active process, conducted in the minds and brains of listeners, dependent on attention, memory, a neural system that also controls our movements, and neural activity that oscillates in time with the regularities we hear, feel, and move to. Future research, involving more sophisticated neuroimaging methods, or incorporating genetic techniques, holds promise for furthering our understanding of humans’ special relationship with rhythm.
