6. Time and rhythm

Music unfolds in time. Rhythm and metre depend on duration, order, and recurrence. They give us the structures we use to predict, move, and coordinate. This week, we begin with broad ideas of time and rhythm, then turn to metre, pulse, and subdivisions. From there we look at microrhythmic nuance and the phenomenon of groove.

This chapter runs across the four levels of description more visibly than most. An onset is a physical event you can find in a waveform; a perceptual centre is where the ear puts it; a backbeat that feels laid-back rather than late is interpretation. Much of the research below exists precisely to measure the gaps between the three.

Musical time is more than clock measurement. It is shaped by perception, culture, and performance practice. Rhythms and metres may be notated on the page, but their feel depends on how musicians and listeners interpret and embody them.

Time¶

Time in music refers to the organisation of sounds and silences in a temporal framework. It is the foundation on which rhythm, beat, and metre are built.

Onset timing¶

When we speak of the “timing” of instruments in performance, we usually mean onset timing more specifically. When analysing the sound signals of rhythms (e.g., waveform analysis), the physical onset is the moment a sound “begins”. It is usually defined as the point where the signal rises above a certain amplitude threshold (zero dB or the noise-floor baseline), or where it starts to rise with a slope above some pre-set value. Various onset-detection algorithms exist, and each can differ slightly, though the principle stays the same.

Besides the physical onset, sound events have other timing-related features:

• Perceptual onset: the earliest a sound is perceived to begin
• Perceptual attack or centre: the “perceived moment of rhythmic placement”
• Energy peak: the highest peak of energy or intensity
• Attack time (or duration): time from physical onset to energy peak
• Temporal centroid: the temporal “balancing point” of the sound

Image source: adapted from Nymoen et al. (2017).

Perceptual centre and attack time¶

When listening to rhythms, the “moment of occurrence” of a sound, the point we use to place it in time, often does not coincide with its physical onset. This percept is usually called the perceptual centre (P-centre) or perceived attack time (PAT): a subjective reference point that typically falls somewhere after the physical onset and before the peak of the sound’s energy. As a result, sequences that are physically synchronous or physically isochronous (evenly spaced in time) may be heard as misaligned or uneven.

Studies show that certain sound parameters affect where P-centres are heard. Attack duration or time (from onset to peak) is the strongest factor: faster attacks yield earlier P-centres, and slower attacks yield later ones. Total duration (from onset to offset) has a weaker but similar influence, with shorter sounds shifting P-centres earlier and longer sounds shifting them later.

Image Source: Guilherme Schmidt Camara 2025

Take two guitar chords, one played by slowly arpeggiating the strings (“swept”) and one played by stroking all the strings in quick succession (“swift”). Although both come from the same instrument, the swept stroke tends to sound as if it occurs slightly later relative to its physical onset, while the swift stroke has a P-centre much closer to its onset timing.

Image source: adapted from Câmara et al. (2020).

Taken together, this means that aligning tracks by physical onsets does not always guarantee perceptual synchrony in a rhythmic sequence. When two identical sounds are physically synchronous (physical onsets evenly spaced) and their P-centres align closely with their physical onsets, they tend to sound perceptually isochronous (example A). But when different sounds with different attack-duration profiles are physically isochronous and their P-centres do not align closely with their physical onsets, they tend to sound perceptually non-isochronous (example B). The same applies to sounds that occur simultaneously in a vertical fashion: if their P-centres are similar, they sound more synchronous; if their P-centres are misaligned, more asynchronous.

Image source: adapted from Villing (2010). Note: IPI = Inter-P-Centre-Interval, IOI = Inter-Onset-Interval.

Rhythm¶

A rhythm can be thought of as a pattern of durations. When a series of sound events occurs, the intervals between them form recognisable shapes in time. In everyday use, we call anything regular “rhythmic”, but in music the term usually refers more specifically to a pattern of durations formed by the intervals between the perceived time points of notes.

Rhythms can be periodic (based on cycles, such as a march rhythm) or aperiodic (irregular, as in speech or improvisation). Both can be meaningful: a drum groove in 4/4 and a free jazz solo each have rhythm, but in different senses.

Rhythms also carry cultural meaning. A clave rhythm in Afro-Cuban music is more than a sequence of durations; it is a structural reference for musicians and dancers. In the same way, speech rhythms shape the flow of rap and spoken-word performance.

Metre¶

Metre provides a hierarchical framework for the organisation of rhythm. It is often described as a nested system of pulses at several periodicities, from fast subdivisions to slower bar lengths:

• Beat (pulse/tactus): the fundamental beat we tend to synchronise or entrain to
• Division levels: subdivisions of the beat, such as 8ths, 16ths, and 32nds
• Multiple levels: slower groupings of the beat, such as half-notes and bar-lengths

Image Source: Wikipedia - Metre (music)

Pulse / beat¶

The beat (also called the tactus or pulse) is the basic time unit of a metre. A pulse can also describe an ongoing stream of beats; one can speak of 8th-note pulses just as much as quarter-note pulses. Either way, the beat level is what we naturally tap our feet to, giving stability and predictability to performers and listeners alike.

Research suggests that we comfortably perceive and move to beats when the time between them (the inter-onset interval, IOI) lies between about 500-700 ms (120-86 BPM). Pulse is thus closely tied to our sensorimotor system: we tend to move along with it. Faster events are heard as subdivisions, and slower ones are grouped into larger spans.

In performance, the pulse is not always marked by sound. Even when silent, it can be inferred as a virtual reference that organises events. Musicians often “feel” the pulse even when they play around it.

Subdivision¶

Subdivisions divide each beat into smaller units. We tend to hear them as subdivisions when their IOI duration is between about 100 and 500 milliseconds. Subdivisions add detail and density, and they often act as stylistic markers (e.g., straight eighths in rock, sixteenths in funk, triplet-based 12/8 in blues).

Metric accent¶

Western theory traditionally frames metre as a pattern of strong and weak accented beats (e.g., ONE-two-THREE-four in 4/4), with accents thought to align where metrical levels overlap. In practice, this is not always how music is felt or performed. Many groove-based styles emphasise off-beat positions. In popular genres such as rock, soul, and R&B, the snare backbeats on 2 and 4 can feel more salient than beat 1. In reggae, the offbeats on the “ands” may dominate more than the downbeats. Metrical accents, then, are not fixed; practice and cultural convention can redefine them.

Asymmetric metre¶

Not all metres divide evenly into twos (binary) and threes (tertiary). Asymmetric metres (such as 5/8 or 7/8) have beats of different durations, organised into uneven groupings of equal subdivisions, like 3+2 or 2+2+3. They are common in Balkan, Middle Eastern, and contemporary art-music traditions.

Performers often feel such metres as cycles of unequal steps rather than a uniform grid. The asymmetry can produce a sense of lilt or forward drive distinct from even metres.

The inter-onset-interval (IOI), or time duration, between the main beats may also be isochronous (equal) or non-isochronous (unequal). In many popular groove-based styles, instruments tend to create a highly isochronous beat structure. In Scandinavian folk styles such as telespringar, the main beats are not always equal in duration but can vary (e.g., long-medium-short), giving the music its signature lilting feel.

A closer look: when beats refuse to be equal¶

Most rhythm research, and most music software, quietly assumes that the beats of a metre are isochronous. For rock, pop, and EDM the assumption mostly holds. Telespringar, the tradition behind the fiddle excerpt above, is a well-documented counterexample, and it is worth setting out as an explicit case.

• The claim under test is that metre rests on equal beats, so that any unevenness is expressive deviation from an underlying regular grid.
• The evidence says otherwise for this tradition. Measurements of telespringar performances show bars divided into stable long–medium–short beats, in proportions that remain consistent across tunes and performers Haugen, 2016.
• The method combined audio analysis with motion capture of a fiddler and a dancing couple. The fiddler’s foot stamping and the dancers’ vertical motion followed the same non-isochronous pattern, suggesting a shared bodily reference structure rather than sloppy timing.
• The limits are a small number of performers, one regional style, and proportions that vary somewhat between players and districts. The finding does not overturn metre theory; it shows that the reference grid itself can be uneven and learned.

If you tapped along to the springar excerpt above, you have already felt the point in your own body: entrainment works, but the thing you entrain to is not a metronome.

Analysing the timing of one instrument inside a full mix is difficult, because the onsets of drums, bass, and vocals overlap. Audio source separation addresses this by splitting a recording into stems, separate tracks for each instrument or voice, and online tools now do this well enough to support rhythm analysis. How these tools work, and their strengths and limitations, is covered in machine listening.

Microrhythm¶

Microrhythm refers to the fine-scale timing and shaping of events around our subjective reference structures (beat, subdivision). Unlike beat- and subdivision-level rhythms, microrhythm concerns variations in timing at a scale below 100 ms. The ethnomusicologist Charles Keil called such small timing and tuning discrepancies between players participatory discrepancies, arguing that they are what give music its characteristic feel.

In terms of timing, we can speak of two related but different forms of microrhythm: asynchrony and non-isochrony. Asynchrony refers to the way musicians can play in a more synchronised (“on-beat”) or asynchronous way (early/“pushed” or late/“laid-back”) relative to one another. Non-isochrony relates to how they might skew the durational ratio of metrical subdivision levels (e.g., 8th or 16th notes) to varying degrees, from isochronous (“straight”) to non-isochronous (“swung”).

Asynchrony and non-isochrony both denote a departure from synchrony and isochrony in rhythmic contexts (Figure 1, example 1), but along different dimensions: asynchrony refers to vertical non-alignment between simultaneously sounding events, whereas non-isochrony refers to unequal horizontal timing relationships between successive events.

Source: Câmara et al. (2025), Figure 1.

Researchers put numbers on both. Asynchrony is measured as onset displacement (d): how many milliseconds early (negative) or late (positive) an onset falls relative to a timing reference grid. Swing is measured either as that same displacement at off-beat subdivisions, or as a swing ratio: how long the first note of a pair is compared with the second. A straight pair gives 1:1; a triplet-based “long–short” pair gives 2:1.

Microrhythm can encompass both expressive moment-to-moment nuance and systematic patterns that recur across a piece or style. In many performance traditions, those systematic patterns are the norm, rather than “deviations” from an ideal of perfect metronomic or isochronous timing.

Beat delay / anticipation¶

Musicians sometimes play behind or ahead of the beat in a systematic way, whether consciously or not. In rock and soul styles, snare strokes on beats 2 and 4 of a 4/4 metre are often said to be delayed, and in funk, downbeats are said to regularly anticipate “One”. What counts as “late” or “early” always depends on a reference in the given context, whether kick, snare, or the overall grid.

Different degrees of beat delay/anticipation are said to convey different feels. Delayed (late) backbeats in groove styles are often described as “laid-back”: a relaxed feel when only slightly delayed, but a “heavy” or “dragging” feel if delayed too much. Anticipated (early) beats are described as “on-top/pushed”, which at lower magnitudes can sound “snappy” and “driving”, but too much may sound “nervous” or “rushing”. Many scholars and musicians have developed their own heuristics for the right degree of asynchrony in a given style. One example is MIDI-based electronic music producer Michael Stewart’s (in Prögler 1995) “feel spectrum”, which sets out his prescriptions for an assortment of rhythmic feels at 130 beats per minute, for use with synthesisers and drum machines:

Image source: adapted from Stewart, in Prögler (1995).

We can look at an example where Bootsy Collins (bassist from the James Brown Band and Parliament-Funkadelic) plays along to a highly isochronous drum machine groove, which serves as a stable time reference to measure bass onset asynchronies against (listen to Audio Ex. 3, where the 2-bar bass and drum riff is looped 3 times). An onset timing analysis reveals that Bootsy systematically plays slightly behind the beat, at around +15 ms on average (dashed white line in plot), what Stewart might call “in the pocket” playing. He does so in the same systematic way in both bars (red and blue lines).

Image Source: Guilherme Schmidt Camara 2025

Swing¶

Subdivision notes need not be isochronous (equal), as they are in a straight-8ths hi-hat pattern in rock. Swing, a form of non-isochrony (non-equal durations), describes systematic long–short patterns at the subdivision level.

In jazz, musicians typically do not swing at a perfectly mechanical “triplet swing” ratio of 2:1. Instead, swing ratios in performance can range from close to 1:1 (straight) all the way up to 3:1 (dotted swing) and beyond, depending on tempo, sub-genre, personal style, and other factors. In funk and hip-hop, by contrast, sixteenth notes tend to be swung more subtly (e.g., 1.2:1) unless played in explicit funk-shuffle styles (closer to 2:1, triplet).

Different swing ratios are thought to impart different degrees of “motional energy” to rhythms. Rhythms with lower swing ratios (closer to 1:1) are described as more “continuous”, “driving”, or “propulsive”, whereas higher swing ratios (up to 2:1 and beyond) tend to give “bounce” or “choppiness”, often accentuating the downbeats and on-beats of the metre.

Looking at Bootsy Collins’ performance again, instead of measuring how early or late each bass onset is, we can calculate the swing ratio between all pairs of odd- and even-numbered subdivisions. The bass swings rather significantly (mean: 1.4) over the two bars, sometimes more and sometimes less, arguably supplying the groove with a certain “bounce”. Again, the swing pattern is applied systematically across both bars. (Audio Ex. 6 gives the bass pattern isolated, without drum machine, looped 3 times).

Image Source: Guilherme Schmidt Camara 2025

Demo: hearing swing in a click track¶

Swing delays the second of each pair of eighth notes. With straight eighths the offbeat sits exactly halfway between beats; with a 2:1 swing it lands two-thirds of the way through. The clicks below let you hear the difference at the same tempo.

Perceptual thresholds of microrhythm¶

Recall from last week that the just-noticeable difference (JND) is the smallest change a listener can reliably detect. Microrhythm has its own JNDs, and they are surprisingly small: differences of a few tens of milliseconds are enough to change how a groove feels. How small depends on the sounds involved (sharp drum attacks are easier to judge than blended sustained tones), on tempo and note density, and on musical training.

For more on JNDs of microrhythm in music, see Câmara et al., 2025.

Entrainment¶

Entrainment refers to the synchronisation of a person’s movements or internal rhythms with an external rhythm, such as a musical beat. This is the course’s main treatment of the idea, so it is worth stating in its general form before we narrow it to music.

The underlying physics is that of coupled oscillators: two systems that influence each other, however weakly, tend to fall into a stable phase or frequency relationship rather than drift independently. Nothing about that is specific to music, or even to biology. What makes it useful here is that a great many things about a person oscillate, including attention, limb movement, breathing, heart rate, and populations of neurons, and a musical pulse is a periodic signal that all of them can couple to.

Entrainment therefore returns twice more in this course, each time with a different oscillator on the receiving end: as coordination between people in the body, and as measurable alignment of breathing and cardiac rhythm in physiology. The mechanism below is the same one in each case.

Metre can be thought of as a musically specific form of entrainment: we synchronise our attention (and often our movements) to periodicities in the sound. This sets up periodic peaks of attention, expectancy moments where events are most salient, and these peaks are arranged in hierarchies (subdivision, tactus/beat, bar, larger cycles). In this view, metre is less a printed grid than a behaviour of attention that locks to temporal invariants and shapes how we group notes and hear accents.

Dynamic attending theory tries to explain where metrical accent “comes from” in cognitive terms. Not all accents are metrical: phenomenal accents (loudness, timbre, leaps) and structural accents (harmonic/melodic goals) can occur anywhere. Metrical accent, however, is said to arise when a rhythmic event lands inside an attentional peak; it is marked by consciousness, not just made louder. A rock backbeat (dynamic emphasis on 2 and 4) thus need not move the metrical accent away from 1 and 3 for enculturated listeners. The listener’s entrainment keeps the metre while reading the backbeat as an idiomatic reinforcement.

Think of metrical accent strength as the height and narrowness of an attention peak. Stronger regularity and clearer cueing tighten the window for “on-time”, while looser surfaces widen it without losing the beat.

You can measure your own entrainment with the Tap along app, which scores the mean and spread of your tap timing against a click at any tempo. It complements the Maître Gnome exercises earlier in this chapter.

Interpersonal synchrony and joint action¶

Much of this chapter focuses on one person locking attention and movement to an external pulse. Making music together adds coordination between people: ensembles, choirs, and dance partners stabilise a shared tempo, align their movements, and predict each other’s timing. The mechanism is the entrainment described above, now with people coupling to each other as well as to the music. The empirical side of such joint action, from ensemble playing and dance to claims about social bonding, is taken up in the body.

Groove¶

Groove can be understood in many ways. Here we focus on groove as “pattern” and as “performance approach”, with an eye on time and rhythm.

As a pattern, a groove can be defined simply as a persistently repeated rhythm, often spanning one or two bars, whose events establish a clear beat and a characteristic subdivision layer. The beat may be externalised (e.g., a kick/snare backbeat in 4/4) or implied by cyclic “isoperiodic” figures that recur predictably. Style identity often hinges on the basic unit (the smallest repeating chunk) and its density referent (the shortest subdivision practically used).

As performance, a groove is the coordinated realisation of that basic unit across parts (e.g., drums, bass, guitar/keys, vocals). Players distribute roles: some layers reinforce the beat (e.g., kicks on beats 1 and 3, snare on 2 and 4), while others supply tension by playing on off-beat subdivisions (e.g., bass accentuating the “2-and”). Grooves often balance stability (an easily entrainable pulse) with off-beat devices that add interest and complexity, such as syncopation and cross-/counter-rhythm (see below).

Syncopation¶

Syncopation is often described as a local contradiction of a metrical expectation: a note on a weak-position accent, a tie across a strong beat, or the omission of a strong beat followed by sound on a weak one. In 4/4, common cases include stressing the “and” of 2 or 4, tying into 1, or placing a salient event on 3-and while 3 itself is silent. Because the beat is usually firmly established in groove styles, such contradictions tend to add tension without destabilising the metre.

Syncopation can also reinforce metre. When an expected strong beat is left unarticulated, listeners feel the “missing” beat more vividly through anticipation, and the following weak-beat event then locks back to the underlying cycle. Backbeat-heavy styles show this: dynamic accents on 2 and 4 do not move the downbeat to 2; instead, they clarify a beat-level “hocketing” against the strong–weak–strong–weak scheme.

Using Bootsy Collins’ bass performance again (bar 1 of the two-bar transcribed pattern below), this time a simpler riff (Audio Ex. 10), we can see that he plays almost exclusively on the off-beat positions of the metre, hitting mainly the “-a” and “-and” notes (think: 1-e-and-a, 2-e-and-a, etc.), with the exception of the “One”. This is a typical trait in funk music, where the downbeat is clearly marked in every repetition of the basic groove unit. Against the drums, which are highly anchored to the main beats and feature no syncopation on the 8th- and 16th-note subdivision level, the bass provides ample tension and rhythmic interest without challenging the metre.

Image Source: Guilherme Schmidt Camara 2025 ©

Counter-/cross-rhythm¶

When syncopated events recur systematically within the basic unit, they can form larger-scale, patterned off-beat groupings that suggest alternative periodicities to the main beat.

Cross-rhythm (often called “polyrhythm”) occurs when these groupings display a systematic overlap of rhythmic streams whose periodicities (i.e., “metrical levels”) are non-integer multiples. Typical examples in 4/4 are two evenly spaced events over three beats (2:3 cross-rhythms) or four events over three or six beats (4:3 or 4:6 cross-rhythms). The regular pattern of overlapping accents contradicts the beats of the prevailing metre, challenging it and creating greater metrical ambiguity, to the point where one might hear the pulse as either binary or triplet.

Image Source: Guilherme Schmidt Camara 2025

In most groove styles, though, such overlapping rhythms are usually bounded. They tend to span less than a bar and to coincide again with beat-confirming positions of the metre before repeating. This generates less metrical ambiguity without fundamentally challenging the main pulse. Typical counter-rhythmic groupings in 4/4 are 3+3+2 over eight eighth notes, or 3+3+3+3+2+2 over sixteen sixteenths; listeners may hear secondary “pulses” riding on top of the main metre.

Image Source: Guilherme Schmidt Camara 2025

Returning to the more complex Bootsy Collins riff from earlier, what looks on the surface like a dense pattern of many 16th notes can be read as roughly accenting a typical counter-rhythm found in groove-based music: a 3-3-2 (repeated twice) (see the transcription below, and listen to Audio Ex. 11, where the counter-rhythm is overlaid by a clave). Although this counter-rhythm produces constant 2:3 cross-rhythms, they never fully create the sense of a triplet pulse above the main binary 4/4 beat, because the bass groove always returns to accent the main metre beats before that happens.

Image Source: Guilherme Schmidt Camara 2025

Tempo¶

Tempo is the rate of a given pulse, usually measured in BPM at the fundamental metrical level (e.g., quarter notes in 4/4). Without a reference, people tend to tap within a spontaneous tempo range of around 100–120 BPM. This overlaps with walking pace and many dance genres, which suggests that musical tempo is linked to bodily rhythms. We return to this later in the course.

Demo: onset strength, beat tracking, tempogram¶

This demo summarises rhythmic activity from audio (a bundled Coltrane excerpt when available, otherwise a jittered click train). The third panel shows the autocorrelation of the onset envelope: the signal compared with time-shifted copies of itself, which reveals how strongly each possible pulse rate is present.

Synthetic micro-jitter grid¶

An isochronous grid versus a lightly jittered one. Use it to discuss feel against notation.

A room’s tempo¶

Everything in this chapter so far has run on musical time scales: onsets tens of milliseconds apart, beats around half a second, phrases lasting a few seconds. Periodicity does not stop where music ends. Rooms have rhythms too, and they run far slower than any drummer.

Refrigerators, freezers, and ventilation systems switch on and off in cycles of minutes, so a kitchen at night has a slow pulse of its own, with a period and a duty cycle like any other oscillator. A dishwasher adds a single long phrase with its own internal wash, rinse, and dry structure on top of that pulse. You can find the tempo of your own kitchen by recording it with a phone for an hour or overnight and plotting the level over time.

The analysis tools are the ones this chapter already introduced. A tempogram asks which periodicities the onset envelope contains. Applied to a room, the same question is asked of the slow level envelope, and the answer comes back in minutes rather than BPM. Soundscape-analysis tools such as ambiscape compute exactly this, giving multi-scale envelope modulation profiles and machine on/off segmentation, and we return to soundscapes as a subject for machine listening in machine listening.

Chapter summary¶

This chapter linked timing perception to metre, pulse, onsets, microtiming, swing, and groove, showing how performers create feel through systematic deviations from the grid and how listeners entrain to and analyse rhythmic structure across genres. The telespringar case showed that the reference grid itself can be non-isochronous. Entrainment, understood as coupled oscillation, also underpins coordination between people; the empirical study of joint music-making continues in the body. The same periodicity analysis extends beyond music altogether: a room’s appliances cycle with periods of minutes — a tempo far below the musical range, but measurable with the same tools. Melody and harmony (scales, chords, voice-leading) interact with these timing patterns; see harmony and melody.

Questions¶

1. How do rhythm and metre differ, and how can phenomenal accents coexist with a stable sense of metre?
2. Why do researchers focus on measurable onsets and timing when studying expressive performance?
3. How do asynchronies between instruments, swing, and syncopation shape perceived groove, and why can “the same” notation feel very different across performances?
4. How does the coupled-oscillator account explain why listeners and players fall into step with a beat, and which oscillating processes in a person can entrain to music?
5. In the telespringar case, what did motion capture add to the audio measurements, and why does the case challenge the assumption of isochronous beats?