Meter, Syncopation and Groove

A time signature is the pair of numbers printed at the start of a piece of music that says how its bars are counted: the upper number gives how many units go into a bar, and the lower number names which note value one of those units is. (also called meter signature, academic writing, which prefers it because the pair of numbers names the meter rather than measuring anything in time)

The two clips above are the same twelve taps at the same speed, and what differs is which level of the counting is being marked. In the first, only the taps a reader of 4/4 would call ONE carry the weight: the downbeat of each bar, every fourth tap. In the second, every half note carries it, and those are the two beats a reader of 2/2 — cut time — counts inside each of the same, unchanged, four-quarter bars. Not a tap moved between the clips; the bars are the same length in both and the downbeat falls in the same place in both. 2/2 and 4/4 are one sound written two ways, and a listener cannot tell them apart: cut time asks for two half-note beats where common time asks for four quarter-note ones, so the counting is half as busy, which is why fast music is written that way. Notice where the second clip's marks land — on the first and third beat of each four — because those are the two beats any four-beat bar already leans on, and you will meet that exact sound again in the next section under the other signature.

The lower number is the part that misleads people, because it looks like the denominator of a fraction and behaves like a name. A 4 means the unit is a quarter note, an 8 means it is an eighth note, a 2 means it is a half note. And in a compound meter the unit is not the beat at all: the six of 6/8 counts eighth notes, while the bar holds two beats, each a dotted quarter and each dividing into three. That is why 4/4 and 2/2 both fill a bar with four quarter notes and are still two different signatures — they are counted differently, and the counting is what the signature is for.

A signature can change mid-piece as often as a composer likes, and plenty of music changes it every few bars. It is an instruction to the reader rather than a property of the sound: the same recording can be written in 6/8 or in 3/4 depending on what the writer wants the player to feel, and the player who is handed the other version will phrase it differently.

An accent is extra weight given to one note or one beat so that it stands out from those around it — produced by playing it louder, by holding it longer, by placing it higher or lower than its neighbours, or by nothing more than where it falls in the bar. (also called stress, everyday and classroom usage, borrowing the word from the way a syllable is stressed in speech)

That last one is free, and it is the reason meter exists at all. The first beat of a bar is heard as the strongest whether or not anything marks it, the third beat of a four is heard as the next strongest, and the second and fourth are heard as weak. A listener supplies all of this. Everything a player then does either agrees with it or argues with it, and the argument is where the interest lives.

The three clips are the same eight taps at the same speed and differ only in which of them carry the octave underneath. The first agrees with the meter, reinforcing the two beats a four-beat bar already makes strong — and you have heard it before, as the second clip of the section above, where those same two beats were the two a cut-time reader counts; one sound, one fact, two signatures. The result is square and slightly stiff. The second puts the weight on the two beats the meter makes weak, and the whole thing starts to move — that is the pattern a snare drum plays on almost every rock, pop and soul record ever made, and it has a name of its own: the backbeat. The third reinforces all four equally, which is the disco bass drum and the marching band, and which feels driving but flat, because nothing is being contradicted.

None of this changes a note, a pitch or a tempo. It is worth saying plainly, because it is easy to assume a groove is something in the notes: the same melody over the same chords at the same speed becomes a different record when the weight moves from one pair of beats to the other.

Syncopation is the placing of emphasis where the meter does not expect it — on a weak beat, on a half-beat between two beats, or on a beat left deliberately unplayed — so that what is heard pulls against the count still running underneath it.

The second clip does the first of those. Its four beats are all present, so nothing has gone missing; what has happened is that an extra tap has been put on the half-beat after the third beat and given the weight that the third beat had in the first clip. Count along and your mouth says "three" on a light tap and then the heavy one arrives while you are saying "and". The music has not lost the beat. You are still supplying it, and that is exactly why the displacement registers.

That dependence is worth stating outright, because it explains why syncopation cannot be heard in isolation. Play the second clip to somebody who is not counting and nothing in it is displaced; it is simply a rhythm. The effect lives in the gap between what the listener predicts and what arrives, which means the meter has to be established first. This is also why syncopation gets stronger the longer a passage has been square, and why a whole song of nothing but off-beats eventually stops sounding syncopated and starts sounding like the beat.

Whole traditions are built from one displaced pattern repeated. The son clave of Cuban music is five strokes laid across two bars of four: in the first bar on beat one, on the half-beat after beat two, and on beat four; in the second bar on beats two and three only. Just one of its five strokes falls between beats — but the second bar leaves its downbeat empty, and those two facts together are enough to keep two bars of music permanently leaning. Every clave-based style, and most of what grew out of them, inherits that lean.

Swing is a way of playing pairs of equally written notes unequally: the first of each pair is given roughly twice as much of the beat as the second, so that the pair sits on a three-part division of the beat rather than a two-part one. (also called triplet feel, jazz teaching and lead-sheet instructions, which name the three-part division the uneven pair is cut from)

The three clips make the arithmetic audible. The third divides every beat into three and strikes all of them. The second strikes only the first and third of each group of three, leaving the middle one silent — so the gap from the first tap of a pair to the second covers two cells, and the gap from there back to the next beat covers one. Two units then one unit is the 2 to 1 pair, and it is the only way a chip with a single step length can produce one. The first clip divides every beat into two instead and strikes both, which is why its taps are evenly spaced. All three last the same amount of time, and the first two have the same number of taps. Where the band plays all three parts of the division out loud rather than leaving the middle one silent, the same feel is called a shuffle.

None of this is usually written out. A chart prints the pairs as ordinary even eighth notes and puts an instruction at the top of the page, because notating every pair as a bracketed triplet with two of its notes joined would make the music nearly unreadable. The consequence is that a printed pair of even eighth notes tells you almost nothing about how evenly it will be played: the instruction decides, or the style the chart belongs to decides for it.

The 2 to 1 ratio is a teaching figure rather than a measurement. Real performances slide along a continuum: the same soloist plays the pairs closer to even as the tempo rises, the drummer behind them may not match, and a programmed track sets the amount with a percentage control that can sit anywhere between the two extremes. What stays constant is the direction — the wider gap first, the narrower one second — and that it is a change to the spacing of the taps and to nothing else.

A polyrhythm is two rhythms sounding at the same time that divide the same stretch of time into different numbers of equal parts — three against two, four against three — so that neither one can be heard as a subdivision of the other. (also called cross-rhythm, the study of West and Central African drumming, and jazz writing borrowing from it, where the word stresses that one pattern cuts across another rather than merely sounding beside it)

Three against two is the smallest case and the one to learn first. Divide a stretch of time into six equal slots. One voice takes every other slot, which gives it three evenly spaced taps; the other takes every third slot, which gives it two. They begin together on slot one and then miss each other completely: the set of three has slots three and five to itself, the set of two has slot four, and slots two and six are empty. Six slots later they meet again, and the whole thing repeats.

What makes it hard to play is not the arithmetic but the ear. Given two competing divisions, a listener picks one as the beat and hears the other as a disturbance — and which one is picked can flip mid-listen, so the same clip sounds like a lopsided three at one moment and a limping two at the next. Performers get round this by counting the six slots underneath until both hands are automatic and then letting the counting fall away, which is exactly what the task below asks for.

The relation turns up in two very different guises. Sounded at once, as in the third clip, it is a polyrhythm. Laid end to end — a bar felt in two groups of three followed by a bar felt in three groups of two — it is called a hemiola, and it is the same six slots regrouped rather than stacked. Once you can hear one you can usually hear the other, because the ear is doing the same work in both cases.

An odd meter is a meter whose bar holds a number of units that will not divide into equal groups — five, seven, eleven — so the bar is counted as unequal groups instead, most often a run of twos with a single three among them. (also called asymmetric meter, academic writing, which names the fact that the bar cannot be split into groups of equal length; irregular meter, British school textbooks and a good deal of popular-music writing)

The first two clips are the same five taps at the same speed and they are not the same music. Reinforce the first and the fourth and the bar is a three followed by a two; reinforce the first and the third and it is a two followed by a three. Both are 5/4, and the time signature says nothing whatever about which. The grouping lives entirely in the accents, in how the notes are beamed, and in what the players already know about the piece.

The practical advice is the same everywhere: do not count to five, and certainly do not count to seven. Count the groups. Saying ONE two three ONE two fits the first clip without effort, where counting one-two-three-four-five evenly over it leaves you having to remember which numbers were heavy. The third clip is seven eighth notes grouped two, two, three, and ONE two ONE two ONE two three fits it the same way.

The word "odd" is a judgement made from one particular tradition. In Anglo-American popular music these meters are rare enough that the handful of songs using them are the ones always named, and reaching for one is a deliberate effect. In Bulgarian, Greek, Macedonian, Turkish and much North Indian music they are ordinary dance and recital meters, played and danced by people who have never had occasion to find them remarkable.