Eight eighth notes in a row can be four groups of two or two groups of four, and those are different pieces of music. The previous lesson gave every note a length; this one gives the lengths a shape.
Pulse, beat and bar
Listen to almost any music and you will find yourself tapping. What you are tapping is the beat, a regular pulse the music implies, and what makes it feel regular in a particular way is that some beats feel stronger than others. Group the beats into a repeating pattern of strong and weak and you have metre.
Notation writes the grouping with barlines, vertical strokes cutting the staff into bars (American: measures). The rule is simple and almost never broken: the beat immediately after a barline is the strongest in the bar. It is called the downbeat, from the conductor's arm, and everything else in the bar is heard relative to it.
Be clear about what "strong" means, because it is not the same as "loud". A strong beat is a position in a pattern, and the pattern is maintained by the listener even when the performer does nothing to mark it. Play a bar of silence in the middle of a waltz and the listener still knows where the next downbeat falls. This is why metre can be contradicted, at the end of this lesson, and still be felt.
What the two numbers mean
The time signature at the head of the piece declares the pattern. It is two numbers stacked without a line between them, and the safest reading is: the bottom number names a note value, the top number says how many of them fill a bar.
The bottom number names the value as a fraction of a whole note. A 4 means quarter notes, an 8 means eighths, a 2 means halves, a 16 means sixteenths. So 3/4 is three quarter notes per bar, 2/2 is two half notes per bar, and 6/8 is six eighth notes per bar. A bar therefore lasts top divided by bottom whole notes: 3/4 gives three quarters of a whole note, 6/8 gives six eighths, which is also three quarters. The two signatures hold identical amounts of time, and, as the next section shows, they are still not the same metre.
Two signatures are printed as letters for historical reasons. C means 4/4, and it is not an abbreviation of "common"; it is the remains of a medieval circle-and-semicircle system in which a full circle meant triple division and a broken one duple. C with a vertical stroke through it means 2/2, called cut common or alla breve.
Example. How long does one bar of 3/4 last at a tempo of quarter note = 144?
Each quarter lasts s and the bar holds three of them, so s.
Now you. How long does one bar of 2/2 last at a tempo of half note = 60, and how many quarter notes does the bar contain?
Answer
A half note lasts s and the bar holds two, so the bar lasts 2 s. It contains four quarter notes, exactly as a bar of 4/4 would, at the same total length.
Simple and compound, or how the beat divides
Here is the distinction that trips up nearly everyone, and it is worth getting right once. The top number does not always give the number of beats. It gives the number of note values, and in some metres those values are divisions rather than beats.
In simple metres the beat is an undotted note and divides into two. 2/4, 3/4 and 4/4 are simple, with two, three and four quarter-note beats, each splitting into two eighths.
In compound metres the beat is a dotted note and divides into three. 6/8 is the important case: it holds six eighth notes, but they are felt as two beats of three, so the beat is a dotted quarter and there are two of them. Counting six in a bar of 6/8 is the standard beginner's error, and it turns a lively 6/8 jig into a slow six. Similarly 9/8 is three dotted-quarter beats and 12/8 is four.
The test is arithmetic. If the top number is 6, 9 or 12, divide it by 3 to get the number of beats, and the beat is a dotted version of the value named by the bottom number. Otherwise the top number is the number of beats already.
That gives the answer to 3/4 against 6/8. Both bars contain six eighth notes. In 3/4 they group as , three beats each divided in two. In 6/8 they group as , two beats each divided in three. Leonard Bernstein's America famously alternates the two bar by bar, and the whole effect of the song lives in that difference.
Example. A piece is in 9/8. How many beats are in a bar, what note gets the beat, and how long is a bar at dotted quarter note = 80?
Nine divided by three is three beats, each a dotted quarter. At 80 dotted quarters per minute each beat lasts s, so the bar lasts s.
Now you. A piece is in 12/8 at dotted quarter note = 80. How many beats per bar, and how long is one eighth note?
Answer
Twelve divided by three is four dotted-quarter beats, so the bar lasts s. Each beat divides into three eighths, so an eighth note lasts s.
The accent hierarchy
Within a bar the strengths are graded rather than binary. In 4/4 the pattern is strong, weak, medium, weak: beat 1 is the downbeat, beat 3 carries a secondary accent, and beats 2 and 4 are weak. That is precisely why 4/4 is not two bars of 2/4 written lazily. In 2/4 every second beat is a downbeat; in 4/4 every fourth is, and beat 3 is audibly subordinate to beat 1. In 3/4 the pattern is strong, weak, weak, with no secondary accent, which is what makes triple metre feel unlike anything duple.
The hierarchy continues below the beat. Count a bar of 4/4 in eighths as "one and two and three and four and": the numbers are stronger than the "and"s, and the beat numbers are themselves graded as above. A note landing on an "and" is metrically weaker than one landing on a number, however loudly it is played, and that is the raw material for both syncopation and, much later in this course, the rules about where a dissonance may fall.
Beaming shows the reader the pattern
Eighth notes and shorter can have their flags replaced by beams, thick lines joining the stems. Beams are not decoration and are not free: they are drawn so that each beamed group fills one beat.
In 4/4, eighth notes beam in twos, one group per quarter-note beat, or in fours across a half bar. In 6/8 they beam in threes, one group per dotted-quarter beat. A page of 6/8 therefore looks different from a page of 3/4 even before you read the time signature, and that is the point: beaming lets a player see the metre rather than deduce it. Beaming across the middle of a bar of 4/4, joining the second and third beats into one group, is considered an engraving error precisely because it hides where beat 3 is.
The one traditional exception is vocal music, where beams were historically drawn to match syllables, one beam group per syllable, so a singer could see the word-setting. Modern editions increasingly beam vocal music by beat like everything else, and reprints of older editions do not.
Anacrusis, tuplets, and the two ways to leave the pattern
A piece need not start on a downbeat. An anacrusis, or pickup, is one or more notes before the first full bar, written in a short bar of their own. The convention, in older engraving, is that the final bar of the piece is shortened by the same amount so the two incomplete bars add to one full one, and Happy Birthday, in 3/4, is the example everybody has already sung: the two notes of "hap-py" are the pickup, and the downbeat of the first full bar lands on "birth".
The other departure is dividing a beat by something the notation cannot express. A tuplet does it by fiat: write the notes, bracket them, and print the number of them that are to fit in the time normally taken by a different number. A triplet is three notes in the time of two, marked with a 3, and it is how a simple metre borrows the compound division. In 4/4 at quarter note = 120, a quarter-note beat lasts 0.5 s, so each note of an eighth-note triplet lasts s, against 0.25 s for an ordinary eighth. Other ratios are written the same way, so a 5 over a group of sixteenths means five in the time of four. Compound metres borrow in the other direction with a duplet, two notes in the time of three.
Example. In 6/8 at dotted quarter note = 60, how long is one eighth note, and how long is each note of a duplet written across one beat?
The beat lasts s and divides into three eighths, so an eighth is s. A duplet fits two notes into that same 1 s beat, so each lasts 0.5 s.
Now you. In 4/4 at quarter note = 100, a beat is filled by a five-note tuplet of sixteenths, marked 5 in the time of 4. How long is each of those notes?
Answer
The beat lasts s and is shared equally by five notes, so each lasts s, against s for an ordinary sixteenth.
Syncopation
Syncopation is an accent where the metre says there should not be one, and it only exists because the metre is strong enough to be contradicted. There are three standard ways to produce it and they are often combined.
The first is the tie. Sound a note on the weak half of beat 2 and tie it over beat 3, and beat 3 arrives with nothing articulated on it, so the ear promotes the note that came early. The second is the rest: put silence on the downbeat and the next attack, wherever it falls, takes the weight. The third is the printed accent mark, which simply insists.
The classic pattern in popular music is the Charleston figure: in a bar of 4/4, a dotted quarter, another dotted quarter, then a quarter. The attacks fall on beat 1, on the second half of beat 2, and on beat 4, so only the first coincides with a beat and the middle one falls in the metrically weakest position available. Backbeat, the rock and pop habit of putting the drum on beats 2 and 4, is the same idea made permanent: the weak beats are the loud ones, and the metre survives because everything else in the texture still points at 1 and 3.
Where metre stops working
Three honest limits. First, metre is a construction in the listener, not a property of the sound, and ambiguous passages exist where two hearings are both defensible until a cadence settles it. Second, plenty of music is not metrical at all: Gregorian chant, much unaccompanied folk singing, and the introductory alap of a raga are all measured in phrases rather than bars. Third, the simple-versus-compound scheme is a Western generalisation. Balkan dance music routinely uses additive metres in which the bar is built from unequal groups, a 7/8 grouped rather than into seven equal beats, and the time signature alone will not tell you which grouping is meant, so good editions print it, as over 8.
Rhythm is now fully readable: every note has a length, and every length has a place in a pattern. Pitch is still only a list of names with nothing said about the distances between them, and that is the subject of the next lesson.