In Unit 2, we first encountered the idea of simple meters, in which the beat regularly divides into halves. This chapter introduces compound meters, in which the beat regularly divides into thirds.
Compound Duple Meter
In most music, not only are the rhythms grouped into patterns within each measure, but the measures themselves also come in groups. Consider the beginning of the French carol “Un Flambeau, Jeanette Isabelle”:
In this notation of the song, the a pulse level is represented by eighth notes and the b pulse level is represented by measures. The meter sign 3/8 directly represents the relationship between levels a and b — a simple triple meter. In addition, we’ve shown level c, at which the measures come in pairs. It’s as if there’s a primary measure. followed by a secondary measure.
If we shift the beat from level a to level b, we can feel a downbeat for each pulse at c and an upbeat for each of the b-level pulses in between. We can also renotate the music, removing the bar lines between pairs of measures. Each measure now contains six pulses at level a. The meter sign therefore becomes 6/8(3/8 + 3/8). We’ll re-notate “Un Flambeau” this way (and illustrate this above the staff with numbers and arrows showing the conducting downbeats and upbeats).
In doing this, we have shifted the beat to the b level, and divided that beat regularly into threes.
A meter in which the beat is regularly divided into threes is called a COMPOUND METER (compare simple meters, first encountered in Unit 2).
The number of beats per measure in a compound meter is determined by dividing the top number in the meter sign by 3. Conversely, in compound meters the beat unit is three times the note value represented by the bottom number of the meter sign.
In 6/16, 6/8, and 6/4 meters, there are two beats per measure, and each beat can be divided into threes. We call these COMPOUND DUPLE meters— COMPOUND because the beats divide into threes, and DUPLE because there are two beats per measure.
Note that in simple meters the bottom number in the meter sign represents the beat unit, but that in compound meters the bottom number represents the triple division of the beat. Therefore, in compound meters the beat unit is three times the note value represented by bottom number. For example, in 4/8 the beat unit is an eighth note but in 6/8 the beat unit is a dotted quarter note (three times an eighth note).
Avril Lavigne’s “I’m with You” is a good example of compound duper. When she sings “I’m standin’ on the bridge,” you’d probably sway twice, while each of the syllables of that line would be the small beats that group into two groups of three. Try listening while tapping both the small beats and then tapping (or swaying!) to the big beats.
Compound Triple Meter
In “Un Flambeau, Jeanette Isabelle,” the beats at level b grouped into level c in pairs. Beats in compound meters may also group into threes, as in the Canadian folk song “Un Canadien Errant.” Measures 7-18 of this song are shown below:
The 3/4 meter sign focuses on the triple relationship between the a and b pulse levels, representing a as the quarter-note beat and b as the measure. But although the 3/4 meter sign doesn’t show it, those measures at level b also group into an even broader c level in groups of three.
If we shift the beat from level a to level b, we can feel a downbeat for each pulse at c and an upbeat for each of the two b-level pulses in between. We can now renotate this example to show these relationships between the b and c levels, removing bar lines within each group of three measures, combining 3/4 + 3/4 + 3/4 to produce a meter sign of 9/4:
In 9/16, 9/8, and 9/4 meters, there are three beats per measure, and each beat can be divided into threes. We call these COMPOUND TRIPLE meters — COMPOUND because the beats divide into threes, and TRIPLE because there are three beats per measure.
Cat Stevens’s “Morning Has Broken” is an example of a compound triple meter. The lyrics “Morning has” are upbeats: start swaying on “Broken,” and you’ll be feeling the big beats. The small beat are pulses like “Black bird has” and “Like the first.” Go between swaying for the big beats, and tapping the small beats as you listen.
Compound Quadruple Meter
Beats in compound meters may also group into fours. We’ll start with another tune in simple triple meter, the German folk song “Freut euch des Lebens,” this time observing how the measures group into pairs of pairs:
The eighth-note level a is grouped into the measure level b in threes (which the simple-triple meter sign represents). The measure level b groups into a broader level c in pairs. Moving even broader, the c level groups into a d level by pairs as well.
If we shift the beat to level b, we can see that there is a quadruple relationship between the b-level pulses and the broadest pulse level (d), as shown above. Let’s renotate this example, removing bar lines within each group of four measures, combining 3/8 + 3/8 + 3/8 + 3/8 to produce 12/8:
In 12/16, 12/8, and 12/4 meters, there are four beats per measure, and each beat can be divided into threes. We call these COMPOUND QUADRUPLE meters — COMPOUND because the beats divide into threes, and QUADRUPLE because there are four beats per measure.
“Memory” from Andrew Lloyd Webber’s Cats is in compound quadruple. The two syllables in the first sung word “Memory,” are both on the big beats (that divide into three small beats). The word “turn your face to the” are each on the small-beat pulse. Again, try to tap or sway to both the big beat pulse and the small beat pulse.
Simple and Compound Meters and Their Beat Units
When you see a 2 ,3 or 4 on the top of a meter sign, this indicates a simple meter (review Unit 2). In simple meters, it’s easy to discern the number of beats per measure directly by looking at the top number in the meter sign — a 2, represents duple meter, a 3, represents triple meter, and a 4 represents quadruple meter.
In simple meters, it’s also easy to discern the beat unit directly by looking at the bottom number in the meter sign — a 2 means the half note is the beat unit, a 4 means a quarter note, an 8 means an eighth note, and so on.
But when you see a 6, 9, or 12 (that is, some multiple of 3) on the top of a meter sign, this indicates a compound meter. Reading and interpreting compound meter signs is a little more complicated.
To determine whether a compound meter is duple, triple, or quadruple, divide the top number in the meter sign by three:
- 6 ÷ 3 = 2 (duple meter)
- 9 ÷ 3 = 3 (triple meter)
- 12 ÷ 3 = 4 (quadruple meter)
To determine what kind of note value is worth one beat in a compound meter, do the following:
So, for example, 9/16 is a compound triple meter (9 ÷ 3 = 3) in which the dotted eighth note is worth one beat…
Here’s a chart that summarizes various compound meters and how they can be arrived at by combining measures of simple triple meter:
Duple and Triple Beat Divisions
We have now encountered two basic kinds of beat divisions. There are those that divide the beat into two equal halves:
And there are those that divide the beat into three equal thirds:
But what if music changes back and forth between duple and triple beat divisions within a single passage, even within a single measure? We’ll introduce special symbols that will allow us to do just that.
Triplets
In simple meters — such as 2/4 — we have encountered only duple (and multiple duple) divisions of the beat. What happens when we want to divide a beat in a duple meter into three equal duration? In other words, while the prevailing divisions are duple in simple meter, what happens when we borrow a triple division from compound meter?
In order to notate these rhythms in a simple duple meter —for example, 2/4 — we would have to use a TRIPLET, which fits three notes of equal duration in the place of two.
Triplets use the rhythmic value that would normally divide the beat in half in any given simple meter, but squeeze three of those notes in the place of two. With a quarter-note beat unit (as in the chart above), the beat is divided into three equal parts by eighth-note triplets. Other beat units use their corresponding half-beat values. For example, half-note beat units divide beats into threes using quarternote triplets:
And eighth-note beat units divide beats into threes using sixteenth-note triplets:
Two of the three triplet divisions can be combined into one longer note, creating a note 2/3 of a beat long. Here’s one such example:
A triplet is an irregular beat-division in simple meter. A beat-dividing triplet can occur only in simple meters. When discussing compound meters, one should never refer to the three-note beat division as a “triplet.” Instead, call them by their actual note values (for example, “eighth notes” in 6/8).
Duplets
As we’ve seen, a triplet is a triple division in simple meter. It’s also possible to see the “opposite” of a triplet — a duple division in compound meter, but this is much more rare. Here’s an example of a duplet. Note how the “2” symbolizes the exception — to divide the first beat in measure 2 into halves, not thirds:
