Compound and Asymmetric Time Signatures

Lessons

Senior 3 · Music

Compound and Asymmetric Time Signatures

4 lessons

Lesson 3 of 4

Compound time: six-eight, nine-eight and twelve-eight

22 min

Tap your foot to a rowing song

Sing "Row, Row, Row Your Boat" and tap your foot. You will tap only twice in each bar: on Row, row, then on row and boat, and in the second half only on the first syllable of each mer-ri-ly. Each tap is a big beat that splits into three, not two. That is compound time.

Look at bars 5 and 6: the quavers are beamed in threes, one group per beat. In bar 1 each beat is a single dotted crotchet. The song was first printed in 1852 and is in the public domain.

Definition

Simple time: time in which each beat divides into two equal parts. The beat is a plain note (crotchet, minim or quaver). Examples: two-four, three-four, four-four, three-eight.

Compound time: time in which each beat divides into three equal parts. The beat is a dotted note. Examples: six-eight, nine-eight, twelve-eight.

Duple, triple, quadruple: two, three or four beats in a bar. They describe simple and compound times alike.

Reading a compound time signature

In compound time, the top number does not give the number of beats. It counts the smaller parts (usually quavers). To find the beats:

Divide the top number by 3. That gives the number of beats in a bar.
Three quavers make one beat, so the beat is a dotted crotchet when the bottom number is 8.

Time signature	Beats in a bar	Each beat	Name	Simple time with the same number of beats
six-eight	$6 \div 3 = 2$	dotted crotchet	compound duple	two-four
nine-eight	$9 \div 3 = 3$	dotted crotchet	compound triple	three-four
twelve-eight	$12 \div 3 = 4$	dotted crotchet	compound quadruple	four-four

The same idea works with other bottom numbers. Six-four has two dotted-minim beats; twelve-sixteen has four dotted-quaver beats. A time with 3 on top, such as three-eight, is simple triple, because 3 divided by 3 would give only one beat.

Six-eight is not three-four

Both bars hold six quavers, so on paper they look alike. The beaming shows the difference: in six-eight the quavers are grouped in threes, in three-four in twos. Clap each line and you feel two swinging beats against three even ones.

Counting compound time

Say "1 & a 2 & a" for six-eight, adding "3 & a" for nine-eight and "4 & a" for twelve-eight.
Crotchet + quaver inside one beat ("row your") is counted "1 (&) a": the crotchet takes two quavers, the quaver lands on "a".
A beat of silence is a dotted crotchet rest. Silence on the first two quavers of a beat may be written as one crotchet rest; silence on the last two quavers of a beat is written as two quaver rests, so the middle of the beat stays visible.

Worked example

Worked example 1: name the time. Classify nine-eight.

Step 1. Top number 9 is divisible by 3 and is not 3 itself, so the time is compound.

Step 2. Beats: $9 \div 3 = 3$ , each a dotted crotchet.

Answer: compound triple time, with three dotted-crotchet beats in each bar.

Worked example

Worked example 2: complete the bar. A bar of twelve-eight holds: dotted crotchet, crotchet, quaver, three quavers. What is missing?

Step 1. Count in quavers: 3 + 2 + 1 + 3 = 9.

Step 2. Twelve-eight needs 12 quavers, so 3 quavers (one whole beat) are missing.

Answer: one dotted crotchet, or a dotted crotchet rest, on beat 4.

Video: "Music Theory: Compound Meter", Breaking Barlines (Aron Bernstein). Watch for how a dotted note becomes the beat, and how six-eight, nine-eight and twelve-eight are counted. Meter is the American word for time.

Tip

Top number divisible by 3, but not 3 itself? Compound. Divide by 3 for the beats; the beat is a dotted note.

Warning

Common mistake: saying six-eight has six beats. At any normal speed it has two. Six is the number of quavers, not the number of beats.

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Practice

How many beats are there in a bar of twelve-eight, and what note is each beat?
Classify each as simple or compound, and duple, triple or quadruple: (a) six-eight; (b) three-four; (c) nine-eight; (d) four-four.
Which compound time has the same number of beats as three-four?
A bar of six-eight holds a crotchet and a quaver, then a dotted crotchet rest. Is it complete? Show your count.
Write the count ("1 & a…") under this six-eight bar: three quavers, then crotchet + quaver.
Explain why six quavers beamed 3 + 3 cannot be in three-four time.
Kalisa says twelve-eight and four-four "are the same because both have four beats". Give one way they are the same and one way they differ.

Show answersHide answers

Four beats; each is a dotted crotchet.
(a) compound duple; (b) simple triple; (c) compound triple; (d) simple quadruple.
Nine-eight (three dotted-crotchet beats).
Yes: 2 + 1 + 3 = 6 quavers.
"1 & a" under the three quavers; "2 (&) a" for crotchet + quaver, with the quaver on "a".
In three-four quavers are beamed in pairs, one pair per crotchet beat. A 3 + 3 grouping shows two dotted-crotchet beats, which is six-eight.
Same: both have four beats in a bar. Different: in four-four each beat divides into two quavers; in twelve-eight each beat divides into three.

Remember

Compound beat = a dotted note, divided into three.
Beats = top number $\div$ 3: six-eight = 2, nine-eight = 3, twelve-eight = 4.
Beam quavers in threes in compound time, in twos in simple time.
Count "1 & a 2 & a".

Sources and credits

Lesson text, notation diagrams, worked examples and practice: written by Ganzaa.
"Row, Row, Row Your Boat", traditional, first printed in 1852: public domain. Re-engraved by Ganzaa.
Treble clef shape in the notation diagrams: Treble clef.svg by Tlusťa (author as recorded on Wikimedia Commons), Wikimedia Commons, released into the public domain. Resized onto Ganzaa's staves.
Video: "Music Theory: Compound Meter", Breaking Barlines: Music with Aron Bernstein, embedded from YouTube.

1Tap your foot to a rowing song

2Reading a compound time signature

3Six-eight is not three-four

4Counting compound time

Tap your foot to a rowing song

Reading a compound time signature

Six-eight is not three-four

Counting compound time