In this lesson we will learn how to count polyrhythms and tuplets. Tuplets groups of notes that won’t fit within a normal beat division. Polyrhythms are unusual rhythms that cannot be counted by simply dividing the beat by counting 1 +, or 1 e + a.

In this lesson we will look at 2 ways to count polyrhythms: using the lowest common multiple, and dividing the beats of the tuplet. Since polyrhythms and tuplets do not fall within a normal beat division, it is easier to count them without using the beats of the measure until they are mastered.

Lowest Common Multiple

In this method, we use the lowest common multiple of the 2 groups of notes to count them. This method is easiest to use for 3 against 4 or 3 against 2 rhythms. For 3 against 2, we would multiply 3 by 2 to get 6 and use that number to count the rhythm. For 3 against 4, we multiply the two numbers and get 12. We use the numbers 1-12 to count the rhythm.

See how to use this method in the next section.

Three Against Two Polyrhythms

The most common three against two polyrhythm is with eighth notes.

To count one rhythm against another, we find the lowest common multiple. Six is the lowest common multiple between three and two. This is not the beat of the music, but it can be used to count until the rhythm is mastered:

We divide the beats evenly among each group of notes. To find how many beats each note gets, divide 6 by the number of notes. Six divided by three is 2, so each note of the triplet gets 2 beats. Six divided by 2 is 3, so each of the 2 half notes get 3 beats.

The following is another way the 2 against 3 rhythm might appear in music. The same method as above can be used to count the rhythm:

Three Against Four Polyrhythms

We can count a three against four rhythm by finding the lowest common multiple. Twelve is the lowest common multiple between 3 and 4.

To count the triplet, we divide 12 by 3. We get 4, so each note lasts for four beats. The triplet notes fall on beats 1, 5, and 9.

To count the quarter notes, we divide 12 by 4. We get 3, so each note lasts for three beats. The four quarter notes fall on 1, 4, 7, and 10.

This is a way to count the rhythm until you master it. Then it can be counted with the beats of the time signature.

Quarter note triplets against eighth notes is another 3 against 4 rhythm:

A piece with a three against four rhythm used for its main theme is Chopin’s Fantaisie Impromptu Op. 66. Two triplets grouped together are marked with a 6:

When you see a multiple of 3 above a group of notes, it is a group of triplets.

Tuplets

Tuplets are used to fit more notes within the beat division. Chopin is a composer who used tuplets frequently in his compositions.

Each note in a group of tuplets has the same length unless otherwise indicated.

Dividing the Tuplet Method

This method can be used to count tuplets against another rhythm that is 2, 3, 4 or a multiple thereof.

First, find the number of notes in the tuplet and make each note a beat. The following tuplet has 5 notes so we will make 5 beats:

Next, divide the beat by the number of notes it is played against. In this case, the tuplet is played against 2 so we will divide the beats in half:

Each note of the tuplet lasts for one beat, each note of the other rhythm will last for as many beat divisions are in the tuplet. Five notes in a tuplet means the other rhythm lasts for 5 divisions of the beat:

Once you master the rhythm, you can count using the time signature of the music.

Tuplet against Two

In 5 against 2, each eighth note will be 5 beat divisions long. The second eighth note is played halfway between the 3rd and 4th notes:

In a 7 against 2 rhythm, each quarter note will be 7 beat divisions long. The second quarter note is halfway between the 4th and 5th beat.

Tuplet against Four

Finding a common multiple can get complicated when dealing with larger tuplets. With a 7 against 4 rhythm, you have to count up to 28. Rhythms such as 7 against 4 and 5 against 4 would have to be counted on these beats:

Using each note of the tuplet as a beat makes it easier to count:

We divide each beat by four since the tuplet is played against 4 notes. Each eighth note is 5 beat divisions long.

For 7 against 4, we count each note of the tuplet as one beat. Each beat is divided into 4 so we can count the four eighth notes:

Each eighth note is 7 beat divisions long.

Tuplet against triplet

Sometimes a tuplet will be played against another triplet. We can still use the tuplet division method to count them:

We divide each beat into three. Each note of the triplet will last for 5 beat divisions.

Triplets, when combined, will look like tuplets. Any tuplet with a number that is a multiple of 3 is a group of triplets. This example from the end of Chopin’s Nocturne in C# minor can be counted by counting to 9 twice, since the tuplet has a large amount of notes. The eighth notes fall on the first beats of each group of 9, and halfway between beats 5 and 6.

More Polyrhythms

Although rare, there are even more polyrhythms possible where you cannot easily divide the notes of the tuplet. These are best learned by playing the note groups separately with a metronome and alternating between the two rhythms.

Practice

Practice counting these polyrhythms with the Polyrhythms and Tuplets Worksheet:

Next: Uncommon Time Signatures