Understanding Polyrhythms
by Kevin Barrett

First we'll begin with a discussion of what a polyrhythm is. A simple definition of a polyrhythm is two or more rhythms played simultaneously. While this definition is basically correct, usually when we speak of polyrhythms we are talking about a more specific relationship between two rhythms. Normally a polyrhythm gives the impression of one musical pulse being superimposed or played against another. In other words we have two different rhythms being played against one another which give the impression of a "cross-rhythm" or "cross-pulse". Perhaps the easiest way to conceptualize polyrhythms is to think of them as rhythmic ratios. For example a ratio of 3 notes to 2 notes, or 3:2, would be considered a polyrhythm. To play such a ratio we must superimpose three notes of equal value over a pulse of two notes. If the ratio were two notes to three notes (i.e. 2:3) we would need to superimpose 2 notes of equal value over a pulse of three notes. Generally two rhythms are only considered a polyrhythm if they have no common divisor (other than one). In the examples above 2 and 3 have no common divisor. There is no whole number (other than one) that will divide evenly into both 2 and 3. The rhythmic ratio of 3:4 would also be considered a polyrhythm. Three and four have no common divisor other than one. On the other hand a rhythmic ratio of 4 notes to 2 notes (i.e. 4:2) is NOT a polyrhythm. Two and four are both evenly divisible by two.

Now let's take a look at some specific examples. Here is a ratio of 3:2.  (Ex 1)  Three quarter notes (i.e. a quarter note triplet) are being played over a pulse of 2 quarter notes. Here is the ratio of 2:3.  (Ex. 2)   In this example two notes are being superimposed over a pulse of 3 notes. Both of the preceding examples are considered polyrhythms.  Now let's look at the ratio of 4:2. (Ex 3)   In this example four eighth notes are being superimposed over two quarter notes. Ex. 3 is NOT considered a polyrhythm.  The eighth notes and quarter notes line up evenly. What's missing in this example is the characteristic "cross rhythm" of a true polyrhythm. To say that the eighth and quarter notes line up evenly is another way of stating that they have a common divisor and therefore do not qualify as a polyrhythm. Now that we understand what polyrhythms are let's look at how to play them.

The first step in interpreting any polyrhythm is to find a common denominator between the two rhythms. We need to have some common note value on which to interpret both rhythms which make up the polyrhythm. Again let's look at the example of 3 against 2. (Ex 4) This ratio means that we are going to play three notes of equal value in the space of time normally allotted to two notes. The smallest common denominator of 3 and 2 is 6. Therefore if we subdivide the basic pulse into six equal parts we will have a common note value on which to interpret both parts of the polyrhythm. To subdivide the basic pulse into six equal notes we divide the quarter notes into eighth-note triplets. (Ex 5) Now we can evenly divide the six notes into two equal parts by playing every third note.  (See Ex. 6 - notes with the stems going down)  We can also divide the six notes into three equal parts by playing every second note. (Ex 6 - notes with the stems going up) If we play the two rhythms simultaneously we have the polyrhythm of 3 against 2.

(Note:  Only play the notes with the actual note heads. One limb should play the note heads with the stems going down.  Another limb should play the note heads with the stems going up.)

Let's take another example. Here's the polyrhythm of 4 against 3. (Ex 7) This ratio means that we are going to play four notes of equal value in the space of time normally allotted to three notes. The smallest common denominator of 3 and 4 is 12. Therefore if we subdivide the basic pulse into twelve equal parts we will have a common note value on which to interpret both parts of the polyrhythm. To subdivide the basic pulse into twelve equal notes we divide the quarter notes into sixteenth-notes. (Ex 8) Now we can evenly divide the twelve notes into three equal parts by playing every fourth note (Ex 9 - stems down) and into four equal parts by playing every third note (Ex 9 - stems up). If we play the two rhythms simultaneously we have the polyrhythm of 4 against 3.

If you haven't guessed it by now there is a very simple formula for figuring out any polyrhythm. The formula can be stated as follows: To play X against Y divide the Y's into groups of X's and play every Yth one.  Let's take a look at some examples.  Here's the 3 against 2 polyrhythm again. (Ex 10) In this example we divide the main pulse (the Y's) into groups of three's (groups of X's). Then we play every 2nd one (every Yth one). Keep in mind that if you want to play X against Y you should think of Y as your main pulse or point of reference. In this example the 2's (i.e. the quarter notes) are your main pulse. By main pulse I mean where you are feeling the beat.  Ex 11 and 11-A show how this may be broken down.  (Remember:  Only play the notes with the actual note heads. One limb should play the note heads with the stems going down.  Another limb should play the note heads with the stems going up.  The stems without note heads are only place holders.)

What we are really doing here is finding the common denominator. By dividing the quarter note pulse into groups of 3's (triplets) we end up with 6 notes just as we did when finding the common denominator. Then, one limb can play every third note and another limb can play every second note to create the polyrhythm.

Let's take a look at a couple more examples. Here's the polyrhythm of 3 against 4. (Ex 12) We divide the 4's (the quarter notes) into groups of 3's (triplets). Then we play every 4th one.  (See Ex 13 and  13-A)  Here's a slightly more complex polyrhythm of 3 against 5. (Ex 14) We divide the 5's (the quarter notes) into groups of 3's (triplets). Then we play every 5th one.  (See Ex 15 and 15-A)  Here's the polyrhythm of 5 against 4. (Ex 16) We divide the 4's (the quarter notes) into groups of 5's (quintuplets). Then we play every 4th one.   (See Ex 17 and Ex 17-A)  Let's end our examples with the polyrhythm of 7 against 5.  (Ex 18) We divide the 5's (the quarter notes) into groups of 7's (septuplets). Then we play every 5th one. (Ex 19) So there you have it:  To play X against Y, divide the Y's into groups of X's and play every Yth one. It's as simple as that.

Hopefully this article has shed some light on the concept of polyrhythms. By using the formula given here you can figure out almost any polyrhythm. Now the next step is to apply them to various musical settings. As a starting point listen to some of the masters of polyrhythmic playing. In the jazz area one of the acknowledged masters is Elvin Jones. Also listen to Jack Dejohnette and Tony Williams. In the area of rock check out the recordings of Frank Zappa.  Almost all of his drummers have been excellent polyrhythmic players. (Frank said Vinnie Colaiuta won the prize.)  Start with some simple polyrhythms. Write them out and analyze them. Then begin to incorporate them into your playing. By incorporating polyrhythms into your own playing you will open up new rhythmic possibilities and add an increased level of rhythmic sophistication to your drumming. Good luck and enjoy!

(A future article will look at some practical applications of polyrhythms to the drumset).