Although it is possible to add a polymeter to an irregular time signature, polymeters are exactly what the term implies; two, or more meters (time signatures) played against each other; four against two; three against two; six against four: three against four: five against four; seven against four. It is also important to understand the mathematical relationships of the polymeters. In four against two, we have the most common polymeter in our music, cut time or two to one. In jazz, if you are playing in 4/4 and you double the tempo in the 4/4 structure, this is called “double time feel” or in essence two to one. Three against two and six against four mathematically are one and one half times faster than the 4/4 or 1-1/2 to 1; three against four is three quarters times slower than the 4/4 or 3/4 to 1; five against four is one and one quarter times faster than the 4/4 or 1-1/4 to 1; and seven against four is one and three quarters times faster or 1-3/4 to 1. These examples are the easiest to deal with when learning polymeters because of their logical mathematical relationships.

To understand a polymeter, the best thing to do is to learn to play one. The one best suited to the study is three against two (quarter note triplet). WE can learn three against two subdividing triplets in 2/4.
subdivide In order to do this properly, you must have a metronome play the basic rhythm while you play the Polyrhythm or at least tap your foot good and loud so you can hear the relationship between the two rhythms. If you lengthen three against two to a 4/4 bar you are now playing six against four.

Now you have two separate meters and you can extend the rhythmic possibilities of the top meter. This is done exactly in the same manner as most musicians learn basic reading when first learning how to divide the quarter note in 4/4. There are six quarter notes against four quarter notes.

If you keep the four quarter notes the same tempo, but double the tempo of the six quarter notes you have this.

eighth notes in six against four. 

Change the eighth notes to triplets and you have;

triplets in six against four. Next would be sixteenths in six against four;

after mastering these Polyrhythms you can then mix them utilizing space with added rests.

Then experiment with improvising in six against four. Before long you will find that this polymeter will become as natural to you as 4/4. The same technique applies basically to any polymeter.

The next question is, “how do Polyrhythms and polymeters benefit the musician?”

Having taught the concept for several years as well as applying the ideas to my own playing technique as a drummer and percussionist, I have found a number of positive musical advantages to the study. First, let me emphasize the fact that Polyrhythms and polymeter are not new concepts. If you listen to the music of Africa, India, Java and Bali, you will find that simultaneous meters are and have been played and understood by the musicians of these cultures for hundred and even thousands of years. Western art music has also had more recent contributors to the art of polymetric composition and improvisation. Listen to Charles Ives, Igor Stravinsky, Elliot Carter, John Coltrane, Elvin Jones, some of the later Miles Davis recordings with Herbie Hancock and Tony Williams, many Latin drummers, etc…. These artists and many more have made dramatic and effective use of polymeter in their respective work. The question: “Why learn polymeters?”, can be answered simply: because today’s composers demand it and today’s jazz is expanding into new rhythmic dimensions that make polymeter and the ability to improvise freely in one time against another an expected technique.

However, I have discovered something I feel to be even more interesting than understanding how to play Polyrhythms, and that is the development and improvement of the whole rhythmic concept while learning them. I have observed how musicians through practice, have come to realize the fundamental skills of rhythmic proficiency as applied to all types of music. I have also found that some musicians seem to acquire the ability, while playing, to concentrate on two meters at the same time, similar to a stereo system playing one recording, however, dividing the sound between two speakers.

Consequently, I feel the study of polymeters broadens a musician’s intrinsic rhythmic ability and increases his insight into the potentials of rhythmic expression.