Unpacking Polyrhythms Part 1: The Basics

According to the Harvard Dictionary of Music, a polyrhythm occurs whenever two contrasting rhythms happen at the same time. That doesn't nail things down for us very well, especially given that there are a number of terms used to describe polyrhythms. What adds to the confusion is that the book uses the same bit of notation to illustrate several of these terms. So what gives?

Terminology is helpful when it clarifies concepts, and a pain in the butt when it serves only to confuse. So I'd like to offer a few suggestions for interpreting the rather imprecise terms available to describe concurrent rhythms.

Polyrhythm (sometimes called a counter-rhythm)

I want to reserve this word for dissimilar groupings played against a regular pulse. One we're all familiar with is quarter note triplets against a 4/4 rhythm. Nine against 4 would also qualify.

Basic Polyrhythms: 3 over 2, 9:2

Systemic Polyrhythm

A systemic polyrhythm is one that forms the core rhythm of the music. This is a very common practice in, for example, African music, where a rhythm in 6/8 is often played in groupings of both 2 beats and 3 beats throughout the tune. So: 123 - 123 is played at the same time as 12 - 12 - 12.

Hemiola

This is a classical term that refers to a specific pattern of two against three. Originally the time signature was 3/4 and the hemiola rhythm was two dotted quarter notes (2:3; 2 over 3; 2 against 3). Regardless of the underlying time signature, two notes in the space of three is a hemiola, and this figure can be found in every style of music. Memorable examples of hemiolas can be found in the Latin clave rhythm and Dave Brubeck’s Take Five. You'll also see them a lot in pop tunes.

Hemiola in 3/4

Hemiola in 4/4

Cross Rhythm (also known as Poly-meter or Meter Within Meter)

In a polyrhythm as described above, a new contrasting pulse is played alongside the basic pulse. In a cross rhythm, the pulse remains constant and the notes are grouped differently, alluding to an intermingling of time signatures. For example, in 3/4 time, one can merrily play in 2/4 and the modification will hardly be noticed. Similarly, you can play a 3/4 or 5/4 pattern in 4/4 time or 5/4 in 3/4 time -- and as long as you keep track of where you are, you can keep it up for awhile ( though it can be somewhat tricky).

Cross Rhythm: 3/4 over 4/4 

Harvard Dictionary of Music: http://www.hup.harvard.edu/catalog.php?ISBN=9780674011632