## Math Forum - Problem of the Week

### Polyrhythms

Please keep in mind that this is a research project, and there may sometimes be glitches with the interactive software. Please let us know of any problems you encounter, and include the computer operating system, the browser and version you're using, and what kind of connection you have (dial-up modem, T1, cable).

## Polyrhythms

When you listen to or play music, or better yet, dance to it, you are very aware of the rhythm. You might notice that every 3rd or 4th beat is played a little louder than the others, or that it is accented somehow. In some types of music, several different rhythms are performed at the same time. When that happens, it is called a polyrhythm. Polyrhythms are a very important feature of African drumming.

In this problem you will be investigating polyrhythms, and then have a chance to build your own so you can investigate the mathematics.

### To Do:

Play with the applet using the various rhythms. Experiment to find out what it means to play a 1:2 or a 1:3 rhythm. See how the different rhythms interact when you play them together. When a 1:2 rhythm and a 1:3 rhythm are played together, the polyrhythm is called a 2:3. The number of beats it takes a pattern to repeat itself is called the phrase length. Explore how long it takes different patterns to repeat.

### QUESTIONS

1. What is the ratio of the mystery polyrhythm? Explain how you know.

2. Create a polyrythm of your own using two of the rhythms in the applet. What is the ratio of the polyrhythm and its phrase length? Explain how you know.

3. A complicated polyrhythm has the ratio 2:3:4:5:6:7. What is its phrase length? How do you know?

 © 1994-2005 The Math Forum http://mathforum.org/pow/