Polyrhythmic beats: Music and multiples
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Youtube has many videos showing polyrhythms. I liked these two, for maracas and piano.

You can create:

  • Polyrhythmic beat patterns
  • Graphs of rhythms
  • Conjectures and theories about musical ratios and multiples

There are two different ways to play polyrhythms. Let's look at them on graphs, using 3:2 polyrhythm often found in jazz.

Method 1 - the piano dude from the video. Imagine a metronome going. Your left hand plays on every second beat, and your right hand plays on every third beat. Practice it with clapping or any instrument. It's hard, but doable. Here is a graph, called "time unit box system" in music:

3 against 2 polyrhythm
X   X   X   X   X   X   X   X   X   X   X   X  
X     X     X     X     X     X     X     X    

Do you see when your left and right hand meet each other? Why does it work like that? The math term for "meeting beats" is "least common multiple."

Method 2 - the maracas dude from the video. The left hand goes "one-two" while the right hand, within the same interval, goes "one-two-three." Here is a graph of it, for percussion:

two to three rhythm

But if you play an instrument like a piano, your notes will have lengths, and your picture will be different. Here is how this method may look like:

two to three lengths
Do you see the relationship between the lengths of your left hand and right hand notes here? This isn't something you usually meet in European music! But you can experiment with fractional ratios of note lengths. In this case, the ratio is 3:2

You can try polyrythms based on different ratios, with both methods. Make graphs of your rhythms, and compose music based on them. Share your music with the multiplication study group! Here is a little applet that can help you experiment with the first method.

Because this activity is for music lovers and everybody who wants to be a Renaissance person, connecting math with everything else!

As you go

  • Note which polyrhythms are easier for us to learn. 2:4 is easy, 3:5 is hard - why?
  • Read on polyrhythms in music of different cultures
  • Find polyrhythms in your favorite musical pieces

Higher and deeper

  • Music composition theory is rich in mathematical topics. Multiples and ratios are just the tip of the iceberg.
  • "Godel, Escher, Bach" is a more advanced book about music, math and art.

Strewing and snippets

Because you can clap or bang any rhythm using your body or everyday objects, this is a perfect activity "on the go." If you want to promote this around the house, strew simple percussion objects or any musical instruments around. Also, you can draw rhythm patterns using simple symbols, or use stamps or colors to create them and then put up these "diagrams" on the walls.

Created: December 6, 2008, 8:23 am, by MariaD
Last edit: January 16, 2009, 10:41 am, by MariaD ( Edit, History )
Co-author: MariaD, foRsaken