Making Complex Ratios (Activity for Teachers)

How about making a more interesting percussion piece, like a 3:2 proportional relationship between two instruments. Here’s an example, try it:

                                               Figure 7

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Where and when do the two instruments meet—line-up (notice the arrow)? One boy commented, “Oh they meet at 12; that’s that least common multiple stuff.” What he noticed was that to arrive at 12, there are 2, 6-beats (2 x 6 makes 12), and 3, 4-beats (3 x 4 makes 12). Where do the two instruments meet up the next time? Someone said, “It’s 24—6 x 4 and 4 x 6 both equal 24. You can actually hear it. Except you have to count the spaces not the lines.” Can you build up the example but adjust the repeats so the two instruments also end up together—i.e., are the same in total time? Remember the repeats—they will also be in a 3:2 proportion but “upside down.”

Go to Complex Ratio Activity for Students ⇒