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Jungle Ice

Welcome to the NRICH website where this month you will find mathematical problems, games and articles which focus on links between Music and Mathematics. This theme has been chosen to coincide with the 2006 Cambridge Music Festival which celebrates Mozart, Maths and Music. We hope that by tackling some of our challenges, you will learn more about the wonderful and varied ways in which these two subjects overlap.

Clapping Times would be a good place to start. You will need to work with a friend on this practical activity - can you predict which number beats will be the loudest? Explore the idea of beats further by having a go at We'll Bang the Drum . How many different rhythms can you make with just two drums? Or, you might like to look at rhythms which are the same played forward as they are played backwards in Beat the Drum Beat.

There are plenty of opportunities to find out more about bell ringing in this month's problems. Investigate the way bell ringing patterns are written down in Oranges and Lemons, Say the Bells of St Clement's and learn about how bellringers arrive at the order of the bells. Can you draw the pattern for eight bells without writing out the numbers? These ideas are extended in You Owe Me Five Farthings, Say the Bells of St Martin's where the interactivity allows you to participate in bell ringing. You may like to read Ding Dong Bell , an article written by Toni Beardon, which complements these problems.

At Stage 4, the problems focus on why it is that some musical notes sound good together and others do not. The Pythagoreans noticed that simple ratios of string length made nice sounds together. Six Notes All Nice Ratios asks you to explore the ratios of the six notes of the Pythagorean scale. In Pythagoras' Comma , the scale now has twelve notes - how far off a closed set were the Pythagoreans? Tuning and Ratio and Euclid's Algorithm and Musical Intervals build on the notion of ratio of string lengths by looking at particular musical intervals.

Finally, it's worth having a read of Dancing with Maths , an article on symmetry and square dancing. What do the symmetries of the square have to do with dos-e-dos or a swing? Surely you're intrigued?

NRICH weekly problem.

This problem is taken from the UKMT Mathematical Challenges.

View last week's solutionsearch engine page