Dear all,
The November NRICH website is now live at http://nrich.maths.org 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
<http://www.cammusic.co.uk/> 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
<http://nrich.maths.org/public/viewer.php?obj_id=5482&part=index> 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
<http://nrich.maths.org/public/viewer.php?obj_id=5493&part=index> . 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.
<http://nrich.maths.org/public/viewer.php?obj_id=5495&part=index>
There are plenty of opportunites 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
<http://nrich.maths.org/public/viewer.php?obj_id=5341&part=index> 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
<http://nrich.maths.org/public/viewer.php?obj_id=5342&part=index> where
the interactivity allows you to participate in bell ringing. You may
like to read Ding Dong Bell
<http://nrich.maths.org/public/viewer.php?obj_id=1320&part=index> , 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
<http://nrich.maths.org/public/viewer.php?obj_id=5499&part=index> asks
you to explore the ratios of the six notes of the Pythagorean scale. In
Pythagoras' Comma
<http://nrich.maths.org/public/viewer.php?obj_id=5500&part=index> , the
scale now has twelve notes - how far off a closed set were the
Pythogoreans? Tuning and Ratio
<http://nrich.maths.org/public/viewer.php?obj_id=5453&part=index> and
Euclid's Algorithm and Musical Intervals
<http://nrich.maths.org/public/viewer.php?obj_id=5454&part=index> 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
<http://nrich.maths.org/public/viewer.php?obj_id=5502&part=index> , 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?
With best wishes from The NRICH Team
--
Liz Pumfrey
NRICH Primary Coordinator
University of Cambridge Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WA
01223 764246
www.nrich.maths.org
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