Beating a path between music and maths
Standing in a circle with tall wooden broomsticks and beaters in their hands, and with red xylophones at their feet, pupils from Chesterton Community College, Cambridge, are rehearsing the Fibonacci sequence. On the count of "one", they stomp their broomsticks on the floor, then, in time with each other, they strike the broomsticks with the beaters.
"Remember, 'one' is always on the floor," Damien Harron, composer, tells them. "Between now and the concert, my plan is to brainwash you with this rhythm."
This was the third rehearsal for a public performance of his new work, Dance of Geometry, at the Cambridge Music Festival, whose theme this year was Mozart, Music and Maths.
The yoking of musical and mathematical ideas strikes the Chesterton group as something of a novelty. "I didn't know you could do the Fibonacci sequence with rhythm - it's a maths thing," says Meisha Lawrence, 14. "It makes it more interesting because you've got to pay attention to what you're doing."
"It's kind of cool," says Jackson Ritchie, 13. "It was a bit weird at first because I would normally associate maths with smart people in white overcoats. Now when I go to maths lessons, I'll think you can use maths in more creative ways, not just counting out how much change someone needs."
When Damien Harron was told of the music and maths theme of this year's festival, he remembered a Stephen Hawking phrase - the "dance of geometry".
He set about constructing a percussion piece for young people which explored different mathematical ideas based around cycles and orbits.
As well as the Fibonacci number sequence, Dance of Geometry incorporates polyrhythms (that is, three and four-beat cycles which regularly converge) and elongated sequences of notes which groups of pupils play simultaneously on xylophones, each group's sequence slightly longer than that of their neighbours.
There are also free-form sections in which pupils create their own sequences on gongs and finger-cymbals, adding a layer of exotic sound over the drums and tuned percussion.
"Music is a complex art form which engages our imaginations, emotions and physical energies, yet it's an equally complex science," says Damien.
"Rhythms have mathematical relationships as they loop and interact, and harmonies can blend sonorously if the constituent sounds relate mathematically. Percussion instruments are a wonderful medium for exploring both the art and the science."
The composer says he didn't much enjoy maths at school. "But since then, having performed a lot of new music, I've had to sit down and work out polyrhythms and I've spent more time thinking mathematically about percussion playing than I ever thought I would."
Yvonne Williamson, head of music at Chesterton Community College, is delighted with the cross-fertilisation of subjects that Dance of Geometry provides - highlighting for pupils the logical, mathematical elements in music and showing them that maths involves creativity and imagination. She hopes that Chesterton's music and maths departments can collaborate more in the future.
"Children are conservative and tend to pigeon-hole things, but the more links we can make between curriculum areas, the better. If we can make the link between maths and music from Year 7, that will really get them thinking. Much of the music we hear through the media is unadulterated four beats in a bar, but a project like this shows pupils that there are other ways of making music"
The Cambridge Music Festival was held last month
NOTES FOR MUSIC TEACHERS
* Introduce and make explicit the link between maths and music in rhythm work from Year 7 onwards. Perhaps build a group composition based on rhythmic playing of the Fibonacci sequence. Explore three and four-beat rhythmic cycles, played at the same time, and see when the patterns converge.
* Use mathematically based rhythms to demonstrate that not all music has four beats in a bar. This will help pupils when they come to study music from other cultures.
* When composing simple four-bar answering phrases, make explicit the underlying mathematical structure.
* Broomsticks make a satisfying clunk when stomped rhythmically on the floor as part of a percussion orchestra - and they're cheap.
A sequence of numbers where, after two starting values, each number is the sum of the two preceding numbers: 0,1,1,2,3,5,8,13,21,34,55 etc. It was named after Leonardo of Pisa, the 13th-century mathematician also known as Fibonacci, and has been applied to create architecture, art, poetry and music.