The sound of mathematics
Basic mathematical and scientific skills can be learned through the art of bell-ringing
Pierre du Bois
If you ever wanted to hear what mathematics sound like, listen closely the next time you hear church bells ring.
The music made when ringing the bells is a string of different possible mathematical combinations called “changes”, which may not be repeated.
With seven bells 5 040 combinations are possible, and a “peal” is only complete once all combinations have been rung.
With eight bells, the number of combinations leaps to 40 320.
In 1963 a bell-ringing band in Loughborough, England, set out to complete a peal of all combinations possible on eight bells. The conductor, Robert Smith, recalls: “Several of the band looked very uncomfortable at about 25 000 changes, so I said that we’d passed all the records but one. My arms started to bleed at about this point, but this seemed to stop the chaffing a little bit.
“By the time we reached 30 000, everybody was parched, and helped themselves to glasses of water; I dropped mine and it broke. At 35 000 everybody had black rings around their eyes and some of the band had a sudden change of colour ... The only way we could lose now was if somebody fell over.”
The band, consisting of 17 to 30 year olds, succeeded, completing the peal in just under 18 hours.
In change-ringing, each bell is rung by one person, demanding considerable endurance, but also skill, concentration and calculation from ringers and the conductor. It comes as no surprise, then, that the ringing master at St Paul’s Cathedral in London is an Oxford graduate in mathematics.
To train people how to correctly ring bells, Rhodes University’s Professor Colin Lewis is teaching a certificate course in change-ringing.
Lewis conducts bell-ringing performances (called peals) lasting several hours and is in the driving seat of South African bell-making. He is the chairperson of the South African Guild of Church Bell-Ringers.
But how did the geography professor get involved with bells? Lewis, originally from Wales, learned how to ring bells at 14.
“As a student I met and rang with some of the leading change-ringers of the 1960s. I became interested in conducting and in the 1960s had a super band in Herefordshire,” says Lewis.
Apart from the demands placed on the bell-ringer, each individual bell needs to be meticulously crafted to give it the right sound to play its part in the huge musical instrument formed by a set, or “ring”, of bells.
Hot bell metal, an alloy of 23% tin and the rest almost entirely copper, is poured into a mould made of loam, a clay-like mixture traditionally made of, among other things, horse dung and goat hair. In the Port Elizabeth foundry, specially prepared sand is used.
Bells may need considerable time to cool, depending on the size. A bell weighing 10 tonnes shipped to Malta in the 1990s took several weeks to cool. A 50kg bell can cool in as little as 24 hours.
The size and shape of a bell determines its note. When the bell comes out of its mould, it still needs to be tuned before it will produce the desired sound. Although many notes can be measured electronically, the bell produces only five clearly distinguishable notes (called partials), caused by the vibration of the bell when hit by the clapper. The partials are produced by vibration in different parts of the bell and vary in loudness and duration.
When Lewis came to South Africa in the 1980s, he found that the Grahamstown Cathedral had eight bells that were difficult to ring. He oversaw their rehanging between 1989 and 1993. In 1997 two more bells were added.
But while he was restoring them, Lewis became concerned that the rapidly falling value of the rand would make importing bells from Britain or elsewhere impossible. He signed an agreement with a British bell company allowing bells for South African school chapels and churches to be made in Port Elizabeth.
Foreigners are helping considerably to ensure change-ringing gains a foothold in South Africa. Hillandale Monastery, just outside Grahamstown, is about to add two bells received as a gift from a British foundry to its four Port Elizabeth-made bells. International ringing organisations are partly paying to fit the bells. “They believe that it is very important that South Africans be given the opportunity to learn how to ring and, through learning that art, are introduced to basic mathematical and other scientific skills,” says Lewis.
Not only maths, but also science is linked to bell-ringing. The Grahamstown Cathedral bells were used by Alison Botha, a postgraduate student of Rhodes University, in the preparation of her MSc thesis on pitch perception. Remarkably, her study shows that people who play string instruments perceive notes differently to those who play wind instruments, and they all differ from those who play no instruments. Lewis says details of the research, paid for by a British company dealing in bells, is confidential at the moment.
There are only a handful of rings in South Africa. They are in Grahamstown Cathedral, St Mary’s in Woodstock (Cape Town), St George’s Cathedral in Cape Town, St Paul’s and St Mary’s in Durban, St George’s in Parktown (Johannesburg) and St Peter’s Church in Hillandale. Worldwide, says Lewis, there are about 6 000 rings, most of them in the United Kingdom and Ireland.
Lewis hopes more ringing bells will be introduced to South Africa. “There are many towers in South Africa that are suitable for ringing bells and, now that suitable bells can be made in Port Elizabeth, it is hoped that many more rings of bells will be installed in future.”
At the Sasol Scifest, Lewis will explain the science behind bell-ringing. He will show people how to ring bells and will try to attract them to change-ringing. “The emphasis will be on enjoyment and arousing interest rather than bombarding youngsters with science,” says Lewis.
Professor Colin Lewis will talk on The Greatest Noise in Town: Learn about Bells and Bell-Ringing on March 15, 16 and 19 at the Cathedral of St Michael and St George