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School curriculum enhancement

 If you are teach in a secondary school would you like to give your pupils something beyond the prescribed curriculum to stimulate their interest and show the broader scope of their chosen subject?

. I have already done this for secondary maths and music teachers, and would be happy to develop material suitable for other subjects.

English style bell-ringing is a unique form of music that is heavily underpinned by mathematics. The instruments on which it is performed rely on technology that has evolved over centuries based on interesting physics. Ringers exploit computers. The social history of ringing covers many centuries, the ringing community is an interesting example of citizenship and ringing has physical, mental and social benefits relevant to PHSE.

In short, ringing is many faceted, with examples and case studies of interest to many subjects, see below.

Already available:

I have delivered specialist lectures to select groups of secondary students of maths and music, and would be happy to discuss adapting either of them to your needs.

The maths of bellringing

Two factors combined to push changeringing in a mathematical direction. One was the physically driven constraint that a bell should never move more than one place between successive rows (sequences). The other was the concept of 'truth', ie that no row should be repeated in a piece of ringing, coupled with the associated desire to ring as many different rows as possible (within achievable limits). As a result, ringing theory is heavily dependent on permutations, group theory and symbolic transformations (as well as arithmetic of course). This lecture has been well received. There is an overview here . 

The music of bellringing

Bellringing generates a distinct musical sound, because of the constraints imposed   on the way the bells are rung. The resulting sound sequence has many musical properties. For example, changeringing satisfies the criterion discovered by researchers in the field of computer generated music, that in order to be perceived as musical a sound should be neither completely predictable nor completely random, but a balance between the two. Repeated recognisable patterns (called 'roll-ups') emerge periodically from ringing music, in some ways analogous to leitmotifs. Some methods include clusters of repetitive sequences, and so on. Leading composers of ringing performances (mainly 'peals' that last about 3 hours) go to great lengths to maximise the musical content of their compositions, and as with conventional music, some of their criteria are widely agreed while others are not. This lecture has been well received. For a musical perspective on ringing, see these articles . For more technical detail on change ringing music, see here  .

 Other subjects:

Ringing could fit well as an exemplar or case study within the ambit of several other subjects in the curriculum. I would be happy to discuss with you how that could be done to meet your needs.


The first program to solve a ringing problem was run in1952, just years after the first stored program computer became available for research. In the early days of home computers, the first thing many ringers did was to write a simple ringing program. I built my first computer  from a kit in 1979 and wrote a ringing program for it before I had finished building the case!

Computers are used by ringers for various purposes from the mundane to the exotic, and no serious ringing composer or theorist would consider working entirely by hand. For example, see this site under 'Composition' and 'Computing'   


 English style ringing is only possible because of the special properties of a compound pendulum swinging near full circle, which makes it possible to vary the swing timing very accurately, and to do so for a heavy bell with moderate force.

The more complex problem of clappering, ie the dynamic inter-relationship of the bell and clapper (one compound pendulum suspended from another compound pendulum) was solved experimentally at Cambridge University in the 1960s to give a simple parametric map of different behaviour for any combination of bell and clapper. More recent research, also at Cambridge, has given insights into the way the clapper bounces on impact with the bell, and the effects that this has.


The technology of bell installations has evolved from the mediaeval to the present, both the design and use of materials. Much of the basic technology is readily visible, and the theory is mostly based on Newtonian mechanics.

Bell bearings need to allow for slight misalignment due to flexure in the bell frame, and unlike almost all other bearings that carry a heavy load, they support an oscillating rather than a rotating motion.

Most bells are cast using formed loam based moulds, though in the past some founders used lost wax casting. Some modern founders have used numerically machined models and sand casting, and one small bell was 3-D printed..

Recent research on tower sway caused by swinging bells led to both a theoretical understanding of the mechanisms, and the development of sensors to measure the movement.

Wrought iron, the traditional material for bell clappers, is no longer readily available anywhere in the world, though small quantities are made at heritage sites like Blists Hill . The modern materials used to replace it have been prone to both fracture and poor tonal quality in heavy bells. Hybrid wood-metal clapper designs emerged as a solution to both of these problems.

Social history

During the last 1000 years, major social changes in society first led to the emergence of bellringing as a recognisable activity and then shaped its evolution in fundamental ways. Ringing bells has been a routine monastic chore, a paid civic service, a fashionable exercise for young gentry, a popular public entertainment, a discredited activity, a cause of zealous reform, an intellectual challenge, and a stimulating modern pastime. Over the centuries, ringers have been both driven from, and welcomed into, the life of the church. The tradition of change ringing began in a few major cities, spread throughout England and then around the English speaking world, but for some reason it never penetrated our nearest trading neighbours in Europe until the last few decades.


The world of bellringers is an interesting example of a dispersed but tight-knit community. Although most ringers are attached to a local tower they are also part of a wider network of district, regional, national and international organisations that provide extensive support, services and comradeship. The widespread custom of ringing across boundaries has led to a strongly inter-connected web of personal relationships between individual ringers. One indication of this sense of fraternity is that a ringer walking unannounced into any tower in the world would almost certainly be made welcome and invited to ring.

As a personal life component and contributor to wellbeing, ringing offers moderate physical activity, the development of co-ordination and timing skills, teamwork and mental exercise - a very 'balanced diet' to obtain from a single activity.


The role of bellringers in the local community provides an interesting, and slightly unusual example of citizenship. Ringers maintain a tradition. Most people appreciate it but few understand. They expect ringing for weddings, but have no idea of the skill and social infrastructure behind it – ringers are mainly hidden. I ring at All Saints Wokingham where we try to bring a fuller understanding of ringing traditions, history and ethos, as well as its practicalities, to a wider audience, through talks, tower visits and offering to work with schools.

The demographic of ringers has changed and we don't yet fully understand the effect it will have. There are more older ringers (some who learnt in their teens, some and some late in life) and fewer in their 20s and 30s (the age that used to provide the most dynamic leaders of ringing bands). That mirrors society in general, where we are all living longer, active lives Young high flyers are still pushing the boundaries whether there will be enough to provide the next generation of top performers and leaders, remains unclear.

If you would like to discuss the possibilities, please – Contact me

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