Bell Ringing

Music takes many forms around the world and while it is easy to show some mathematical structure in scales and rhythm, nothing beats the English form of bellringing, known as change-ringing, for pure mathematical elegance. The "music" is the same mathematics behind the Rubik's cube and cryptography. Change-ringing is however, much older than the formal field of group theory and it is not surprising that the two areas have entirely different nomenclatures and much reinvention.

The aim in change-ringing may be summarised as ringing a set of permutations, without repetition or pause, entirely from memory by a band of bellringers. By analogy, consider taking a Rubik's cube through an ordered sequence of patterns but with eight people looking after the cube in synchrony. It is clear that change-ringing is a unique mix of music, physical sport, teamwork and mathematics.

Change-ringing has its beginnings as early as the fourteenth century. As many as three bells would have been in a church steeple, forming a combination church and secular public address system. The bellringers also found that by swinging a bell, rather than hitting it with a clapper, the bell was able to ring clearly. Over time, bells began to be swung higher and higher until eventually a mechanism was developed to allow bells to be swung full-circle, as they are today, and with the additional advantage of timing control.

Each bell swings full circle but does so in a forward and reverse direction. This implies that there are two strokes which need to be considered one in which the rope is wrapped around the wheel (the "handstroke") and the other in which the rope unwraps (the "backstroke"). The two strokes allow bellringers to follow what is happening by watching the ropes around them ("ropesight") as well as listening to the bells.

The system by which the different unique rows can be ordered was formalised by the end of the seventeenth century. The bell mechanism has improved significantly, especially with the introduction of steel frames (instead of oak) and roller bearings (instead of plain greased bearings). The number of bells in a tower has increased to a typical ring of six or eight and in some cases to twelve and even sixteen. Finally, a systematic method of bell tuning was developed around 1900, bringing bells and their harmonics into standard tuning.

The ultimate bellringing marathon is the Peal, in which all 5040 permutations of 7 bells are rung in sequence, without pause or interchange, entirely from memory, taking three to four hours. Many peals have been rung in Adelaide over the last 40 years or so, in addition to many Quarter Peals.

To find out more, visit or search for "Change Ringing" online.

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