The Mathematics of Bellringing

Today I attended a U3A Online Learning Event

The Maths of Bell Ringing given by the mathematician and bell-ringer John Harrison from Wokingham.

There were over 160 attendees on the Zoom call where John took us through a presentation about bell ringing changes, how they are presented and how they are composed.

John quickly took us through the basics of the possible permutations of different numbers of bells and how a method of changes is composed. I've no idea how bell ringing conductors manage to memorise these things!

Along the way he delved into group theory and then the mapping of into multi-dimensional representations, which you can read about on his website here. And this is what his website says about the talk:

"All forms of music show some mathematical structure in scales, chords and rhythm. English-style change-ringing is a very special type of music. It has no chords and no variation in rhythm, but it is underpinned by some elegant and fascinating mathematics. The continually changing sequences that constitute the music use what mathematicians call permutative group theory, which also appears in areas as diverse as cryptography and the solutions to Rubik’s Cube. The principles of group theory were formalised in the 19th century, but ringers were using them 200 years earlier without being aware of it. This talk explains the mathematical principles behind change ringing. They flow from the physical constraints on a swinging bell, from the desire for patterns that can be executed from memory, and from the concept of ‘truth’, which is unique to change ringing. The talk concludes with an explanation of the models  that I built in 1968. This talk was first given to the Wokingham U3A Maths Group, You don't need a strong mathematical background to enjoy it."

I can't say I followed it all completely, but it was fascinating. Thank-you John.