English Change Ringing Patterns
Change Ringing has been developed in English church towers since the 16th century. The number of towers in England dominates other countries in the British Isles - hence English, rather than British Change Ringing. Strangely, it occurred in few places other than former British colonies.
Bells have provided symbolic and cultural messages for civilisations throughout the centuries. They can provide signals and important information (someone’s coming, bring out your dead…). Composers’ have used bells for a corresponding amount of time, whether it is to investigate the spectral content (the very sound of a bell) or the envelope or pattern created through a peal of bells (Sir Peter Maxwell-Davies, Sir Harrison Birtwistle and Anthony Gilbert most notably in the 20th and 21st Centuries).
Permutations found in English Change Ringing Patterns can be very beautiful as a pure self-contained logical entity. They are not rung to sound a melody but rather create different mathematical patterns using the permutations on the set of the bells. The paper discusses a variety of applications within musical composition.
Permutate v.tr = PERMUTE
Permutation n. 1. an ordered arrangement or grouping of a set of numbers, items, etc. 2. any combination or selection of a specified number of things from a larger group
Permute v.tr alter the sequence or arrangement of (from Latin permutare ‘to change thoroughly’)
Algorithm n. Math, a set of rules used for calculation or problem-solving
Permutations of bells are rung obeying the following simple rules (there are practical and compositional reasons for this):
1.bells are first rung in order from highest to lowest pitch (treble to tenor);
2.each bell is struck once in each row;
3.a bell can move one place from one row to the next or stay in the same position (again there are practical reasons for this);
4.no repetition of the permutation is allowed until the last row returns.
A simple four-bell permutation demonstrates these rules - note the movement of numbers (elements), rule 3.
1 2 3 4
2 1 4 3
2 4 1 3
4 2 3 1
4 3 2 1
My paper ‘Assigning English Change Ringing Patterns (Permutation) in Acoustic and EA Music’ has been published widely (including the ICMC 2008) and is available from various sites online. However, click here for access to all of my papers, including the paper mentioned.