Change ringing (nonfiction)

Change ringing is the art of ringing a set of tuned bells in a tightly controlled manner to produce precise variations in their successive striking sequences, known as "changes". This can be by method ringing in which the ringers commit to memory the rules for generating each change, or by call changes, where the ringers are instructed how to generate each change by instructions from a conductor. This creates a form of bell music which cannot be discerned as a conventional melody, but is a series of mathematical sequences.

Change ringing originated following the invention of English full-circle tower bell ringing in the early 17th century, when bell ringers found that swinging a bell through a much larger arc than that required for swing-chiming gave control over the time between successive strikes of the clapper. Ordinarily a bell will swing through a small arc only at a set speed governed by its size and shape in the nature of a simple pendulum, but by swinging through a larger arc approaching a full circle, control of the strike interval can be exercised by the ringer. This culminated in the technique of full circle ringing, which enabled ringers to independently change the speeds of their individual bells accurately to combine in ringing different mathematical permutations, known as "changes".

Speed control of a tower bell is exerted by the ringer only when each bell is mouth upwards and moving slowly near the balance point; this constraint and the intricate rope manipulation involved normally requires that each bell has its own ringer. The considerable weights of full-circle tower bells also means they cannot be easily stopped or started and the practical change of interval between successive strikes is limited. This places limitations on the rules for generating easily-rung changes; each bell must strike once in each change, but its position of striking in successive changes can only change by one place.

Change ringing is practiced worldwide, but it is by far most common on church bells in English churches, where it first developed. Change ringing is also performed on handbells, where conventionally each ringer holds two bells, and chimed on carillons and chimes of bells; though these are more commonly used to play conventional melodies.

See also

• The Australian and New Zealand Association of Bellringers (nonfiction)
• Braid group (nonfiction) - the braid group on n strands (denoted {\displaystyle B_{n}}B_{n}), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see § Introduction). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see § Basic properties); and in monodromy invariants of algebraic geometry.
• Change ringing software (nonfiction)
• Grandsire (nonfiction)
• John Taylor & Co (nonfiction)
• Steinhaus–Johnson–Trotter algorithm (nonfiction) - an algorithm named after Hugo Steinhaus, Selmer M. Johnson, and Hale Trotter which generates all of the permutations of n elements. Each permutation in the sequence that it generates differs from the previous permutation by swapping two adjacent elements of the sequence. Equivalently, this algorithm finds a Hamiltonian cycle in the permutohedron. This method was known already to 17th-century English change ringers; Robert Sedgewick (1977) calls it "perhaps the most prominent permutation enumeration algorithm". As well as being simple and computationally efficient, it has the advantage that subsequent computations on the permutations that it generates may be sped up because these permutations are so similar to each other.
• Veronese bellringing art (nonfiction)
• Whitechapel Bell Foundry (nonfiction)

Links

• Change ringing @ Wikipedia