Method ringing (also known as scientific ringing) is a form of change ringing in which the ringers commit to memory the rules for generating each change of sequence, and pairs of bells are affected. This creates a form of bell music which is continually changing, but which cannot be discerned as a conventional melody. It is a way of sounding continually changing mathematical permutations.
It is distinct from call changes, where the ringers are instructed on how to generate each new change by calls from a conductor, and strictly, only two adjacent bells swap their position at each change.
In method ringing, the ringers are guided from permutation to permutation by following the rules of a method. Ringers typically learn a particular method by studying its "blue line", a diagram which shows its structure.
The underlying mathematical basis of method ringing is intimately linked to group theory. The basic building block of method ringing is plain hunt.
The first method, Grandsire, was designed around 1650, probably by Robert Roan who became master of the College Youths change ringing society in 1652.Change Ringing – The History of an English Art. Vol 1, P56. General Editor J Sanderson. Details of the method on five bells appeared in print in 1668 in Tintinnalogia (Fabian Stedman with Richard Duckworth) and Campanalogia (1677 – written solely by Stedman), which are the first two publications on the subject.
The practice originated in England and remains most popular there today; in addition to bells in church towers, it is also often performed on handbells.
Fundamentals
There are thousands of different methods, a few of which are the below.
Plain hunt
Plain hunt is the simplest form of generating changing permutations continuously, and is a fundamental building-block of change ringing methods. It can be extended to any number of bells. It consists of a plain undeviating course of a bell between the first and last places in the striking order, with two strikes in the first and last position to enable a turn-around. Thus each bell moves one position at each succeeding change, unless it reaches the first or last position, where it will remain for two changes before proceeding to the other end of the sequence.Central Council of Church Bell Ringers, "Learning plain hunt" retrieved 20.3.2017
Grandsire
Plain hunting is limited to a small number of possible different changes, which is numerically equal to twice the number of bells that are hunting. However, by introducing deviations from the plain hunt, by causing some of the bells to change their relationship to the others, change ringing "methods" were developed. These allow a large range of possible different changes to be rung; even to the extent of the full factorial sequence of changes.
Grandsire, the oldest change ringing method, is based on a simple deviation to the plain hunt when the treble (bell No.1) is first in the sequence or it is said to "lead". The treble is known as the "hunt bell" because it hunts continuously without ever deviating from the path. The diagram for the plain course is shown here.
The Grandsire variation on the plain hunt on odd numbers adds a second hunt bell, which is "coursing" the treble: that is, the second hunt bell takes its place at the front of the change immediately after the treble. The single deviation away from hunting for the rest of the bells now takes place as the two hunt bells change places at the front of the lead.
Furthermore, because there are two hunt bells, not the second bell but the third remains in place: 13254 – Treble leads 12345 21354 – The second hunt bell, No.2 in this case, leads after the treble. It is coursing it. 23145
This forces a dodge on the other bells in 4/5 positions. After this, the bells immediately return to the plain hunt pattern until the next treble lead.
This rule can now be extended to any number of odd bells in changes, making Grandsire an easily extendable method. The hunt bell is changed many times during such ringing to enable the full factorial number of changes to be achieved.
Plain Bob
"Plain Bob" is one of the oldest change ringing and simplest of these, first named "Grandsire Bob". The deviations when a plain course is extended with "calls" are much simpler than those in Grandsire.
A "plain course" of plain bob minor is shown in diagrammatic form, which has the following characteristics; all bells plain hunt, until the treble bell is first, when depending where they are in the pattern, they; perform "Dodges" in the 3–4 position or perform dodges in the 5–6 positions, or sit for two blows if they are just above the treble, then go first again.
The red bell track shows the order of "works", which are deviations from the plain hunt. 3/4 down dodge 5/6 down dodge 5/6 up dodge 3/4 up dodge make 2nds place. And then it repeats. Each bells starts at a different place in this cyclical order. A dodge means just that; two bells dodge round each other, thus changing their relationship to the treble, and giving rise to different changes.
The plain bob pattern can be extended beyond the constraints of the plain course, to the full unique 720 changes possible ( this is factorial 6 on 6 bells, which is 1×2×3×4×5×6 = 720 changes). To do this, at set points in the sequences one of the ringers, called the "conductor" calls out commands such as "bob" or "single", which introduce further variations. The conductor follows a "composition" which they have to commit to memory. This enables the other ringers to produce large numbers of unique changes without memorising huge quantities of data, without any written prompts.
Ringers can also ring different methods, with different "works" – so there is a huge variety of ways of ringing method changes.
Key points
Numbering the bells The highest bell in pitch is known as the treble and the lowest the tenor. The majority of bell towers have the ring of bells (or ropes) going clockwise from the treble. For convenience, the bells are referred to by number, with the treble being number 1 and the other bells numbered by their pitch (2, 3, 4, etc.) sequentially down the scale. The bells are usually tuned to a diatonic major scale, with the tenor bell being the tonic (or key) note of the scale.
Ringing rounds and changes The simplest way to use a set of bells is ringing rounds, which is sounding the bells repeatedly in sequence from treble to tenor: 1, 2, 3, etc.. (Musicians will recognise this as a portion of a descending scale.) Ringers typically start with rounds and then begin to vary the bells' order, moving on to a series of distinct rows. Each row (or change) is a specific permutation of the bells (for example 123456 or 531246)—that is to say, it includes each bell rung once and only once, the difference from row to row being the order in which the bells follow one another. Plain hunt is the simplest way of creating bell permutations, or changes.
Obtaining the maximum unique changes Since permutations are involved, it is natural that for some people the ultimate theoretical goal of change ringing is to ring the bells in every possible permutation; this is called an extent (in the past this was sometimes referred to as a full peal). For a method on bells, there are (read factorial) possible permutations, a number which quickly grows as increases. For example, while on six bells there are 720 permutations, on 8 bells there are 40,320; furthermore, 10! = 3,628,800, and 12! = 479,001,600.
Key rules of valid method ringing "Truth" of a ringing method Estimating two seconds for each change (a reasonable pace), we find that while an extent on 6 bells can be accomplished in half an hour, a full peal on 8 bells should take nearly twenty-two and a half hours and one on 12 bells would take over thirty years! Naturally, then, except in towers with only a few bells, ringers typically can only ring a subset of the available permutations. But the key stricture of an extent, uniqueness (any row may only be rung once), is considered essential. This is called truth; to repeat any row would make the performance false.
Allowable position changes Another key limitation keeps a given bell from moving up or back more than a single place from row to row; if it rings (for instance) fourth in one row, in the next row it can only ring third, fourth, or fifth. Thus from row to row each bell either keeps its place or swaps places with one of its neighbours.Ringers sometimes experiment with ignoring this rule, making a "jump change." This rule has its origins in the physical reality of tower bells: a bell, swinging through a complete revolution with every row, has considerable inertia and the ringer has only a limited ability to accelerate or decelerate its cycle.
Start and finish with "rounds". A third key rule mandates rounds as the start and end of all ringing. So to summarize: any performance must start out from rounds, visit a number of other rows (whether all possible permutations or just a subset thereof) but only once each, and then return safely to rounds, all the while making only small neighbour-swaps from row to row. These rules dramatically limit the options open to a method-maker.
For example, consider a tower with four bells. An extent includes 4! = 24 changes and there are, naturally, 24! possible orders in which to ring each change once, which is about 6.2 × 1023. But once we limit ourselves to neighbour-swaps and to starting and ending with rounds, only 10,792 possible extents remain.Minimus extents
Reason for methods It is to navigate this complex terrain that various methods have been developed; they allow the ringers to plot their course ahead of time without needing to memorize it all (an impossible task) or to read it off a numbingly repetitive list of numbers. Instead, by combining a pattern short and simple enough for ringers to memorize with a few regular breaking points where simple variations can be introduced, a robust algorithm is formed. This is the essence of method ringing.
Lead A lead is part of the plain course. It commences when the method starts and lasts until the treble gets back to the same place. In the diagram of Plain Bob Minor shown, the lead starts when the treble rings in second place and lasts until the treble has rung twice at lead. It is common practice in diagrams to draw a line under the lead end to assist in understanding the method. Most methods have a plain course consisting of a number of leads where the pattern is the same, but different bells are in differing places. In the diagram given, the number 4 bell rings the same pattern as the number 2, but one lead earlier.
In principles (where the treble does the same work as other bells and is affected by calls) the definition of a lead can become more complex.
Calls and compositions
To obtain more changes than available in the plain course, a conductor makes a call directing the ringers to make a slight variation in the course. (The most common calls are called bobs and singles.) These variations usually last only one change, but cause two or more ringers to swap their paths, whereupon they continue with the normal pattern. By introducing such calls appropriately, repetition can be avoided, with the peal remaining true over a large number of changes. For example, an extent in a minor method is 720 (6!) changes, so would require 12 repetitions of the plain course shown.
To know when to make calls and which ones to make, a conductor follows a plan called a composition which he or someone else devised; if properly constructed it will ensure a true performance of the desired length. Today computers make checking a composition's truth easy; but the process once involved a mix of mathematics and laborious row-by-row checking.