The Tower Handbook

Change ringing has four defining characteristics:

- The bells ring with an even rhythm (unlike normal tunes that have long and short notes),
- The order in which the bells sound changes continually,
- Each bell strikes once before any of them sound again,
- No bell moves more than one place in the order in which they sound.

This is what makes the sound of change ringing unique. The constraints come partly from the mechanics of the swinging bells. It is impossible to change the interval between successive blows of any one bell by a very large amount.

As in most walks of life, ringing has precise terminology, but most ringers use it in a loose way because in their day to day conversation they do not need to make the precise distinctions the terminology is designed to support. Most ringers say change when they mean row and they never need to talk about (what really are) changes. Some people who do know the difference, but want to use familiar terms talk about 'change row' when they mean row. We have tried to use the correct terms in this handbook.

A **row** is a sequence in which the bells strike (eg 123456 or 132546). A **change** is the transformation used to obtain one row from the another. The diagram shows this for the two rows above. The first and last bells in the sequence stay put, while the bells in 2nd & 3rd places, and 4th & 5th places are crossed over. Changes can be written using Is for places and Xs for the swapping pairs, in this case I X X I.

Strictly this question should be about the maximum number of rows possible, see above. It depends on how many bells are involved. The more there are, the more different orders in which they can be arranged. For small numbers of bells you can work it out by trial and error. For 2 bells, there are only 2 possible sequences (12, 21). For 3 bells, there are 6 sequences (123, 213, 132, 312, 231, 321). For larger numbers it would be too tedious to find them all by trial and error, and there is a mathematical formula to work it out. On n bells, the number of rows is the factorial of n (written as n!). 2! = 1x2, 3! =1x2x3, 4! = 1x2x3x4, etc. Notice that on any number of bells n, the number of rows is n times the number of rows for one fewer bells [20], ie n!=n.(n-1)!. These numbers go up very rapidly. The first few are:

2!=2; 5!=120 ; 8!=40,320 ; 3!=6 ; 6!=720 ; 9!=362,880 ; 4!=24 ; 7!=5,040 ; 10!=3,628,800 ;

The number of different changes (ie ways of getting one row from another) also goes up with the number of bells, but less rapidly. The figures are:

Number of different changes

Bells | Total | Single | Double | Triple | Quadruple | Quintuple |

2 | 1 | 1 | ||||

3 | 2 | 2 | ||||

4 | 4 | 3 | 1 | |||

5 | 7 | 4 | 3 | |||

6 | 12 | 5 | 6 | 1 | ||

7 | 20 | 6 | 10 | 4 | ||

8 | 33 | 7 | 15 | 10 | 1 | |

9 | 54 | 8 | 21 | 20 | 5 | |

10 | 88 | 9 | 28 | 35 | 15 | 1 |

Most popular methods use changes that move most of the bells, ie triple and double changes in Minor, quadruple and triple changes in Major. (Cambridge is the only 8 bell method in *The Ringing World Diary* with a double change). Pure Doubles methods only use double changes (ie 3 out of the 7) and pure Triples methods only use triple changes (4 out of the 20), and so on. See section 4.3f.

It isn't always, but read on. In the early years of change ringing, 'peal' was synonymous with 'extent'. You can see early peal boards recording peals of 720 changes of Minor. In the early 18th century, ringers became more interested in ringing long lengths, and since the most advanced method ringing was on seven bells, so the most advanced peal which was attempted was a 5040 (the maximum number of rows that can be produced without repetition on seven bells). Eventually this became the standard length for a peal (ie 1 extent of Triples, 7 extents of Minor, 42 extents of Doubles or 210 extents of Minimus). But the old terminology continued to be used for quite a long time with 5040s of Minor often described as consisting of 'seven peals'. There is a peal board at Horham in Suffolk dating from the second half of the 18th century which describes a 10,080 of Plain Bob Major as a quarter peal [21].

5040 changes takes about 3 hours to ring. This is long enough to be a notable performance, but achievable by most ringers. The extent of Major (40,320) takes almost a day of continual ringing and has only been rung once on tower bells. It could not become the standard peal length. On 8 or more bells 5040 has no special significance, so a peal is standardised as 5000 or more changes.

They are in Grandsire Doubles, but not Plain Bob Doubles. All rows are of two types. An even row (also known as in-course or positive) is one which can be produced from rounds by swapping pairs of bells an even number of times. An odd (out-of-course or negative) row is one produced from rounds by an odd number of such swaps. Of all the possible rows, half are odd and half even. Grandsire is a true Doubles method (two pairs of bells always change between successive rows), except at a single when one pair changes (that's why it is called a single). So all rows produced by plain leads and bobs alone are even rows. To get odd ones you need a single, and since rounds is an even row, you need another single will be needed to get back to rounds.

Plain Bob Doubles is different because although all the changes until the treble gets back to lead are double changes, there is a single change when the treble leads (only the pair of bells in 3-4 swap). A bob also involves a single change (the pair in 2-3 swap), so any touch of Plain Bob Doubles consists of ten even rows followed by ten odd rows, then ten even ones, and so on, irrespective of whether the leads are plain or bobbed. This gives rows of both sorts without the need for any singles.

A pure Triples (Doubles) method is a Triples (Doubles) method with all triple (double) changes, except at a single. Grandsire and Stedman are pure Doubles, but most of the other commonly rung methods are not. There are eleven pure (treble dominated) Triples methods, and they all have two hunt bells like Grandsire. Stedman is also pure Triples.

For many years ringers sought to do this. After much trying in the eighteenth century they believed it was probably impossible, but composers tried to use as few singles as possible, and found they could do it with two. All these compositions are rather hard to call (e.g. Holt's Original, which for the first few times was called from manuscript by a conductor who was not ringing), unless they use non-standard singles. The first peal of pure Triples to be composed used more than one method. The next one used a rather tricky principle called Scientific Triples. Some people considered it unacceptable on account of its lack of symmetry. In 1995 Andrew Johnson and Philip Saddleton composed a peal of Stedman Triples using bobs only. Two others working on the same problem solved it independently at almost the same time, but Johnson's peal was the first rung.

One with the same lead heads as Plain Bob (or Grandsire in the case of twin hunt methods). Also no bell should lie more than two consecutive blows in one place except possibly at a call. This latter condition is relaxed for Doubles methods and when bells lie behind for four blows in odd-bell stages of Plain Bob and even bell stages of Grandsire.

It has a special sort of symmetry. All regular methods are symmetrical - if you look at the 'blue line' you will find an axis of symmetry from which point the progress of the line is a mirror image of what has gone before. One consequence of this is that, in theory at least, you only need to learn half the method in order to be able to ring it. But there are dangers in learning this way only, see section 13.8c.

A double method has two axes of symmetry, so that the work on the front when the treble is at the back is the mirror image of the work at the back when the treble is at the front. In fact the whole of the work over the treble is a mirror image of the work under the treble. The simplest example of a double method is Double Bob, in which the bell turned from the back by the treble makes the adjacent place and then returns to the back, in addition to a bell making seconds as the treble leads.

Many double methods have double in their name - Double Bob, Double Oxford, Double Norwich - but some, most notably Bristol and Superlative Surprise, do not. In theory, you can ring a double method by learning a quarter of the line, but most people find it easier (and more reliable!) to learn it all. See also section 13.9e.

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