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The Carter Ringing Machine


Some Notes on Change Ringing Principles

I'm not an expert on change ringing and don't profess to understand all the details. This page is intended as a short introduction to some of the ideas that go into composing METHODS which are basically recipes for constructing a sequence of changes.

First of all, I'll define some of the terms I'll be using:


1925 Article
Ringing Theory
About Bells
Bill's Contribution
  • A STRIKE is what a bell does when it is rung. It is equivalent to a note in orchestral music.
  • The highest pitched (and smallest) bell is known as the TREBLE and the lowest pitched (and largest) bell is the TENOR. Note that if only a subset of the bells available is used, these names refer to the highest and lowest bells being used. A tower with ten or twelve bells may decide to ring on only six bells for a particular event.
  • A ROW is a sequence of strikes, one from each bell, in some order. In theory, the strikes making up a row should be equally spaced in time, otherwise it will not sound very good.
    Rows are usually written as a sequence of digits, e.g: 123456 is known as ROUNDS and consist of the bells striking in a descending musical scale. 132546 is a different row - the bells are striking in a different order.
  • A CHANGE is what happens between rows. I'll be saying a lot more about this later. One confusing thing is that ringers tend to use the word change when they mean a row. I'm deliberately avoiding this usage here.
  • The number of different rows that can be rung on is called the EXTENT. This numbers grows rapidly as the number of bells increases:
Number of Bells 3 4 5 6 7 8 ...
Extent 6 24 120 720 5,040 40,320 ...
  • A sequence of rows, each one different, is called a TOUCH. If a touch is long enough (usually 5000 rows or more) it can be referred to as a PEAL. A Peal will normally take about 3 hours to ring.
  • Touches must follow a set of rules, known as METHODS. There are many different methods in use. The rules allow for variations so each method covers a wide range of touches.
  • Two final definitions: HANDSTROKE and BACKSTROKE. When ringing a bell, it swings round in a circle, controlled by the bell-rope which is connected to a wheel. The rope is attached in a manner that allows a lot of rope to hang down at one extreme, and much less at the other. When there is a lot of rope hanging down, there is a section of rope that has a woollen coating, called the SALLY in a position convenient for the ringer to hold and pull on. When it is in this position, this is referred to as the handstroke. In the other position, the ringer can just hang on the the end of the rope, and this is the backstroke. When bells are in position ready for ringing to commence, the bells are all in the handstroke position. As a result all touches commence with a handstroke. Some touches have an odd number of rows, and so end with a handstroke, but as this is always followed by at least two rows of rounds, it is no problem to slip an extra row so that when STAND is called, the bells can stop in the handstroke position. For more details on this topic see here.

Some basic rules

That's enough definitions for the moment. Lets consider some of the basic rules, common to all methods.

Every touch begins and ends with rounds, thats 123456 (assuming 6 bells). It sounds like a descending musical scale. Before ringing a touch, the ringers will start by ringing several rounds. This allows each ringer to establish a rhythm which will then be maintained throughout the touch. Once the touch starts, each row must be different from ALL previous rows, until the progression returns to rounds.

When moving from one row to the next, the order of striking changes, so 123456 may change to (a) 214365 or (b) 132546 or even (c) 213546. Can you spot the simple rule that covers the changes made here? The rule is - when a bell moves from its place it can only move one place at a time. Thus for row (a), bells 1 and 2 have swapped places, 3 and 4 have swapped and 5 and 6 have swapped. You can't move more than one place at a time and so what must happen is two adjacent bells exchange places. The number of possible exchanges depends on the number of bells - thus with 6 bells a maximum of three swaps can occur. There can be less than three, but there must always be at least one, otherwise the row will repeat and this is against the rules.

The transformation from one row to the next is referred to as a change, and can be expressed in various ways. From rounds to (a) above, you could say 1x2,3x4,5x6, which defines the changes, but ringers usually prefer to specify those bells that don't change, as this is usually shorter. In the case above, this would result in a null specification so in this case they write 'x' instead. This can be interpreted as 'all change'. The change from rounds to (b), on the other hand, can be written '16' as bells 1 and 6 remain in the same place, while 2 and 3 swap and 4 and 5 swap. Rounds to (c) would therefore be '36' as 3 and 6 remain in the same positions. When a bell doesn't move, it is said to Make a Place.

One thing that can cause confusion is that the above notation refers not to the bells themselves, but to the place in the row. Suppose we have a different row: 352146, and we apply the change '16' to it. Then the bells in places 1 and 6, that is bells 3 and 6 are the ones that hold place, and we get 325416 as the next row.

The Simplest Touch

The most basic touch that can be made is known as the Plain Hunt. This is a simple sequence whereby two changes are applied alternately. It's not very exciting, but it illustrates some basic ideas. On 6 bells the changes are 'x' and '16'. We can illustrate how it works by listing the rows:

2 214365x
3 24163516
4 426153x
5 46251316
6 645231x
7 65432116
8 563412x
9 53614216

There is a simple pattern in this. The treble bell starts off in the lead position and makes its way up to the back or the row. After making place at the back, it moves down to lead again. The other bells follow a similar pattern, 3 and 5 moving up to back initially while 2 4 and 6 move up to lead initially. Follow any two of the bells through and you will see a similar path being traced out, but starting at different points along the path.

If you wish to use a 'shorthand' notation, you can simply write the changes needed: x16x16x16x16x16x16 suffices for the above. Since it is repetitious, it can even be abbreviated to x16!

Many of the methods involve this basic hunting pattern for some of the bells. For more complex methods, it often happens that the Treble will follow this Plain Hunt path, while the other bells follow a more complicated route. The path of the Treble is therefore a reference for other bells, and the period between the rows where the Treble leads in referred to as a LEAD, an economy of vocabulary, here a noun rather than a verb or adjective.

Since it repeats after 12 rows (on 6 bells - in general it will repeat after 2*n rows for n bells), it does not employ all the available rows (unless n <= 3).In order to get more variation into the pattern, a different change is made, usually at the last row of the sequence. To obtain the method known as Plain Bob, the bell in second place, when the Treble reaches the lead position holds place for one change, while the remaining bells exchange places as best they can. Taking the last three lines of the above we have:

Plain Hunt   Plain Bob
11 315264 16   315264 16
12 132564 x   132564 x
13 123456 16   135246 12
  ------     ------  
14 214365 x   312564 x

Since row 13 in the Plain Hunt is the same as row 1, the Plain Hunt is repeating, whereas the Plain Bob has reached a totally new row. If you continue the next twelve rows in like manner you will see that these are all different from the first twelve rows, and if the special change is applied to row 24, row 25 will be different again from 1 or 13. When you do this a third time, though, you will see that row 37 matches row 1 and we have come to the end of this possibility.

Using the 'shorthand' notation we have: x16x16x16x16x16x12. In this case there are five repetitions of the basic pair: x16, followed by one of x12.

Note that when using this notation, you need to separate changes if they are both numeric. To do this you write them with a full stop between them. So 16 followed by 12 would be written 16.12.

Since there are 720 different rows that can be produced by 6 bells, we have only used up a fraction of them. To include the remaining it is necessary to introduce additional changes at suitable points, this will introduce further variations and with a little ingenuity it is possible to devise different ways of obtaining all 720 rows. The additional changes are called Bobs and Singles for reasons that I don't propose to go into here. There are various points in the basic sequences where they may be introduced, and the process of choosing such points, and ensuring that the resulting touch does not break the other rules, is referred to as Composing.

I don't propose to go into details of the many other methods that are available, but just state that these can all be expressed as patterns of changes, with the occasional Bob or Single thrown in at suitable points. In order to be able to ring touches, it is necessary to memorise the patterns of changes. The introduction of the variations, i.e. calling Bobs and Singles at the correct points is the responsibility of one person - the Conductor. All the other ringers need to know is the basic patterns and how to perform the Bobs and Singles when they are called.


I have written the above, not to provide another tutorial for people learning to ring, but to explain how the process operates. I am not a ringer, and I have no real practical experience of ringing. I am interested in the mathematics of ringing, and in the mechanical devices, such as Carter's Ringing Machine, which attempt to simulate the process. If there are any errors in what I have said, please contact me (bill 'at' billp.org) and I will attempt to make amends. Constructive criticism is always welcome!

A footnote: I have recently started learning to ring in a local church tower. At my age it's slow going, but I am making some progress. I doubt if I'll ever become really proficient, but it's good exercise and fun!

By Bill Purvis - 21st August 2015


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