If you are not a bell ringer yourself, you may find the text below contains bell ringing jargon which you do not understand; if so, please try accessing the bell ringing glossary of terms.
Bells were originally just rung in order from the smallest
(highest note, usually called the treble)
to the biggest (lowest note, usually called the tenor), this is called rounds and is
written out on a line, like this:
1 2 3 4 5 6
This sounds boring after a while, so about 400 years ago, change ringing was invented. Ways of changing the order were found and written down, with the next order on the next line, as in the column on the far left, which represents a method called 'A Plain Course of Bob Doubles'.
The leftmost column, is only 'B' or 'H', to show which row is handstroke and which a backstroke. The path of the treble is shown by a red line, that of bell 3 by a blue one. In this method there are 10 rows between where the treble starts in the first place and where it gets back to the first place, these 10 rows are called a lead. A black line is drawn under the line where this happens to make it easier to see, and a letter 'P' written at the end of the next line to show this is a Plain lead. The method continues in a predefined way until the bells return to rounds at the bottom, after 4 leads or 40 rows.
Since there are 5 changing bells if we want to ring the bells in all possible combinations of the 5 numbers, we must ring 120 rows (factorial 5, 5*4*3*2*1), making 12 lead-ends. The other changes and lead-ends are visited by changing the type of lead-end; the conductor calls "Bob" two rows before the treble gets back to the first place. This tells the ringers to change their order and then continue as before; when this happens a 'B' is printed at the lead end.
120 lines take much more space to write out than 40, so to make a more compact diagram leave out the lines where the bells are just 'plain hunting', look at the column on the right showing just the path of the bells, with each bell its own colour. The pattern only changes at the lead ends, so we can print just those rows, leaving the ringers to plain hunt in between.
2 3 4 5 3 5 2 4 5 4 3 2 4 2 5 3 2 3 4 5To show we were carrying on we could write more similar rows underneath but since these are always the same as those above, the numbers can be thought of as the corners of a square, shown at the right of the diagram below. The arrows show which way to move and the 'P' indicates a Plain lead.
This figure shows part of what is possible with Bob Doubles - only three of
the six squares of Plain leads are shown. There are eight hexagons
altogether made from alternating Plain and Bob lead-ends.
Folding up the complete plan of squares and hexagons makes a 3D solid (called a Truncated Octahedron by mathematicians), where the 24 possible lead-ends are arranged at the vertices of a polyhedron and the edges of the polyhedron show how to get from one lead-end to the next. If you visit all the vertices in turn obeying the directions given by the arrows you will have completed all the possible combinations on 5 bells ringing Bob Doubles.
A Truncated Octahedron
This is the plain model without the bell sequences or arrows printed on it.
Similarly the Grandsire Doubles method can be represented by a Truncated Tetrahedron.
You can download templates with instructions to make both these models
either as zipped Draw files (10K)
or as a PDF file (10K). These polyhedra have the bell
numbers for that lead printed on them, and arrows drawn along the edges
which are plain leads.
You can find out more about polyhedra by looking at some of our other pages.