AN INTRODUCTION TO CHANGE-RINGING

by Lawrence I. Phelps

Whenever there are a number of bells whose pitches are arranged according to the progression of a musical scale, it is possible to ring them in a number of ways other than that of the simple scale. The total number of different sequences possible using a given number of bells is equal to what mathematicians call the factorial of the number representing the number of bells. For example, the number of sequences possible on four bells is symbolized by the mathematical expression 4! (read “four factorial”) which means 4 x 3 x 2 x 1 and equals 24. For five bells, the number of possible sequences is 5! or 120; for six bells, 720; seven bells, 5,040; and for eight bells, 40,320. For twelve bells, the largest number used for change-ringing, the total number of possible sequences is 479,001,600 and would take 37 years and 355 days to ring at a normal ringing rate.

Early in the development of the practice of bell ringing, the sequences became known as changes and the art of ringing these changes has for several hundred years been known as change-ringing.

Heretofore, change-ringing has been accomplished only by a trained crew of ringers with each ringer handling the rope of one bell. In order to realize the changes in an ordered way a basic system was devised early in the game. The fundamental rules of the system are:

  1. There must be an alteration in the sequence of the bells at each successive strike of the clapper.
  2. A bell can alter only one place, either up or down, at a time.
  3. The first sequence is “Rounds” - a descending scale-wise progression.
  4. The “touch” or “peal” (the composition of the changes) is not completed until the sequence of Rounds is again reached.

The “plain hunt” is the simplest method of ringing changes. In the following illustration the No. 1 stands for the highest pitched or treble bell, and the No. 5 represents the lowest pitched or tenor bell in a set of five bells tuned to the notes of the major scale, the tenor being the “tonic” or starting note of the scale. (The tenor is only the starting note for purposes of determining the tuning of the bells for, as will be seen below, when ringing it is the treble bell that begins, or “leads” as bell ringers say.)

1 2 3 4 5

2 1 4 3 5
2 4 1 5 3

4 2 5 1 3
4 5 2 3 1

5 4 3 2 1
5 3 4 1 2

3 5 1 4 2
3 1 5 2 4

1 3 2 5 4
1 2 3 4 5

Each row in the above example, after the Round in the first row, is a change. Note that each pair of changes begins with the same bell leading. Recognizing this fact, each pair of changes is called a lead and is usually referred to by the number of the bell in lead. Thus, we have “treble's lead”, when bell No. 1 is in lead position, “second's lead”, “third's lead”, etc., and “tenor's lead” when the biggest bell is leading (No. 5 in our example):

                   Round         1 2 3 4 5
Course begins:
  2nd's lead       1st change    2 1 4 3 5

                   2nd change    2 4 1 5 3

  4th's lead       3rd change    4 2 5 1 3

                   4th change    4 5 2 3 1   Rules
                                             require
  5th's lead       5th change    5 4 3 2 1   Course to be
   (tenor)         - - - - - - - - - - - -   symmetrical
                   6th change    5 3 4 1 2   mirror image
                                             about mid-
  3rd's lead       7th change    3 5 1 4 2   Course

                   8th change    3 1 5 2 4

  1st's lead       9th change    1 3 2 5 4

    (treble)      10th change    1 2 3 4 5

                               Course ends

A bell working its way from the lead or first place (front) to the last place (behind) is said to be hunting up, while a bell working its way from behind to lead is said to be hunting down. In this peal of “plain hunt” on five bells, the treble bell (No. 1) can be followed as it “hunts up” and the tenor bell (No. 5) can be seen to “hunt down” beginning with the second change. These bells reverse their hunting course beginning with the sixth change and the Course returns to a Round with the tenth Change. However, as mentioned above, the full extent of changes possible on five bells numbers 120. To extend the number of changes in a given peal, the Course of the plain hunt must be altered before the hunting bells return to Rounds. Arising from this need and still adhering to the fundamental rules outlined above, many methods, more or less intricate, have evolved for producing changes. The composer's goal is to bring about the most musical sequences possible while scrupulously observing the rules. Within the rules of each method, the peal conductor is free to introduce certain standard variations in the Course of the bells to eventually bring about the desired extent and/or quality of the peal. The three variations in the normal hunting pattern that can be used to bring about the desired effect are called: the “plain end”, the “bob”, and, used only in peals on more than five bells, the “single”.

For example:

The ten changes outlined above can be extended to 40 changes by using a “plain end” each time the treble bell (No. 1) returns to lead, which occurs every tenth change. Thus, the tenth change, instead of being a Round (1 2 3 4 5) as in the above ten-change example, becomes 1 3 5 2 4, and we have:

               8th change    3 1 5 2 4

               9th change    1 3 2 5 4

              10th change    1 3 5 2 4

              11th change    3 1 2 5 4
              
and the next time the treble comes to lead we have:

              18th change    5 1 4 3 2

              l9th change    1 5 3 4 2

              20th change    1 5 4 3 2

              21st change    5 1 3 4 2

and the next:

              28th change    4 1 2 5 3

              29th change    1 4 5 2 3

              30th change    1 4 2 5 3

              31st change    4 1 5 2 3

and the next:

              38th change    2 1 3 4 5

              39th change    1 2 4 3 5

              40th change    1 2 3 4 5

and we get back to a Round 30 changes later than if we had not used the “plain end” as a device to extend the possibilities.

We may describe what happens in a plain end this way: the bell that is replaced in lead by the treble bell stays in the second position (or, as the bell ringers say, “marks second's place”) and then returns to lead while the other bells “dodge” - exchange places with each other in each change - until the maneuver is completed. This takes four changes and since we are using only five bells for our example, the bell “in fifth's place” must stay there for all four changes, and is said to “lie the four blows behind”.

Diagrammatically therefore the plain end looks like this:

 7th change  O   O   O   O   O
             |    \ /     \ /
             |     X       X
             |    / \     / \
 8th change  O   O   O   O   O
              \ /     \ /    |
               X       X     |
              / \     / \    |
 9th change  O   O   O   O   O
             |   |    \ /    |
             |   |     X     |
             |   |    / \    |
10th change  O   O   O   O   O
              \ /     \ /    |
               X       X     |
              / \     / \    |
11th change  O   O   O   O   O
             |    \ /     \ /
             |     X       X
             |    / \     / \ 
12th change  O   O   O   O   O

The diagrams for every plain end will look exactly the same regardless of the numbers of the bells actually participating except that with even numbers of bells all “behind second's place” dodge.

A plain end on six bells therefore looks like this:

O   O   O   O   O   O
|    \ /     \ /    |
|     X       X     |
|    / \     / \    |
O   O   O   O   O   O
 \ /     \ /     \ /
  X       X       X
 / \     / \     / \
O   O   O   O   O   O
|   |    \ /     \ /
|   |     X       X
|   |    / \     / \
O   O   O   O   O   O
 \ /     \ /     \ /
  X       X       X
 / \     / \     / \
O   O   O   O   O   O
|    \ /     \ /    |
|     X       X     |
|    / \     / \    |
O   O   O   O   O   O

To extend the peal from 40 changes to 120 - the full extent possible on five bells- it is only necessary to “call” a “bob” to take place every 40 changes. Thus, if we put a bob in the 40th change in the sequence shown above instead of the plain end, we get:

38th change      2 1 3 4 5

39th change      1 2 4 3 5

40th change      1 4 2 3 5

41st change      4 1 3 2 5

We may describe what happens in a bob this way: the bell that moves into fourth's place when the treble bell comes to lead stays in fourth's place while the treble completes its lead, and then returns to lead while during this all other bells follow their normal Course.

Diagrammatically a bob looks like this:

Five bells              Six bells
O   O   O   O   O       O   O   O   O   O   O
|    \ /     \ /        |    \ /     \ /    |
|     X       X         |     X       X     |
|    / \     / \        |    / \     / \    |
O   O   O   O   O       O   O   O   O   O   O
 \ /     \ /    |        \ /     \ /     \ /
  X       X     |         X       X       X
 / \     / \    |        / \     / \     / \
O   O   O   O   O       O   O   O   O   O   O
|    \ /     \ /        |    \ /     \ /    |
|     X       X         |     X       X     |
|    / \     / \        |    / \     / \    |
O   O   O   O   O       O   O   O   O   O   O      Note that whereas with
 \ /     \ /    |        \ /     \ /     \ /
  X       X     |         X       X       X        five bells, the bell
 / \     / \    |        / \     / \     / \  
O   O   O   O   O       O   O   O   O   O   O      “in fifth's place” stays
|    \ /    |   |       |    \ /    |    \ /
|     X     |   |       |     X     |     X        there for “four blows”,
|    / \    |   |       |    / \    |    / \
O   O   O   O   O       O   O   O   O   O   O      with six bells, the bells
 \ /     \ /    |        \ /     \ /     \ /
  X       X     |         X       X       X        in fifth's and sixth's
 / \     / \    |        / \     / \     / \  
O   O   O   O   O       O   O   O   O   O   O      places dodge
|    \ /     \ /        |    \ /     \ /    |
|     X       X         |     X       X     |
|    / \     / \        |    / \     / \    |
O   O   O   O   O       O   O   O   O   O   O    
 \ /     \ /    |        \ /     \ /     \ /
  X       X     |         X       X       X
 / \     / \    |        / \     / \     / \
O   O   O   O   O       O   O   O   O   O   O
|    \ /     \ /        |    \ /     \ /    |
|     X       X         |     X       X     |
|    / \     / \        |    / \     / \    |
O   O   O   O   O       O   O   O   O   O   O

The device called a “single” is used in the same way as the plain end and the bob to manipulate the Course of the bells in peals on six or more bells in all methods for composing changes except the one known as “treble bob”.

In the single, the bells in the second's, third's and fourth's places stand still through the treble lead and then the bells that came from lead and marked place in second's and fourth's places return to lead, while the bell that came down from behind to mark third's place returns “up behind” to whence it came before starting to hunt its way back to lead.

A single on six bells:       In diagram:
      5 3 6 2 4 1          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      3 5 2 6 1 4          O   O   O   O   O   O
                           |    \ /     \ /    |
                           |     X       X     |
                           |    / \     /  \   |
      3 2 5 1 6 4          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      2 3 1 5 4 6          O   O   O   O   O   O
                           |    \ /     \ /    |
                           |     X       X     |
                           |    / \     /  \   |
      2 1 3 4 5 6          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      1 2 4 3 6 5          O   O   O   O   O   O
                           |   |   |   |    \ /
                           |   |   |   |     X
                           |   |   |   |    / \
      1 2 4 3 5 6          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      2 1 3 4 6 5          O   O   O   O   O   O
                           |    \ /     \ /    |
                           |     X       X     |
                           |    / \     /  \   |
      2 3 1 6 4 5          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      3 2 6 1 5 4          O   O   O   O   O   O
                           |    \ /     \ /    |
                           |     X       X     |
                           |    / \     /  \   |
      3 6 2 5 1 4          O   O   O   O   O   O
                            \ /     \ /     \ /
                             X       X       X
                            / \     / \     / \
      6 3 5 2 4 1          O   O   O   O   O   O

Here follows the full extent of 120 changes on five bells expanded from the simple Course of ten changes shown above by using a plain end when the treble bell makes its first, second, third, fifth, sixth, seventh, ninth, tenth and eleventh lead, and a bob when the treble is in its fourth, eighth and twelfth lead.

        1 2 3 4 5           (continued)         (continued)
        2 1 4 3 5           4 1 3 2 5           3 1 2 4 5
        2 4 1 5 3           4 3 1 5 2           3 2 1 5 4
        4 2 5 1 3           3 4 5 1 2           2 3 5 1 4
        4 5 2 3 1           3 5 4 2 1           2 5 3 4 1
        5 4 3 2 1           5 3 2 4 1           5 2 4 3 1
        5 3 4 1 2           5 2 3 1 4           5 4 2 1 3
        3 5 1 4 2           2 5 1 3 4           4 5 1 2 3
        3 1 5 2 4           2 1 5 4 3           4 1 5 3 2
plain  /1 3 2 5 4   plain  /1 2 4 5 3   plain  /1 4 3 5 2
 end   \1 3 5 2 4    end   \1 2 5 4 3    end   \1 4 5 3 2
        3 1 2 5 4           2 1 4 5 3           4 1 3 5 2
        3 2 1 4 5           2 4 1 3 5           4 3 1 2 5
        2 3 4 1 5           4 2 3 1 5           3 4 2 1 5
        2 4 3 5 1           4 3 2 5 1           3 2 4 5 1
        4 2 5 3 1           3 4 5 2 1           2 3 5 4 1
        4 5 2 1 3           3 5 4 1 2           2 5 3 1 4
        5 4 1 2 3           5 3 1 4 2           5 2 1 3 4
        5 1 4 3 2           5 1 3 2 4           5 1 2 4 3
plain  /1 5 3 4 2   plain  /1 5 2 3 4   plain  /1 5 4 2 3
 end   \1 5 4 3 2    end   \1 5 3 2 4    end   \1 5 2 4 3
        5 1 3 4 2           5 1 2 3 4           5 1 4 2 3
        5 3 1 2 4           5 2 1 4 3           5 4 1 3 2
        3 5 2 1 4           2 5 4 1 3           4 5 3 1 2
        3 2 5 4 1           2 4 5 3 1           4 3 5 2 1
        2 3 4 5 1           4 2 3 5 1           3 4 2 5 1
        2 4 3 1 5           4 3 2 1 5           3 2 4 1 5
        4 2 1 3 5           3 4 1 2 5           2 3 1 4 5
        4 1 2 5 3           3 1 4 5 2           2 1 3 5 4
plain  /1 4 5 2 3   plain  /1 3 5 4 2   plain  /1 2 5 3 4
 end   \1 4 2 5 3    end   \1 3 4 5 2    end   \1 2 3 5 4
        4 1 5 2 3           3 1 5 4 2           2 1 5 3 4
        4 5 1 3 2           3 5 1 2 4           2 5 1 4 3
        5 4 3 1 2           5 3 2 1 4           5 2 4 1 3
        5 3 4 2 1           5 2 3 4 1           5 4 2 3 1
        3 5 2 4 1           2 5 4 3 1           4 5 3 2 1
        3 2 5 1 4           2 4 5 1 3           4 3 5 1 2
        2 3 1 5 4           4 2 1 5 3           3 4 1 5 2
        2 1 3 4 5           4 1 2 3 5           3 1 4 2 5
   bob/ 1 2 4 3 5      bob /1 4 3 2 5     bob  /1 3 2 4 5
       \1 4 2 3 5          \1 3 4 2 5          \1 2 3 4 5

The full extent could also be obtained by calling the bob on the first, fifth and ninth treble lead, or on the second, sixth and tenth, or the third, seventh and eleventh.

These brief examples demonstrate all of the basic rules and techniques used to compose changes.

A device that automatically conducts a set of bells through the Course of a peal must observe the traditional rules for ringing and introduce the appropriate alterations in the normal progress of the ringing to produce the desired effect. The Ringing Crew™, by FUTURA Music Research is the only such device now available that can conduct a set of electrically operated bells through peals of change-ringing according to any of the time-honored methods. See the description of the Ringing Crew™ for further details.