We will start with a recap of terminology and what is meant by a method, place notation, a lead of a method and the plain course of a method. At the end, there will be work sheets to print out and complete and I hope this will be a fun way of discovering things about methods.
To make this more manageable, we will look at Minor methods, ie on 6 bells, with 5 “working bells” plus the treble. And I will also define below, two constraints which are common to the great majority of methods rung.
A method is a sequence of changes. For the purpose of this exercise we will look at so-called “treble dominated methods” where the treble follows a fixed path; we will look at plain hunt and treble bob hunt for the treble’s fixed path as these are the most common. After following the sequence of changes once, the hunt bell (the treble) returns to the place it started (leading) and all the working bells usually end in a different place from where they started. The block of rows produced by applying the sequence of changes once is called a lead, as shown in this lead of Plain Bob Minimus. The numbers to the left are the Place Notation - see below.
Starting from rounds, the sequence of changes that produced a lead of the method can be applied repeatedly until rounds is produced again. All the rows that have been produced on the way constitute a plain course of the method as shown in this plain course of Plain Bob Minimus.
A change is the transition from one row (e.g. rounds) to the next, in which some or all of the bells swap places with one of their neighbours, and some or none of the bells stay in the same place in the row. A change can be defined by numbers representing the places in which bells do not move from one row to the next, or by the symbol × denoting a “cross change” in which none of the bells stay in the same place because they all swap places with a neighbour. This way of defining a change is called “place notation”. For example, the place notation 34 means the bells in 3rds place and 4ths place stay in the same place, while all the other pairs of bells swap; for Minor, the bells leading and in 2nds place swap, and the bells in 5ths place and 6ths place swap. From rounds, the diagrams below show what happens, a) if the place notation of the first change is ×, and b) if the place notation of the first change is 34:
The construction of nearly all methods is symmetrical about two points, and these are usually the half lead change and the lead end change. These points are marked with arrows in this lead and a half of St Clement’s College Bob Minor.
The place notation is the same whether it is read forwards or backwards from either the half lead change or the lead end change (giving the method palindromic symmetry). And if the blue line of the plain course is written out, it also will be symmetrical about two points.
Some methods have the same work on the front as on the back and these often have the word “Double” in their name, such as Double Oxford Bob Minor shown here as a grid, with lines through the paths of all the bells. Such methods look as if you need to learn only a quarter of the blue line then remember it forwards and backwards and upside down, but I sometimes find them inherently confusing and harder to ring!
(If you want to know more about method symmetry, click here, then click on the green “plus” signs on that page for examples. You may have noticed that Double Oxford Bob Minor also has rotational symmetry, so this grid has the same shape if it is rotated through 180°, but “rotational” is not commonly used and ringers refer to these methods as “double methods”.)
Breaking this down into the individual changes, the position of the treble moves as follows:
from 1 to 2
from 2 to 3
from 3 to 4
from 4 to 5
from 5 to 6
from 6 to 6 (this is the half lead change)
from 6 to 5
from 5 to 4
from 4 to 3
from 3 to 2
from 2 to 1
from 1 to 1 (this is the lead end change)
For each of these changes, there are several possibilities for the place notation that would cause the treble to move. In the illustrations below, the working bells could be in any order, but we will start from rounds.
When the treble moves from 1 to 2, the place notation can be any one of these:
BUT there is a problem with having 56 for the first change. Traditionally, ringers avoid having the last two bells strike in the order 65 at backstroke in Minor because it does not sound nice. (The same thing applies to 87 at backstroke as the last bells in Major, and so on for Royal and Maximus). The row 214356 above is at handstroke, so the only way to avoid them swapping to 65 at the next backstroke, when the treble hunts from 2 to 3, would be to have the place notation 1456. BUT, that would mean that only a single pair swap and, traditionally, this is something else ringers try to avoid except for the call “single” in Minor.
So for the purpose of this exercise, here are two semi-artificial constraints on the method design that I mentioned near the beginning of this page:
When the treble moves from 2 to 3, the place notation can be any one of these:
When the treble moves from 3 to 4, the place notation can be any one of these:
(or 56, but I have already disallowed 56 except at the half lead)
When the treble moves from 4 to 5, the place notation can be any one of these:
When the treble moves from 5 to 6, the place notation can be any one of these:
When the treble stays in 6ths place at the half lead, the place notation can be any one of these:
As the treble hunts down to lead, the possible place notations at each change are the same as above. For this exercise, we will limit the choice to symmetrical methods so they will be identical to the actual places selected from above, but in the reverse order.
When the treble leads for two blows at the lead end, the place notation can be any one of these:
(or 14, but this is reserved for a bobbed lead end)
The above can be summarised in a table as follows:
|Treble moves||Possible places|
|1 to 2||×||34||36|
|2 to 3||14||16|
|3 to 4||×||12|
|4 to 5||16||36|
|5 to 6||×||12||14||34|
|6 to 5||×||12||14||34|
|5 to 4||16||36|
|4 to 3||×||12|
|3 to 2||14||16|
|2 to 1||×||34||36|
The possible place notations summarised in the table above can be shown against the path of the treble as shown below:
To design your method, select one of the possible place notations for each change from the rounds to the half lead, and work out the resulting rows. After the half lead change, use the same selected place notations in the reverse order for each row, checking at each change that there are no rows repeated from the first half of the lead. Then, when the treble has returned to lead (at handstroke) select the place notation for the lead end change (either 12 or 16) and check whether or not all the working bells are in a different place from rounds. If any of the bells has returned to the position it was in rounds, you have produced a method with an additional hunt bell. If two bells have swapped with each other you may have produced a “differential” method (click here for an explanation).
You can print out this work sheet, which also contains a worked example.
You have now written out the first lead of your method. To produce a plain course of the method, simply repeat the process above, using the same place notation as for the first lead, until rounds is produced. For most Minor methods there will be 5 leads in the Plain Course but this will be different for methods with more than one hunt bell and for differential methods. Perhaps you could work out how many leads your method will have? Alternatively, you can use on-line software such as Martin Bright’s
Method Printer, and type in the place notation of your method. You will need to use an acceptable syntax for the place notation, as explained in the help button on that page. For example, the place notation for Double Oxford Bob Minor (the example from the above
work sheet) is:
&x.14.x.36.x.56,12 where the ampersand indicates a symmetrical place notation, and the comma separates the lead end place notation.
A treble bob method can be designed in much the same way, with the same possible place notations for the corresponding positions of the treble as shown below:
As for plain methods, you can print out this
work sheet, which also contains a worked example. To produce the plain course of your method, follow the same procedure as described
(Some Treble Bob methods are further catagorised as “Delight” or “Surprise”. The definitions of these terms is not important for this exercise but can be checked here.)
It is quite possible that the methods you have created already exist. You can check this against the method library held on Composition Library as described in the help pages. You will need to create an account to input data to Composition Library.
Alternatively, you could check against these printed lists for Plain Minor and Treble Dodging Minor methods.
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, June 2020