Handbell Compositions: symmetrical leads (1)

Generally speaking, in tower as well as in hand, we ring symmetrical methods - the place notation for the second half of the lead is the reverse of the place notation for the first half of the lead. This means that the blue line of the method is symmetrical, and place bells occur in pairs that ring each other's work in reverse; there is also a symmetrical place bell, sometimes known as the pivot bell. For example, in Cambridge Major, 3rds place bell is the symmetrical one, and the pairs that reverse each other are 2nd/5th, 4th/7th, and 6th/8th. This is all familiar and it's a significant aid to learning methods.

On handbells there is the possibility of ringing a symmetrical pair of place bells simultaneously. In fact, for every method, there is one lead of the plain course in which all of the handbell pairs are ringing symmetrical pairs of place bells, and the 2nd is ringing the symmetrical place bell. In Cambridge Major it's the 4th lead: 7-8 ring 6th and 8th place bells, 5-6 ring 4th and 7th place bells, and 3-4 ring 2nd and 5th place bells. The fact that this lead is in the central position of the plain course is a consequence of the place bell order - actually it's a consequence of the lead end group, which is the combination of the place bell order and the place (2nd or 8th) made at the lead end. The table shows the pivot bell and the symmetrical place bells for each handbell pair, for each of the 12 lead end groups.

Group Place bell order Pivot 3-4 5-6 7-8
A 8753246 8 6,7 4,5 2,3
B 8526734 3 2,5 4,7 6,8
C 8365472 6 4,8 2,7 3,5
D 8274563 5 3,7 2,8 4,6
E 8437625 4 2,6 3,8 5,7
F 8642357 7 5,8 3,6 2,4
G 8753246 3 2,5 4,7 6,8
H 8526734 6 4,8 2,7 3,5
J 8365472 5 3,7 2,8 4,6
K 8274563 4 2,6 3,8 5,7
L 8437625 7 5,8 3,6 2,4
M 8642357 2 3,4 5,6 7,8

Ringing the symmetrical lead on handbells has a distinctive feel, as your bells cross with each other at the half lead (this could be a dodge or a hunting blow) and you reverse the work with your bells ringing the opposite way around. Some time ago, I wondered whether it would be possible to arrange a quarter peal of Spliced Surprise Major in which the tenors always ring symmetrical leads. The answer is yes, and the idea produces an elegant structure which I will now explain.

We have to start with a group M method, so that 7-8 ring a symmetrical lead at the beginning. This takes them to 6th and 8th place bells. The next method must be either group B or group G, but group G has the opposite place bell order to group M and would bring us back to rounds unless we insert a bob. So let's use group B, which takes the tenors to 5th and 7th place bells. This is the symmetrical pair for groups E and K, but group E has the opposite place bell order to group B and would take us back to a repeated lead end, so let's use group K, taking the tenors to 4th and 6th place bells. Continuing in this way, we find that the lead end group is forced at each step, and we get the following sequence of methods and lead ends.

  12345678 
M 14263857 
B 13527486 
K 16482735 
D 15738264 
H 18674523 
F 17856342 

The next method has to be group A because the symmetrical lead has 7-8 ringing 2nd and 3rd place bells. This would reverse the effect of the preceding group F method, so we'll have to insert a bob; in any case it's the 7th lead, so we can't continue with a plain lead. We get

A- 17864523

and then continue as before, at each lead ringing a method of the group that keeps the tenors ringing symmetrical leads:

A 18472635 
L 16758342 
C 14283756 
J 15637284 
E 12345867 
G 13526478 

The next method has to be group M, and again it has to have a bob, otherwise we would have seven consecutive plain leads:

M- 12356478

Now we are back to a course end, with 2 and 3 back in their home positions and 4,5,6 rotated. So repeating the whole block twice gives a round block of 42 leads, i.e. 1344 changes - just right for a quarter peal. There are now two directions we can go in. We have a structure for a composition in 12 methods, one of each lead end group, and we could try to find specific methods that make a true composition. This is possible. Alternatively, we can reduce the number of methods by taking groups B to L in pairs and considering them to be 2nds and 8ths place lead end versions of the same method. For example, if our group B method is Yorkshire then our group G method can be Yorkshire with an 8ths place lead end, which is called Woodstock. Actually it's nice to view an 8ths place lead end as a call, which I will write #. If we write out the composition again with this notation it looks like this:

   12345678 
M  14263857 
B  13527486 
E# 16482735 
D  15738264 
C# 18674523 
F  17856342 
A- 17864523 
A  18472635 
F# 16758342 
C  14283756 
D# 15637284 
E  12345867 
B# 13526478 
M- 12356478

and now we can see an attractive structure: the place notation for the entire composition is palindromic. It's also interesting that there are always seven leads between bobs, and therefore the composition has the minimum number of calls.

With a little computer searching we can fill in methods, using as many standard methods as possible.

1344 Spliced Surprise Major (7m)
By S.J.Gay

              12345678
----------------------
Norwich       14263857
Yorkshire     13527486
Cray#         16482735
Ipswich       15738264
Somerset#     18674523
Wembley       17856342
Westminster-  17864523
Westminster   18472635
Wembley#      16758342
Somerset      14283756
Ipswich#      15637284
Cray          12345867
Yorkshire#    13526478
Norwich-      12356478  
----------------------
3 part
- = 14, # = 18

192 Cray, Ipswich, Norwich, Somerset, Wembley, Westminster, Yorkshire

36 changes of method

For handbells: 7-8 always ring symmetrical leads.