The simplest way to compose a 40320 in a Plain Major method is to produce a three-course block in which the two tenors ring in every relative combination to each other once and once only, and to ring this 120 times with all the 120 combinations of xxxxx78 as the part ends.

​

For example, in Bob Major you call a bob at 'V', when the tenor dodges 5-6 up, in every course, which affects the 7th. Doing this creates the three-course block described above, and while the tenors are back together you add the calls which affect bells 2-6. By symmetry, instead of calling blocks of 3V, you can call the tenor to Run In, Run Out, and Make the Bob.

​

The 3V in every course plan (or 3F in 8ths place methods using 6th place bobs) is by far the most common for extents in Plain Major methods, and is almost certainly what would have been used for the 40320 rung at Leeds, Kent in 1761 (indeed, there had probably been extents of Major around long before then.)

​

But there are other plans that can be had, some of which are below. Again, forgive me for including quite a lot of my own work here, but I inevitably have easier access to it than to other sources!

​

                                                         Seven parts

I seem to remember that a seven part of Double Norwich Court Bob Major by Alan Cattell has been published, the part ends being the lead ends of the plain course. I also remember that the composition had an extremely low number of singles - possibly only two in each part. I have the figures on a disc somewhere, and can send them if you're interested. There is certainly an extent of Bob Major by him on CompLib which fits this criterion.

​

On 28th March 2010 I completed my own seven part 40320 of Plain Bob Major which has cyclic part ends, the first part end being 3456782. The peal has 574, of which 504 are bobs and 70 are singles.

​

To compose a 7-part extent of Major you have to account for the three 'shunt' courses. It is inevitable that these 'shunt' courses exist, because each course (or P-block) is made up of seven leads, which is the same as the number of parts in the peal. The seven lead ends in a shunt course bear the same relation to each other, dictated by the part end. In other words, you can only have one lead of the shunt course in each part, and the course is then equally split across the seven parts. This is also what prevents the peal from coming back into Rounds after one part.

​

In regular Major methods the three 'shunt courses' for cyclic 7-part compositions are the ones with the course ends: 453627, 274563, 632754 (any of these can be rung backwards instead.) The first of these courses is very well-known in composition, and called the 'Mega-Tittums' course, because the bells follow each other round in the order 8-2, leading to an interesting sounding effect. This course is used on many numbers of bells to shunt across cyclic part ends.

​

The 274563 course is also well-known in Major ringing, and another popular cyclic shunt, being only one single away from the plain course. The reason that there are three of these shunt courses is because they are all related to each other by the following transposition: 234567, 357246, 526374. Rounds, Queens, and Tittums! This is a further demonstration of how these three changes are intrinsically and mathematically linked to one another! Perhaps this means that the other two shunt courses should be technicallly referred to as the 'Mega-Queens' course, and the 'Mega-Rounds' course!

​

Considering the 3 shunt courses, means that there are 357 'normal' courses in the extent, giving 51 courses and 3 shunt leads in each part. Interestingly, if a B-block plan was used for Bob Major, the shunt courses would be eliminated altogether as B-blocks in Bob Major have five leads rather than seven. In my own 7-part 40320 the singles can be reduced from a total of 70 to 46, by isolating the shunt courses in full to one part only. Obviously this turns the composition into an imperfect 7-part.

​

             Exact 2-part with only two singles (harking back to 3V in every course)

In about Easter 2012 it suddenly occurred to me that a 40320 of Plain Major called in two identical halves with only one single in each half would be possible. This may not sound particularly surprising (take the standard 720 of Bob Minor), but it is often the case that such extents are not possible for various reasons. It is not possible in Grandsire Triples, for example, to have a peal in two identical halves with only one single in each half.

 

It is possible for Plain Major because the 6th needs to occupy five different positions in the tenor-together course ends. Five is an odd number and can be easily attained, in Bob Major for example, by calling 2M, 3W, M. This creates a five-course block in which the 6th occupies evey position in the tenor-together course ends once and once only, and without needing to resort to singles. 180 courses are needed for half the extent, of which 179 can be attained by bobs alone. A pair of singles, a course apart, can be used to get the missing course. One of these singles can then be replaced with a bob as the 'halfway call,' which swaps over a pair of little bells, and doubles the 20160 to a 40320 with only two singles. Here is the composition:

 

40320 Plain Bob Major

RBP

W  V  M  H

-  3  -    42635|

   3  -    62534|

-  3       36524|A

-  3       23564|

-  3  -  - 45236|

   3  -    25634

   3  -    65432

-  3       36452

-  3       53462

-  3  -  s 42536

     A     53426

-  3  -    45632|

   3  -    65234|

-  3       36254|B

-  3       53264|

-  3  -    25436|

     A     43256

   3  -    23654|

   3  -    63452|

-  3       56432|C

-  3       35462|

-  3  -  - 24356|

     C     32456

     A     45326

     C     34526

     A     52346

    2C     23546

Repeat.

​

It would have been nice to have just had an A Block and a B Block, but this is not an option when only two singles are used!

​

                                                      72-part

Very soon after composing the above I became interested in the possibility of a 40320 based on the following part ends:

​

(2345)(678)

​

All possible combinations of 2345 are included, but only the in-course combinations of 678 are included (xxxx678, xxxx867, and xxxx786, but NOT xxxx768, etc.)

​

Two of the 72 part ends would be: 4532867, and 5324678.

Two lead ends which are NOT in the group include: 2346857, and 2345876.

​

I find that different part plans are generally possible for extents in Plain Methods - even unusual part plans such as this - so long as the number of changes in the part divides into a exact number of leads. This is certainly the case here, and it was surprisingly easy to work out a five-course part block. Here is the composition:

​

40320 Plain Bob Major

RBP

1  2  3  4  5  6  7

s  s     s  ss    ss 5742368

         s           5742638

   s     -        -  4532867

72 part, omitting final bob in parts 12, 24, 48 and 60, and calling a single at the same place in parts 36 and 72.

​

Naturally the singles can be reduce by replacing the first two with bobs in all parts, and I'm sure there are possible versions with even fewer singles.

​

Long after composing this I discovered that Daniel Brady had used the same idea to produce a very neat extent of Double Norwich. In contrast to my 72-part, Daniel's uses groups (234)(5678).

​

                                                   Exact 5-part

Though bobs affect three bells, and singles affect two bells, it is still possible to compose an exact 5-part 40320 of Bob Major. To do this you have to compose the first part which, by necessity, will come round at the first part end. You then look at a suitable point in the part that can be rung backwards between a pair of singles. The first single jumps you a few leads later into the part, but it is from another part being rung backwards. Because of the backwards flow you eventually reach the point where the first single was called, call a second single before repetition occurs, and you are magically in the correct point to proceed fowards. The bells will then have shunted into one of he desired part ends, rather than Rounds.

 

This technique of using irregular q-sets to shunt the part ends is well-known. It explains why exact 3-part 5040s and 21-part 5040s of Stedman Triples are possible, and bobs-only exact 5-part 5040s of Bob Triples. The closer the two singles are, the neater, as this means that only a small section of the part gets rung backwards. This is what happens in my exact 5-part 40320 of Bob Major.

 

                                                        21-part parts

I also used irregular q-sets to compose my 21-part 40320 of Bob Major. Like the celebrated 21-parts of Stedman Triples, the part ends are cyclic rotations of Rounds, Queens, and Tittums. This peal divides into an imperfect 7-part. It would be possible to have a variation that divides into an exact 3-part, and I will look into that one day. (An exact 7-part would also be possible).  The peal is made up of 252 S-Blocks, which is by far the easiest approach for a 21-part of Bob Major.

​

This is obviously designed for an a-group lead end order, and so is not universal to all lead end groups (though a variation of the calling might work for f-group methods like Double Oxford.) To compose a 21-part made up from P-Blocks would be a significant challenge, as you would have to work out the 17 course-types in each part; the fact that there is no observation bell(s) system makes this very difficult. Anyone who succeeds would be able to produce a universal composition that could be varied to work for all lead end groups.

 

Failing this, I still wanted to experiment with another lead end order - one which would work well for the 21-part group. Here I should point out that blocks of fixed bell-pairs work well for 21-parts, because in Major there are 21 different pairs of inside bells, and these are all of the 21 pairs of bells in 2nds and 3rds place at all of the 21 part ends. This is why the S-Blocks work so well in Bob Major, because it keeps the same pair of bells fixed in each lead, making it easy to marshall the part-block into course-types.

 

The d-group lead end order would be an interesting one to try. A bob-course alternately swaps pairs 2,3 and 7,8 between 2nds/3rds and 7ths/8ths, while bells 4,5,6 cycle round in the middle. The lead ends are: 7864523, 2356478, 7845623, 2364578, 7856423, 2345678. This would be a slight step up from the a-group S-Blocks, but still manageable as there is a pattern to how the bell-pairs work. This block can be quadrupled by swapping over 2,3 and 7,8 with singles, resulting in a clean block where bells 4,5,6 ring their extent in 4ths/5ths/6ths. At 24 leads long, only five of these blocks would be required to form a part-block: this is an amazingly low number, making it far easier to put the part-block together than it was for the Bob Major composition.

 

As the pairs alternate (a lead in 2nds/3rds, a lead in 7ths/8ths, over and over again) within the block, I had to work out what the lead ends were from another part. For example, in the block shown above, I had to transpose the 178xxxx lead ends into 123xxxx lead ends from the part where bells 2,3 would be in that position, to make sure that there would be no repetition. I worked out the 5 different blocks by using this process, effectively accounting for all 123xxxx lead ends. I then realised that, starting from Rounds, the 5 blocks were extremely easy to join together. The 5 blocks are headed 12345678, 12345867, 12345786, 12347685, 12348657, and you just have to add q-sets of omits on bells 678 and 578 to link them all together. I made sure that all 4 q-sets were used for both, to maximise omits.

 

I was able to devise a part block with mostly bobs and comparatively few singles. There are far more plain leads than in the Bob Major 21-part. The part-block ended in Rounds, so I used an irregular q-set to shunt the bells into a 7-part part end. This produces an extra pair of plain leads in each part. The first part end is 8234567. Very neatly, the alteration to rotate bells (235)(467) for the Queens and Tittums part ends can be made in the first 14 leads of the 1st, 8th and 15th parts. Again, an irregular q-set is used to ring a section of the part backwards (the first 14 leads) and shunt the bells into the new order. The irregular q-sets produces two extra plain leads, and enables the composition to start with 3 consecutive plain leads.

 

The method I used was Oxenwood Bob Major - an excellent d-group method. Unlike my Bob Major 21-part, this composition divides into an exact 3-part.

 

 

                                                   Exact 10-part

By cycling a set of five bells while getting the remaining two to continually swap over makes an exact 10-part possible, with every part called exactly the same and no substitutions of any kind made in any of the parts. My own 40320 on this plan uses Middleton's part-ends with 7,8 swaping over in alternate parts. There are peals of Stedman Triples that use the same idea.

 

This is rather an unusual type of group to use. A more 'conventional' 10-part group would be the reversals (32546, 24365, 46253, 65432, 53624) to go with the original group (35264, 56342, 64523, 42635, 23456), but in this case the reversals are effectively rung backwards. This makes it trickier to compose a part that runs true to this set of part ends (my first two attempts were false!) Ten parts is surely the greatest possible number for a peal of Major where every part is called exactly the same.

 

                                                            20-part

Soon after composing the exact 10-part, I produced a 20-part 40320. Like the 10-part, this uses irregular q-sets to attain five-part shunts. Forming four mutually true 10080s, the composition uses the same twenty part-ends as in Thurstans' Masterpiece for Stedman Triples - an idea that I've also applied to Grandsire Triples and now Bob Triples.

 

                                                 Non-group part ends

Bob Major and most other Plain Major methods are special in the respect that extents can be produced where the part ends do not form a group. Some examples can be found on the page about non-groups.