As I have described elswhere, there are many ten-part peals of Grandsire Triples. These are formed of two identical half-peals (five parts) which then have to be joined irregularly, as shown in this example by E. Bankes James. In 2010 I wondered about the possibility of a ten-part formed of five two-parts, instead of two five-parts. If so, the touch would come back into Rounds after two parts, at 1008 changes. You could then turn this into a peal by adding a bob at the correct place in alternating parts - a Q-set that would link the five two-part touches into one peal. This would be far neater and easier to call than the normal ten-parts, as every part would be unbroken and the same length. In the normal ten-part peals, two parts have to be broken up, as you can see from the James peal.

 

I became quite excited in 2010 when I thought I'd managed to come up with a peal on this plan, but realised that the part block was a few leads missing (not missing B-Blocks, but a number of leads not divisible by three, which showed that I had at least one q-set member missing.) The fact that the part was incomplete allowed it to become a two-part rather than a five-part.

 

And that, sadly, is the answer to this question. Once the part is complete and has all q-set members included, it will always become a five-part. It could have any of the five possible part ends (including Rounds) from the first half, but none of the five possible part ends from the second half. The same thing happens with the in-course six parts. You will always end up with 1423567 or 1342567, but never the 6578 part ends. I don't quite understand why this is the case, but it is definitely something to do with the completeness of the part. It is possibly because the five-part containing Rounds is always the subgroup you will start in, even if the full group is a ten-part. It is also possibly because there a five leads in a P-Block, so the part end is determined by the special 'shunt' leads when the observation bell is in the hunt. This can only be a five-part transposition owing to the five-lead P-Block, and can never be a two-part transposition. But there must be more to it then this, as the in-course six-parts are still not accounted for. 

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A perfect ten-part, with bobs-only, was actually composed and conducted in 2017 by Thomas Perrins, but this is not an extent. It is an arbitrary length more than 5040 changes, which has now sadly become permitted by the CCCBR rule changes. This composition has an extra bob in alternate parts, as described above.

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                               Perfect ten-parts (part 2)

The nearest point that two indentical in-course half peals can be joined together is three leads. An example is this fine ten-part by E. Bankes James. Not only does it have the lead ends of the plain course and partner plain course as the part ends, but the composition is also very palindromic. It can also be seen that there are lots of bits singled in to the part in interesting ways, rather than just the usual SBBS blocks. And, importantly, the linking points for the two halves are as close to each other as possible.

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Except, that I wondered (in about 2012) whether the two linkage points could be made even closer together. I speculated that two consecutive bobs could be replaced with two singles, or SB could be replaced with BS. Either trick would swap two pairs of bells, and could therefore link up to the other in-course half peal. I was aware that this in itself would not be sufficient, as the single-to-single Q-sets would be incomplete. I wondered whether this could be amended in a separate bit of another part (preferably the first part.)

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The problem: this amendment would itself swap the same pairs of bells over, cancelling out the halfway substitution in advance. However, the amendment could be two-part in nature, applied to one part only, and would therefore be entirely self-contained and wouldn't alter the part ends.

Another problem: this amendment would itself prevent the peal from being a 'perfect' (i.e: all parts the same length) peal, and it seems to defeat the purpose of the easy substitution halfway and end.

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With this in mind, I think that I tried to come up with a ten-part and then a six-part (where there is more room in the part to manoeuvre), but didn't have any success. I may have another look one day.

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                      Something a bit more complicated

I find it can get a bit boring that the single-to-single Q-sets are always at the same stroke. For example, if the lead ends 324567 and 234567 are both linked by a single-to-single q-set, then they must both occur at backstroke. The same, of course, goes for all q-sets of this kind.

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In 2011 I composed this quarter peal of Grandsire Triples, which deliberately incorporates the lead end 325476 at backstroke (as can be clearly seen in the first part) and ending with 234567 as usual. These lead ends are both produced by singles, to prevent falseness. Clearly, then, this is a special case of single-to-single q-set that is rung in opposing strokes. In about 2012 (around the time of the perfect ten-parts part 2 query) I got quite excited at the idea that these opposing stroke q-sets could be used in peal compositions, and would double the number of potential compositions available. New 12-parts similar to Parker's but never seen before, perhaps the long sought after 24-part, new bicycle three-parts, etc.

 

I got to work on a part block. Unfortunately I soon found out that this type of peal isn't possible. In the normal single-to-single q-sets, there is a B-Block in between the two singles. These SBBS blocks can very easily be broken up by one of the bobs being replaced by a q-set group of plain leads. This is very common. However, the opposing stroke q-sets require more than this. They cause the intermediate B-Block to become torn in half, because the opposing strokes force the B-Block in opposite directions. As a B-Block is made up of three leads (an odd number) it is impossible to split it in half in this way. You either get a repeated lead or a missing lead, and a true or complete peal is therefore impossible. (The problem is also due to the fact that B-Blocks can be rung either forwards or backwards, but single leads can only be rung in one direction.) The novelty of opposing stroke q-sets, therefore, have to be left for fun quarter peals. Interestingly, opposing stroke q-sets do exist elsewhere in Change Ringing, and they allow the existence of bobs-only 360s of Bob Minor and bobs-only 5040s of Bob Triples.

 

                        Revd E. G. Benson's one-part

This one-part peal has caught my attention for several reasons. It produces the changes in a particularly pleasing and aesthetic way - and I have a strong intuition that this was intentional and that Benson knew exactly what he was doing. Like Parker's One-Part it has the one and only SBBS right at the earliest possible opportunity, and then the peal finishes with four full leads of the plain course. After the SBBS you get PBPBPPB which produces most of the pretty touch of 112 changes (BP x 4) but has an omit to prevent it from coming back into the plain course.

 

The peal has 120 calls - this seems a nice balance. Not so few as to become tedious, but not too many either. For those who call one-parts by the bells before (I personally don't), after the first four leads the only bells to be called before for the entire peal are 2,4,5. This should make it easier to call than if more bells were called before. Of the P-Blocks that rung in full unbroken five-lead courses, the best ones seem to have been selected for this. Examples are the P-Blocks starting from 453627, 546732, and 243576.

 

Due to the small number of bells called before and the fairly low number of calls, the bobs occur in interesting combinations. There are many cases of call intervals at 5, 4, 5, for example. This may be followed by a more concentrated section of calls like 2, 2, 2. These combinations seem very efficient at producing nice sounding leads and courses in effortless and seemingly relentless ways. The following section, for example, is pretty to listen to all the way through and includes Queens and Tittums both very close together (note that the Queens and Tittums respective P-Blocks are both rung in their unbroken entirety):

 

346725 1

743562 5

257643 1

652374 5

526374 4

325467 5

 

The peal has well thought out bits like this from start to finish. Some bits seem so repetitive, that I do wonder whether this had been composed with a view to being in parts, but then became a one-part instead. At some point I will have a look at the q-sets to see if that may be the case.

 

And what of the man himself? The name Revd E. Geoffrey Benson sometimes pops up in the peal books of Sidney T. Holt, and it seems that Benson was the curate at Tewkesbury Abbey in the early 1930s. This is interesting, as I believe that the Revd Charles D P Davies - another well-known Grandsire Triples composer - lived in Kemerton, not far from Tewkesbury, in the later years of his life, which I suspect would have been around this time. Later on, Benson seems to have moved further west to the Welsh Marches, ringing several peals in that area in the 40s and 50s. His last peal seems to have been in about 1960. He was a Cambridge University alumnus - again, like Davies - and rang several peals for the CUG.

 

He produced a very neat and satisfying one-part of Grandsire Triples, and I hope to ring it someday.

 

                          8-parts

8-part peals of Grandsire Triples aren't very common, as rounds will invariably come up as the first part end. Because of this, 8-part peals require a repeated section in some of the parts. Brian Price came up with a very neat composition, with comparitively few calls. As has been said elsewhere, the peal is made up from a 24-part block. It is a very enjoyable composition to ring, with blocks of four consecutive plain leads when bells 6,7 are coursing each other. All of the 678s occur at backstroke. The repeated section is very neat, being on either side of a pair of singles at Home. The repeated section includes two of the 678 course ends, and is an enjoyable part of the composition. When the composition was first published in the Ringing World, Price explained why 8-part peals have to be "lopsided" in half of the parts.

 

I came up with my own 8-part in 2014. It is nowhere near as good as Price's, with more calls, more singles, and many of the calls producing non-descript and uninspiring lead ends. What is interesting, though, is that the repeated section in my peal is added into alternating parts, in contrast to Price's peal where his repeated section is added into the first four parts. This means that the halfway point for my peal really is at halfway. Another advantage of my peal is that the halfway substitution is made at the part end, unlike Price's peal where - by necessity - the substitution must be made elsewhere in the part. For the record, here's my 8-part:

 

5040 Grandsire Triples

RBP

  234567

  672453 2

  346572 1

  673425 3

s 526347 2

  475632 2

  264375 1

s 572436 2

s 465372 1

  234765 1

  572634 1

s 645372 1

  236745 1

s 752436 1

  367245 2

s 473652 3

  264573 1

  352764 1

s 743652 1

  267543 1|

  432756 2|

  674532 1|

  436725 3|

  574236 1|

  365427 2|

  743265 1|

s 567324 2| A

  245736 2|

  672345 1|

  246753 3|

  372546 1|

  463257 2|

  724563 1|

  637452 2|

s 426537 1

  754326 1

  267435 2

s 452367 1

8 part, replacing A with a single 1 in alternate parts.

Call bob for single, halfway and at end.

Composed 16th February 2014.

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An attractive prospect would be 8-part peals where bells 6,7 swap over halfway through. For example, the part ends: 345267, 452367, 523467, 234576 x2.

Such an 8-part would be on a distinctly different plan to the two already discussed. Unfortunately they aren't possible. One of the part ends is 452376, which is rounds with three pairs of bells swapped over (24, 35, 67). This would entail falseness whenever these pairs cross over at the half leads or lead ends. Cyclic six-parts are impossible for the same reason. You could confine the false blocks to alternating parts, but the resulting peal would hardly resemble an 8-part.                                                                    

                   Equal-call extents

It seems that a 5040 containing 120 each of bobs, singles and plain leads is probably not possible, for reasons explained here.

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