When we think of palindromic compositions, Grandsire Triples is not necessarily the first method that comes to mind. We might be more inclined to think about peals of Major - particularly Spliced Surprise. But palindromic peals or blocks can be composed for Grandsire Triples too, thanks to the way that the P-Blocks work.

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To refresh our memories, a P-Block is the technical term for a plain course. In Grandsire Triples the P-Block is 5 leads long and has a bell in the hunt, hunting in parallel to the Treble. There are 72 different P-Blocks which collectively form a peal composition, and bobs are used to join the P-Blocks together.

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Lets have a look at the lead ends of these two P-Blocks:

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P-Block 1             P-Block 2

234567                 235476

253746                 243657

275634                 264735

267453                 276543

246375                 257364

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There is a special relationship between these two P-Blocks. You might notice that the lead ends for P-B 1 are similar to the leads for P-B 2. And if you write out all of the changes for both P-Blocks side by side, it should become clear that P-B 2 is P-B 1 with bells 3 - 7 rung backwards. However, bells 1 and 2 are still ringing the same way round as in P-B 1, so none of the actual changes are repeated and the two P-Blocks are mutually true to each other. For example, in P-B 1 you get the combination of bells 34567128 at backstroke, and in P-B 2 you get the combination 34567218 at handstroke. Because of this, P-Bs 1 and 2 are partners of each other. Every P-Block has its own partner (i.e: 36 pairs of P-Blocks in total) and the relationship between each pair is always the same as above.

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For example, these two P-Blocks are partners and a careful examination will show that the relationship between them is exactly the same as for P-Bs 1 and 2:

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P-Block X              P-Block Y

563427                   564372

546732                   536247

574263                   523764

527346                   572436

532674                   547623

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With the existence of partner courses, which are effectively reversals of each other, we can see that a basis for palindromic compositions is becoming evident. If partner P-Blocks are kept separate from each other, it is possible for long touches of P-Blocks to be put together, and a separate touch consisting of all the partner P-Blocks joined together in exactly the same way, rung in the opposite direction. To make it clearer, lets have a look at this example:

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     Touch 1                Touch 2

  253746      463725

  275634      476532

  267453      457263

  246375      425376

- 532746    - 634725

  573624      673542

  567432      657234

  546273      625473

  524367      642357

- 735624    - 736542

  763452      753264

  746235      725436

  724563      742653

  752346      764325

- 637452    - 537264

  643275      523476

  624537      542637

  652743      564723

  675324      576342

- 436275    - 235476

  423567      243657

  452736      264735

  475623      276543

  467352      257364

- 234567    - 432657

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If you look from the top of Touch 1 downwards, and from the bottom of Touch 2 upwards, you should spot that these two touches are palindromic reversals of each other, and that every P-Block in Touch 1 is the partner of a P-Block in Touch 2. The first P-Block in Touch 1 has its partner as the last P-Block of Touch 2, the second P-Block in Touch 1 has its partner as the penultimate P-Block of Touch 2, etc. The apex of the palindrome is when the 7th is in the hunt, and you can see that these partner P-Blocks are side by side on the diagram.

 

Because of all this, the q-set groups (the sets of bobs used to join the P-Blocks together) also have palindromic partners. The q-set for Touch 1 is the partner q-set for Touch 2. Another pair of partner q-sets would be:

 

652437    654273

456723    256347

754362    352764

357246    753426

253674    457632

 

The relationship between these two q-set groups is the same as for the two q-set groups in Touches 1 and 2. The relationship is always the same for all partner q-set groups.

 

As long as we make sure that each q-set group in a composition has its partner included as well, we have a strong chance of coming up with a palindromic composition. It is still difficult though, and care has to be taken to prevent partner sections corrupting each other. Such a composition will still be true, but will not be a complete palindrome, even if it has palindromic features. An example of such a composition is my unpublished five-part, which I am happy to send you if you would like to see it.

 

One of the oldest peal compositions of Grandsire Triples is a palindrome. This is the beautiful composition called Holt's ten-part, dating from the 1750s. The composer, John Holt, was one of the greatest minds in the history of Change Ringing. Not only was he was the first person who appears to have known about the q-set law for Grandsire Triples, but there is nothing mediocre about his ten-part composition - it is, quite simply, perfect. An exceptional composition of the highest order. This and his other two peals of Grandsire Triples were completely groundbreaking for ringing composition in a way that has never been seen before or since. He worked out the theory all by himself (unlike in so many other branches of ringing composition where progress is made by many different contributors over a long period of time) and was so ahead of his time that nobody knew how to compose peals in a similar style for almost 150 years. And instead of producing something rather sloppy (which could be expected from someone who didn't have past examples to work from), he came up with a perfect palindrome with only 100 calls. Here is this incredible composition:

 

5040 Grandsire Triples

by John Holt (Holt's ten-part)

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234567

752634 1

347265 2

243576 5

542637 5

765342 1

367254 5

543726 2

745632 5

647253 5

246375 5

Call five times, with Holt's Bob Single to produce:

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235476

642735 1

746523 5

547362 5

345276 5

763524 2

567432 5

245367 1

342756 5

743625 5

257364 2

Call five times, with Holt's Bob Single to finish.

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Strictly speaking it is a palindromic five-part, rather than a ten-part. A Holt's Bob Single is place notation 3.14567. It joins the two halves of the palindrome together because it reverses the direction of the four heaviest working bells. It is easy to see that this peal is a palindrome as the distribution of the bobs (1, 2, 5, 5, 1, etc) is also palindromic. A composition known as Reeve's Variation has an extra bob in each part when the 2nd is taken from lead by the Treble, which shunts the part ends into a different order.

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John Holt produced another perfect palindrome for Grandsire Triples, a peal in six parts. This isn't as well known as the ten-part and deserves a wider public. The figures are here:

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5040 Grandsire Triples

by John Holt (Holt's six-part)

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234567      473265 3

672453 2    654327 2

256734 3    736254 1

472356 1    237465 5

254763 3    542637 1

372654 1    375264 2

673425 5    753264 4

546273 1    257436 5

675432 3    572436 4

476253 5    475623 5

324576 1  p 423567 3

Call three times, with Holt's Plain Lead Single to produce:

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235476      234756 3

572364 3    672534 1

375426 5    576423 5

753426 4    625734 3

457632 5    476325 1

574632 4    374562 5

325467 2    253674 1

743625 1    372546 3

647532 5    653472 1

256347 1    376524 3

472635 2  p 345276 2

Call three times, with Holt's Plain Lead Single to finish

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This is another masterpiece. It only has 120 calls, which I have a strong feeling is the minimum for a six-part. When looking at the first half, you can see that the calls become less frequent at the end of each part - like all elegant composers, Holt stacks up the busy section at the start and then allows the q-sets to unravel as the composition progresses. Arguably this is not as good as the ten-part, but is probably of the premier six-bell peals ever composed in the method (though of course it is technically a palindromic 3-part!)

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Why might have such an early composer as Holt used palindromes? With no older compositions of Grandsire Triples for him to study, and an age in which ringers thought very differently about methods than we do today, Holt probably turned to the 72 P-Blocks as the one solid basis that he could rely on. It must have been obvious that each P-Block had a partner rung in the opposite direction, and that a peal composition can therefore be formed from two mirror images (rather like an in-course half and an out-of-course half, though of course not the same.) Perhaps these concepts were more obvious to Holt than they would be to a modern person, as the poverty of his own resources and education made these mathematical certainties easier to grasp. There is no doubt that his mental gifts were exceptional. Holt was a Londoner born into poverty, and his trade was shoemaking (we only know this thanks to a chance remark made many years later.) We have no idea what he looked like, and next to nothing in the way of a biography. He died when still in his late twenties.

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On the 9th April 2010 I came up with my own palindromic peal in ten parts, but on sending it to Eddie Martin he replied that Revd Charles D. P. Davies had already claimed it in the 1880s. This is not surprising as various history texts state that Davies had looked at Holt's ten-part and come up with peals on the same plan. Here is the peal:

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5040 Grandsire Triples

by Revd Charles D P Davies

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234567

752634 1

347265 2

523647 1

345276 3

623745 1

456372 2

724635 2

567324 1

725643 3

257643 4

652374 5

436752 1

734265 5

527634 1

275634 4

Call five times, with Holt's Bob Single to produce:

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235476

642735 1

426735 4

574326 1

375642 5

263475 1

462537 5

624537 4

436275 3

524736 1

365472 2

723546 2

657423 1

726534 3

457326 1

264735 2

Call five times, with Holt's Bob Single to finish.

First rung at Hull on 23rd January 1886.

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This peal has 150 calls.

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