Richard Pullin's Change Ringing Site
Grandsire Triples
Cyclic Part Ends
Cyclic part ends have been all the rave for some years now. In 2009 I was in my early teens, and took an interest in compositions based on this idea - particularly in Triples.
In a sense, cyclic compositions of Grandsire Triples have already been published, with the 7th as observation bell and the other five bells rotating. A very old example is Shipway's five-part, which has part ends 34562, 45623, 56234, etc. Another old example is J. F. Penning's five-part, with the 2nd as the observation bell, which has part ends 273456, 267345, 256734, etc.
But for a 15 year old, these were not very exciting or convincing examples of the cylic genre. I wanted the real thing: a six-part composition with part ends 345672, 456723, 567234, 672345, 723456, 234567. At that time I had not yet learnt about the Q-set law, so started to pad up my own touch with long strings of B-Blocks until I had a half peal of 2520 changes. This was an exact cyclic six-part, with the proper part ends. I wasn't able to pad this up any further than 2520. I longed to get a peal length on this plan, and dreamed of an 18-part, after that, with the cyclic rotations of Rounds, Queens and Tittums.
Around Christmas 2009 I emailed the Triples specialist Eddie Martin (sadly no longer with us) to ask for his advice about this. He pointed out the inherent falseness problem with this group. The six cyclic part ends divide into three groups of two, or two groups of three. This entails that a cyclic six part divides into an exact two-part, with 567234 as the halfway part end. This lead end is Rounds with three pairs of bells swapped over: 25, 36, 47 (note the closeness to Tittums - these things are all closely related.)
The fact that three pairs of bells are swapped over at the halfway point is a huge problem. This is because three pairs of bells always cross over at the plain and bob lead ends, and at all of the half leads. This means that the lead ends and half leads in which 25, 36, 47 all cross over in the first half peal would run false against the equivalent lead ends and half leads in the second half peal. It would be like having a two-part peal with the halfway part end 325476! Unfortunately, the cyclic six-part group creates an insoluble falseness problem right from the start!
There is a rather inelegant way round this problem. All of the offending leads in which duplication occurs can be marshalled into special blocks that are singled into the first half peal and omitted from the second half. In 2011 I composed a two-part peal on this plan, with the part end 765432 (bells 27, 63, 45 swapped over at the part end.) The two halves are, of course, very unbalanced, and it does not make for a very neat or easy composition at all. An exact two-part is impossible, as is a cyclic six-part.
And if that wasn't already bad enough, there is another problem for cyclic compositions of Grandsire Triples. As there are six part ends, there would need to be some kind of call that affects six bells in one stroke, to prevent the composition from coming round at the first part end. But there isn't a call that does this. Bobs and omits both affect five bells, not six. Singles technically do create a six-part shunt, but the single affects the bells over two strokes, not one (the 'bob' part of the call, and the 'single' part of the call), which would lead to six repeated changes. So the six parts would have to be joined together irregularly.
Despite all this, I did start to put together a cyclic six-part peal in 2012, fully aware that the end result would be an ugly mess. I think I got very close to a 5040, but couldn't find a place to single in the final B-Block (if I remember correctly.) And as for an 18-part; no chance! Unlike in Stedman Triples, the cyclic rotations of Rounds, Queens, and Tittums does not even form a group in Grandsire.
Sad to say, a peal composition of Grandsire Triples with 345672 the first part end and the footnote "repeat five times" is impossible.
Price's peal
In my opinion, the closest that we can get to an 'authentic' cyclic peal composition of Grandsire Triples is the exceptional 12-part peal by the late Brian D Price. I believe it was composed, or published, in 1948. This composition is incredibly neat, and is typical of Price's genius. The twelve parts are very similar to one another, with only a minor tweak of difference at the same point in different parts. The peal divides into an exact 'bicycle three part,' with part ends 456723, 672345, 234567. The other part ends are near misses, flirting close to cyclic combinations. (This plan is very similar to some of Price's 12-parts of Stedman Triples.) It is as easy to call as any non-observation bell composition can be, and has only 180 calls. Can fewer calls be had on this plan? With Price at the helm, probably not. Here are the figures:
5040 Grandsire Triples
by Brian D Price
672453 2 325674 2 457326 2 324765 2
536247 2 743562 2 264735 2 653472 2
s 275436 1 s 527643 1 572364 1 s 426753 1
s 462375 1 s 635427 1 645237 2 374526 1
754236 2 276543 2 376524 2 s 563274 1
367425 2 432657 2 s 753462 5 745326 2
s 643572 5 s 364725 5 s 427653 1 267534 2
s 526743 1 s 753264 1 s 634527 1 s 652473 5
s 735426 1 s 247653 1 756234 1 s 436752 1
647235 1 362547 1 s 247356 1 s 724536 1
s 256347 1 s 573462 1 632547 1 657324 1
732456 1 245673 1 326547 4 s 346257 1
327456 4 452673 4 753426 1 723546 1
643527 1 364752 1 457632 5 237546 4
546732 5 763245 5 652437 1
456723 5
Repeat the whole, twice
Each 1680 is made up as follows. A bicycle three-part produces 1260 changes, and comes round at the third part end. A fourth part is then singled in. Being the same as the other three parts, this causes a bicycle three-part transposition. Consequently, when singled back out of that part, a shunt has been made to produce the part end 456723 at 1680 changes. This then triples itself to form the full 5040, incorporating all twelve parts. A truly remarkable composition.
Unfortunately some well-meaning but misguided person decided to rotate the calling for the 1680, to the make the peal have Tittums and Queens at the 4th and 8th part ends. This completely eradicates the elegant structure of this composition, disguising the fact that it is a 12-part (not a three part) and masking the closely related set of cyclic and cyclicish part ends. For what it's worth, here are the figures for that variation, presented in a functional but charmless format. As this version of the peal is on ringing.org and in the 2004 Grandsire book, it has a far wider public than the beautiful peal above in its original notation. I hope Price was aware of this and approved of it, as it is bad form to play around with someone else's composition, especially if it becomes more well-known than the original.