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Spliced Twin-Hunt Triples

A entire book about the splicing of twin-hunt Triples methods was written by the late Edward W Martin, and there is little that I can add to that here. What I can add, though, are my own specific interests and observations of this very pretty and enjoyable genre of spliced ringing.

A. J. Pitman seems to have been the pioneer for Spliced TH Triples, with his composition of spliced Grandsire and Oxford Bob, published in 1926. This is a brilliant peal, with almost certainly the fewest possible number of calls on this plan. And the combining of a method with a 7ths place lead end (Grandsire) to a method with a 5ths place lead end (Oxford) allows for a bobs-only composition. This is because many other types of q-set groups are introduced by the mixings of the 7ths and 5ths, and some of these q-set groups contain an even number of members, unlike in the normal 7ths or 5ths place method q-sets which only have an odd number of members. These new q-set groups make it possible to arrange the blocks of a peal without a parity barrier.

Pitman realized that a composition will always be internally true as long as there is a particular hunt bell allocated for each method. In the peal above, for example, the method is always Oxford Bob when one of bells 2,3,4 is in the hunt, and always Grandsire when any one of 5,6,7 is in the hunt. This keeps truth because all the leads with the 2nd in the hunt for example, are mutually exclusive, and won't cross contaminate with the leads where the 4th, for example, is in the hunt. This applies to a single method rung on its own, and also to spliced methods. However contrastingly the bells may dilly-dally around in two different methods, they will always dilly-dally in the same relative way within their respective hunt bell blocks, so long as the allocated hunt bell rule is strictly kept. It is basically an example of a q-set rule applied to sections of the method within the lead (not the lead end.) It is analogous to certain spliced extents of Cambridge and Surfleet Surprise Minor, which are true so long as a particular bell always rings 3rds place bell for one of the methods.

 

In about 2014 I came up with a system for ringing three methods to a spliced peal - Grandsire, St Clement's College Bob, and Oxford Bob. You always call the methods in that order, 120 times for a peal, and there is a bob (or sometimes a single) at every lead end. It works because the 7th rings Grandsire throughout, creating a mutually true three-lead block. It is very similar to the three-lead course peals of Grandsire Triples.

 

Designed to be very easy to call, this is a very poor way of ringing Spliced Twin Hunt Triples. To ring the methods in an unvarying three-lead combination, with the 7th never joining in with the Oxford or St Clement's rhythms, and with a call at all 360 lead ends, this system is a shadow of the great richness of Spliced Twin Hunt Triples.

 

The great thing about spliced is that you can get some very contrasting methods into a single composition, and the different ways that we can enjoy multiple methods can be appreciated in one touch or peal. This is especially the case, I think, with Spliced TH Triples, and in this genre we often have fewer methods spliced together then we sometimes do in, say, Spliced Surprise Major, so we get more of a chance to compare longer excerpts of only a few methods. It is also true that every method has its own rhythm (by this I mean the rhythm of the method itself, rather than the rhythm of the actual piece of ringing), so it is equally fascinating to have these contrasting rhythms all in the same peal.

 

In about 2012 I thought that a good way to compose a quarter peal of three Spliced TH Triples methods would be to allocate hunt bells 2,3 for one method, bells 4,5 for the other method, and 6,7 for the last method. This would allow for a two-part composition with a part end like 325467, and a fairly equal method balance. Previously I had come up with three-parts using the 423567 part end, but this does not provide good method balance for three methods, as one of the methods can only be rung for one hunt bell (the 5th in my compositions), causing an uneven method balance, and one person gets to ring only two of the methods.

 

We rang my three-method quarter peal in 2012, and it was satisfying that this plan allows for all hunt bells to have a fair go in all three methods - nobody gets shortchanged. I am also quite pleased with how it sounds, being the combination of three differing but very pretty methods. It has subsequently been rung from time to time. In 2013 we added Double Oxford to the mix - a difficult but very rewarding Triples method - and rang this 1260. As Double Oxford and St Clement's are structurally quite similar, we can introduce a new splicing trick: lead splicing. As an example, the three leads of St Clement's starting with 1234756, 1234675, 1234567, can all be replaced with a lead of Double Oxford and the composition will be true. But all three leads MUST be used. For these three leads of either method, bells 3,4 dodge together on the front while 5,6,7 move above them. This is why these three leads holistically contain the same 42 changes for both methods. Another group would be 672534, 672453, 672345. St Clement's and Double Oxford are, therefore, lead splicers of each other.

 

The deficiency of six-part compositions becomes apparent in some of Pitman's peals. The 2-method peal is fine, because every hunt bell gets a fair go at each method, but when more methods are added to this composition it is inevitable that some bells - such as the 7th - don't get to ring all of the methods. The only advantage of the six-parts is that they are easier to call.

 

This is why I was very keen to extend my two-part 3-method plan to a full peal composition. Three methods divides perfectly for the six working bells. I first had this idea in 2012, but it wasn't until 2015 that I composed the peal. Though it says that the peal was composed on 2nd April 2015, this was only in the sense that the composition was finished then. It took some days, and a great deal of paper, to put it together. The reason it has so many calls was to avoid using singles. More bobs were needed to join the blocks together than if I had resorted to using singles. There is always a call whenever bells 6 or 7 are taken from lead by the treble, and consequently there are only two full 5-lead courses in the whole peal, which is a pity. To get the part end 324576, I deliberately used a q-set group made of two halves, of which 324576 was the halfway transfigure. Intriguingly, all bar one of the 678s are at handstroke in the first part, and at backstroke in the second part.

 

I was certainly pleased with the composition, as it allows exactly 1680 of each method, and is all-the-work (if you don't count the second hunt bell as part of 'the work'). I suspect that this is the first part plan that was purpose built for a three method peal with exactly a third of each method - all previous compositions using unequal compromises in six-parts, etc. And these three particular methods are a great combination. Faithful old Grandsire, a method with extra dodges at the back, and another method with dodging on the front. The composition does have its drawbacks, of course, such as the length of each part, the high number of calls, and the hunt bell rule which restricts the full range of bell interaction - for example, it is impossible in this composition for bells 4,5 to dodge with each other on the front in the St Clement's because of the hunt bell rule. So there is a slight feeling of loss there.

 

Other peals have been composed since then, and more ideas brewing, but I won't say much about them until they are rung or published.

 

Back at the start of 2014 I came up with quite a pleasing three-part quarter peal of Grandsire and Oxford Bob. This time, the part ends rotate bells 2,3,5 and leave 4,6,7 fixed, so that pretty combinations of 4,6,7 can be exploited and repeated throughout each part. The composition doesn't stick as firmly to the hunt bell rule as others, and makes use of the similarity between the two methods. At home I have some extended versions of this composition, which include more 468s and 748s. Several variations are possible by mixing the different parts.

In 2015, not long before composing the three-method composition, I came up with a peal of spliced Grandsire and St Clement's. This was an interesting thing to do, as I don't recall having previously seen a peal composition for two spliced 7ths place methods - only a combination of 5ths and 7ths place methods. Bobs-only compositions are not possible for two 7ths place methods, so I had to include singles. However, I deliberately devised the composition so that a B-Block of Grandsire would be missing from each part. This meant that I could still use normal Grandsire singles, instead of the unfamiliar in-course singles. The peal is a six-part, the two in-course halves being joined by teleporting from one half to the other, as seen in many ten-part and six-part peals of Grandsire Triples.

If you search on Roddy Horton's spliced website, there is another interesting composition by A. J. Pitman, which is a ten-part of St Clement's and Double Oxford. As I said above, these two methods are lead splicers. Because of this, Pitman does not have to stick to the hunt bell rule in this peal, so it is quite different from other compositions of Spliced TH Triples. Not only is it a bobs-only peal, but it is an exact ten-part. By adding an extra bob in every other part, all of the parts can be had, and there is no need for an irregular linking system as is the case in single method peals. As I described elsewhere, an exact ten-part like this is not possible for Grandsire Triples. A very clever composition by Pitman.

                                          Discarding the hunt bell rule

In April 2019 I realised that by using partner courses, long touches of Spliced TH Triples could be put together that don't stick to the rule of having a hunt bell strictly allocated for each method. Elsewhere, I have discussed what the partner courses are in Grandsire Triples (and this applies to all twin hunt methods with 'regular' lead ends.)

When a course is compared to its partner, the 5 working bells all ring exactly the same changes (but the order of the changes is reversed) while the two hunt bells ring the same way round in both courses. Because this relationship between the 5 working bells is the same throughout both courses, it means that one method could be rung for the first course, and another very different method could be rung for the partner course, but no falseness is introduced because the difference between the two courses is always a 2-part transposition, and never a 3-part. We can look at this in more detail.

 

The two methods I chose to work with for this experiment were Grandsire and St Clement's College Bob. Here are two courses - one for each method - which are NOT partners of each other and DO run false against each other:

 

Grandsire                                St Clement's

234567                                      245367

253746                                      256473

275634                                      267534

267453                                      273645

246375                                      234756

The two courses differ by a 3-part transposition: bells 3,4,5 are rotated in the St Clement's (and, by symmetry, so are bells 5,6,7)

This means that in the lead of St Clement's when bells 3,4 are dodging on the front, you get repeated changes from the course of Grandsire. The same thing happens when 6,7 are on the front. So the two courses are false against each other.

 

But if you chose almost any other course of St Clement's with the 2nd in the hunt, that too would also run false against the Grandsire, because there will be a 3-part difference lurking somewhere in the course. 

 

Now take a look at the Grandsire plain course, and its partner course rung to St Clement's:

 

Grandsire                                 St Clement's

234567                                       243657

253746                                       235476

275634                                       257364

267453                                       276543

246375                                       264735

The difference between any of the Grandsire lead ends compared to the St Clement's lead ends is always by a 2-part transposition, so no falseness can occur.

This means that these two courses are true to each other, and any other course of Grandsire will be true against its partner being rung to St Clement's.

I believe that the only other course of St Clement's with the 2nd in the hunt that runs true against Grandsire's plain course is 256347. This course does contain some 3-part transpositions, but the trios of bells concerned do not group together in Grandsire's plain course.

 

Why did I choose St Clement's for this experiment? Because it is different enough from Grandsire and yet the same enough to introduce low level falseness opportunities. For example, St Clement's is Grandsire-above so there is no room for inter-method falseness there. The dodging on the front causes the easy-to-see 3-part falseness between the two methods, and the fact that the pairs of the bells on the front in the St Clement's are always the same as the pairs of bells on the front in Grandsire means that the falseness doesn't get out of control.

 

Now that we know that the partner courses are mutually true to each other, the obvious question is: how long is the longest possible touch on this new plan?

 

I knew full well that a 5040 isn't possible, as at some point you will reach a course that is false to both the St Clement's and Grandsire. It seems that, with the 2nd in the hunt, these six courses are the most that can be had:

 

Grandsire                   St Clement's

234567                        235476

253467                        254376

245367                        243576

 

That's six out of twelve courses. Though I haven't done a deductive investigation, falseness appears to be unavoidable in the other courses with 6 and 7 split. Naturally the relationship between this group of courses applies to all other hunt bells.

 

So that's a total of 50% availablee courses, making the longest length possible on this partner course plan 2520 changes (if I've made a mistake anywhere, please get in touch.)

 

I came up with some touches on this plan, including a 1260 and an 1820. As the courses have a palindromic relationship with their respective partners, the touches are made up of two halves: a Holt's Bob-Single is called halfway through, and all of the partner courses rung in the second half (though the compositions aren't actual palindromes, because Grandsire and St Clement's have different lead end orders.) This also means that there a fewer changes of method than in compositions which stick to the hunt bell rule. And for those who consider the second hunt bell to be part of "the work" (I personally don't), these compositions are almost unique in being "all the work" for both methods. Exactly a month later I came up with this virtually identical 1260. I then realised that Single Oxford and Double Oxford share a similar relationship, so produced a 1260 for those methods.

 

I never did compose a longer touch than the 1820, partly because it was tricky finding and fitting the right courses in, and partly because this project gave me a similar idea for Major.

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