Grandsire Singles

As you might guess from the name, St Clement's is the method with lots of dodging on the front - not to be confused with St Simon's Bob Triples which is the six-lead method without an extra hunt bell, like Bob Triples. St Clement's is the equivalent twin-hunt method, i.e: closer to Grandsire. For me, St Clement's Triples is much better than St Simon's and I would suggest that bands who want to try something different should opt for the former rather than the latter. As the lead end order for St Clement's is the reverse of Grandsire, this gives St Clement's the equivalent of an 'Mx' type lead end order - very unusual for twin-hunt Triples!

​

I have mentioned elsewhere more than once that very few twin-hunt Triples methods have reversible B-Blocks, and consequently, very few twin-hunt Triples methods can easily use ordinary Grandsire singles in peal compositions.

​

St Clement's is one of the many methods that has non-reversible B-Blocks, so at first glance it seems that Grandsire singles can't be used in a peal composition. But when we take a more discerning look at the method, we find an opportunity to simulate symmetry, with the exciting possibility that a peal using Grandsire singles might be possible after all.

​

But what is this feature? If we look at the lead starting from Rounds, followed by a bob at the next lead, bells 5,6,7 all end up back where they were at the previous lead end - this is the 'repeat lead feature' characteristic of the Mx lead end order. A further look at bells 6 and 7, we can see that they alone do in fact ring a perfectly symmetrical path. Take a look at the diagram:

​

  1234567

  2135476

  2314567

  3241657

  3426175 Place notation '1' here

  4362715

  3467251

  4376521 Half lead, and bells 6,7 cross over

  3475612

  4357162

  3451726 Place notation '1' is NOT reflected here, so the lead is asymmetric

  4315276

  4132567

  1435276

- 1342567

​

Bells 2,3,4,5 do not ring a symmetrical path, because they are all involved in the non-matching place notations illustrated in the digram. Bells 6,7 are not affected by this, so they do ring a symmetrical path - but it is important to keep in mind that we are treating 6,7 collectively as one pair of bells - not as two separate bells.

​

How then, can the collective symmetry of bells 6,7 be of use to us? It entails that we can have a set of out-of-course leads (viz: a set of leads rung backwards, entailing that normal Grandsire singles - which always changes the direction of a touch's flow without exception - can be used, and in-course singles are now not mandatory.)

​

What then is this group of leads that can be rung backwards? In a peal composition that doesn't use Grandsire singles and only uses in-course singles, there will be 12 lead ends ending xxxx76 and 12 lead ends ending xxxx67. But because 6,7 ring a symmetrical path, we can remove all of the xxxx76 lead ends and replace them with the 12 out-of-course xxxx67 lead ends, so there are now 24 lead ends ending xxxx67, all at backstroke. The new xxxx67 leads are not direct reversals of the discarded xxxx76 leads because the leads are not symmetrical, but thanks to the path of bells 6,7 - which is symmetrical - the new xxxx67 leads holistically share between them what was in the old xxxx76 leads. Thus, the new leads are completely self-contained and mutually true to the rest of the hypothetical peal composition - we don't need to worry about extra falseness problems introduced, because there aren't any.

​

So if we make this little alteration and replace all of the old xxxx76 leads with new xxxx67 leads, by using Grandsire singles, does this mean that a peal is now possible with Grandsire singles?

​

No. Sooner or later we will be forced into circumstances where one of the xxxx76 leads will make a reappearance - like your girlfriend's ex - and the peal will instantly be false. For example, take a look at these lead ends:

​

  352647

- 523647

  534276

​

No combination of bobs and omits will escape the xxxx76, because you can see that bells 6,7 are fixed in the position xxx6x7 beforehand, regardless of whether there is a call there or not. The xxxx76 is a deadlocked situation.

​

Clearly all of the xxxx47 lead ends will now have to be replaced by extra xxxx74 lead ends at backstroke to eliminate this problem. But we can guess that this won't be enough to prevent cross contamination. Perhaps we can close all of the out-of-course pairs into a group. I wondered whether A. J. Pitman's peal of Grandsire Triples, with all of the 678s, 468s, and 748s at backstroke could be used to form such a group, and maybe point directly towards a peal of St Clement's using Grandsire singles, but it was pretty obvious that Pitman's peal would be useless for this, as it is constructed of Grandsire B-Blocks - no help at all for St Clement's.

​

And clearly the group of out-of-course pairs would have to be quite large, as it would have to also include xxxx75s, xxxx73s, xxxx72s, but also xxxx46s, xxxx36s, xxxx56s, xxxx26s, which all occur before the xxxx67 lead ends. I have looked for possible part blocks using this group of 9 pairs, but problems start when the pairs of little bells meet each other at the back - all the xxxx23, xxxx35 leads, etc. A part end system based on xxxx67 would mean that the little bells get mixed up at the part ends, causing no control over contamination when they meet each other at the back.

 

On this basis, I think that our group has to spread to all possible pairs, otherwise there will always be a point at which contamination will occur. Of all the 30 possible combinations to dodge in 6-7, we can only use 15 for a true peal of St Clement's with Grandsire singles. So either all of the xxxx45 lead ends must occur at backstroke, or all of the xxxx54s - every possible pair of bells can only occur the one way round.

 

This is the kind of block I have been looking for on and off since 2011, but I highly doubt that I will ever be able to find it. I also highly doubt that it can be found. One of the drawbacks of St Clement's B-Blocks is that you cannot use singles to 'teleport' from one lead of the B-Block to somewhere else in the composition, as you can in Grandsire. Instead, you simply end up teleporting to another point in the same B-Block, which you may be able to see from the diagram here:

 

  543267

- 435267

s 534267

- 345267

- 453267

s 354267

 

This greatly reduces the possibilities. I have searched with pen and paper for many different approaches to get 15 pairs of bells into some kind of harmony, but have never succeeded and don't know how to start looking for an efficient system. It's entertaining to browse through my repeated attempts to tackle the problem over the years in my composition pads. Some blocks were very exciting, but still failed. My intuition is that it is not possible, but I would be interested to hear a deductive proof. If you have a proof yourself, please email me using the address at the top of the page.

​

The Ringing World index of compositions shows that Eddie Martin published a 4,452 of St Clement's Triples in about 1999. Was this possibly his effort at using the 15 pairs and Grandsire singles? I don't have access to the 90s issues, so I'd be grateful if anyone who does could send me the figures.

 

To escape the problem shown earlier  on, of inevitable contamination, you could use some other kind of call - in addition to the bobs and Grandsire singles - to prevent the xxxx76s from popping up. A 5ths place call could do the trick.

 

Perhaps the answer then is that, just as with Oxford Bob Triples, a peal of St Clement's Triples is possible with bobs and Grandsire singles, but that you also have to incorporate some kind of third call. 

​