[r-t] Grandsire Triples.

Alexander Holroyd holroyd at math.ubc.ca
Wed Oct 30 14:43:13 UTC 2013

As per the previous discussion, it is very likely that it could be done in 
4 quarters of lengths 1260 and 3*1261 (which is certainly the minimum).

One just needs a peal composition in 4 round blocks with part ends e.g.
and a 1sts place lead end at the part end.
(I don't know whether this exists for Grandsire, but I'm sure it will for 
any 1sts place symmetric plain triples method).

Then we can just insert rounds in between the lead head and lead end using 
two funny calls (and a backstroke start) to get a 1261, e.g.



On Wed, 30 Oct 2013, Simon Gay wrote:

> The question about ringing all the triples changes in a series of quarters 
> is similar to the question of ringing all the major changes in a series of 
> normal length peals. Certainly it is straightforward to ring all the major 
> changes in a series of peals of Plain Bob, by reducing a composition for the 
> extent. From time to time there are reports of bands ringing such a series. 
> I don't know what the minimum number of peals is. I seem to remember working 
> out 12 peals that between them contain all the changes, a long time ago, but 
> probably the minimum is less than 12.
> For the triples question, here is one straightforward approach using Plain 
> Bob.
> Start with a peal composition of the following form:
> 23456     H
> -----------
> 42356  A  -
> -----------
> 6 part, single for bob half way and end.
> I'm sure there are many such compositions. In other words, the A block is a 
> round block of 10 courses. Omitting 5 A blocks gives a length of 15 courses, 
> i.e. 1260 changes. So this idea gives 6 quarter peals, one with each A block 
> preserved, which between them contain all 5040 changes. Equivalently these 
> can be arranged as rotations of a single composition, satisfying Alan's 
> other criterion.
> In order to minimise the total number of quarters, maybe it would be 
> acceptable to inrease their length. The theoretical minimum overlap between 
> quarters is, I think, 4 leads. This is because it takes 2 leads to be able 
> to get to 4 different courses away from the plain course, and similarly it 
> must take at least two leads at the end of the quarter to be able to return 
> from 4 different courses to the plain course. So perhaps the problem can be 
> solved with 4 quarters of 1260 + 4 * 14 = 1316 changes each. Maybe the total 
> overlap can be reduced; for example perhaps two of the quarters only need to 
> overlap by 2 leads, while the other pairs overlap by 4 leads.
> Simon Gay
> On 29/10/2013 10:51, alan Buswell wrote:
>> There is a touch of 111 changes as well as 112. There is also a touch of 
>> 97
>> but not 98. Can anyone tell me why this can not be achieved?
>> There are many quarter peals of Triples, mostly bringing out the musical
>> qualities of the method. Many ringers do not want to ring full peals but
>> would like to experience the fact of knowing that they have, at some time
>> rung ALL the 5040 possible changes to either Grandsire or Plain Bob. Is
>> there a common composition whereby, starting at a different place in the
>> same composition, one is able to ring the extent? This will entail five,
>> possibly more, quarters since the first lead will be common to all and 
>> thus
>> repeated.
>> Ringers setting out to achieve this proposal can then say that they have
>> completed ringing the [name of composition] [name of method] Ring Cycle
>> knowing that they have heard the Extent  I have not heard of this before
>> nor know if it is original. It may open a new vista on the subject of
>> composition. Your views would be appreciated.
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