[r-t] Grandsire Triples.

Simon Gay Simon.Gay at glasgow.ac.uk
Wed Oct 30 11:35:43 UTC 2013

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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