# [r-t] Grandsire Triples.

Alexander Holroyd holroyd at math.ubc.ca
Wed Oct 30 14:59:36 UTC 2013

```It turns out that there is a quite nice composition of Grandsire that does
the job (obviously, check for typos before ringing!)

1260 Grandsire Triples
Alexander E. Holroyd

234567
------
672453 2
346572 1
543267 5
675324 2
246537 2
s 572346 1
s 365472 1
723546 2
467352 2
s 634275 5
s 256734 1
s 742356 1
637542 1
s 526437 1
745326 1
p 763245 2

3 part

1261 Grandsire Triples
As above, but start at backstroke with p.n. 167 and finish with 12345

1261 Grandsire Triples
As above, but start at backstroke with p.n. 123 and finish with 14567

1261 Grandsire Triples
As above, but start at backstroke with p.n. 145 and finish with 12367

On Wed, 30 Oct 2013, Alexander Holroyd wrote:

> 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.
> 324567,235467,325467,234567
> or
> 325467,235476,324576,234567
> 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).
>
> two funny calls (and a backstroke start) to get a 1261, e.g.
>
> 1234567
> 1324567
> 3142657
> ...
> 2153746
> 1235476
> 1234567
>
> Ander
>
> 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.
>>
>>
>> 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
>>
>>
>> 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.
>>>
>>>
>>> AAJB
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>>> ringing-theory at bellringers.net
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>>>
>>
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>>
>

```