[r-t] Extent of caters

[Wyld Family e-mail]

I think the minimum number of singles for an extent of Grandsire Caters is 6 
unless there are some unexpected problems joining blocks together in which 
case the minimum is 14.

In Grandsire Caters every change can be rung in two ways either at 
handstroke or at back.  I don't know if it is possible to identify a set of 
plain courses that contain the extent but would not be surprised if it were 
not.

It is possible to divide the extent into B blocks i.e. 4 leads with a bob at 
every lead.  Each block can be rung backwards or forwards (one of the 
features that makes extents of treble bob minor and bob triples possible) 
however because a plain lead destroys the symmetry of the leads in Grandsire 
Caters B blocks, if a lead from a particular block is rung in one direction 
then the other three leads must be rung in the same direction.  So the peal 
must contain 5040 complete B blocks and the half peal 2520.

The bob Q set affects 7 bells so changing a Q set reduces or increases the 
number of blocks by 6.  If it is possible, when building the composition, to 
identify a Q set where the number of blocks added is just 2 and the rest of 
the calls/plains simply reorder the main block, then it will be possible to 
reduce the two half peals to two round blocks each and it will take six 
singles to join them.  If a Q set that adds in just 2 blocks can't be found 
(I can't think of a good reason why this should be but have no intention of 
testing it) then the two half peals could only be reduced to 4 blocks each 
and 14 singles would be necessary.

It should be possible to compose a bobs only touch that does not come round 
and is just 2 changes short of the half peal in the same way as the 5038s of 
Grandsire Triples.  Although as Philip Saddleton established for Grandsire 
Triples the missing changes occur before the start there is no way of using 
singles to join the two halves.

Colin


----- Original Message ----- 
From: "Ted Steele" <ted.steele at tesco.net>
To: <ringing-theory at bellringers.net>
Sent: Thursday, August 13, 2009 6:48 PM
Subject: [r-t] Extent of caters


> While browsing the Bell News DVD I saw a advertisement for the figures of 
> the extent of Grandsire caters as composed by James Hewett of Gosport  in 
> 1895. It raised a few questions that will probably be trivially easy for 
> you theorists to answer.
>
> What, if any are the special problems in composing the extent of Grandsire 
> caters? I assume that because of the different nature of the rows, being 
> all quadruple changes the  problems will be different to triples and the 
> possibility of a bobs only extent does not exist; but can the extent be 
> obtained with just two singles?
>
> Has anyone else bothered to publish an extent of caters, or indeed 
> anything above major?
>
> Was James Hewett a notable composer and if so for what is he remembered?
>
> Ted
>
>
>
>
>
>
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