[r-t] Double Grandsire Minor

[Alexander Holroyd]

This is great stuff, Richard.  I think it would actually be quite fun to 
ring (Grandsire Minor certainly can be - I've rung an enjoyable peal of 
it).  I would like to know whether more plains are possible.

There is no bobs-only extent of Grandsire Minor, unfortunately - I one did 
an exhaustive search.

Ander

On Sat, 16 Feb 2013, Richard Pullin wrote:

> Those who follow Change Ringers M.L will know there has been recent
> discussion about Double Grandsire Minor, and particularly about extents of
> that method.
> Being asymmetric, half-lead bobs are needed- naturally these are exact
> mirror reflections of their lead-end counterparts.
> I mentioned that I'd managed to work out a bobs-only extent on this system
> and, after kind interest shown by a couple of people, decided to write up
> the figures here:
>
> BB 34625    BB 23645     BP 64325    BB 42653
> BP 56243    BB 36524     BB 43562    BB 26345
> BB 62354    BB 65432     *BB 35246*    BB 63524
> BB 23465    BB 54263     BB 52634    *BP 45236*
> PP 25643    *PB 23546*     BB 26453    BB 52643
> BB 56324    BB 35624     BP 34562    BP 36425
> BB 63452    BB 56432     *PB 52346*    BB 64532
> BB 34265    BB 64253     BB 23654    BB 45263
> *BB 42536*    BB 42365     BP 46532    *PB 23456*
> BP 65324    *PB 35426*     BB 65243
> BB 53462    BB 54632     BB 52364
> *BB 34256*    BB 46253     *PB 34526*
> BB 42635    BB 62345     BB 45632
> BB 26543    BB 23564     BP 26354
> BP 35462    PP 24653     BB 63425
> *PB 42356*    BB 46325     *BP 54236*
>            BB 63542
>            BB 35264
>            *BB 52436*
> *
> *
> Many thanks to Ander Holroyd for computer proving this on my behalf.
> The experts will decompose it easily enough for themselves, but for others
> I'll describe the key function.
> Due to the presence of half-lead calls, it is easy to select an omit Q-set
> at the lead-end which mirrors an identical Q-set at the half-lead.
> This effectively splits one round block into two, meaning we can easily
> switch the parity of the total number of blocks without adding any extra
> material (sort of similar to the magic blocks in bobs-only Stedman Triples).
> By using this technique, the extent formed itself out of four mutually true
> detached blocks, and a 'keystone' Q-set divided over the four blocks was
> found to finish it off into a 720.
> A fun method for composition, but probably not very enjoyable to ring or
> listen to!
>
> (On a similar topic, I was also dabbling with normal Grandsire Minor and
> managed to work out an extent formed of four detached bobs-only blocks.
> This was a moment of excitement.
> "Perhaps a bobs-only extent really *is* possible!" I thought.
> But on thoroughly examining the starting block, there is clearly no Q-set
> equally split across all four blocks- pity!)
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