[r-t] Double Grandsire Minor

[Richard Pullin]

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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