[r-t] Double Grandsire Minor
holroyd at math.ubc.ca
Sat Feb 16 20:44:28 UTC 2013
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.
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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