[r-t] Extent of spliced treble-dodging minor
pje24 at cantab.net
Thu Sep 19 19:37:31 BST 2019
Big congratulations to Austin Paul, who has managed to put together an
extent of spliced surprise major, following a plan I've been pushing for a
Austin's proof-of-concept extent is in 7 (previously rung) methods: Wendy
S, Brynbuga S, Moose S, Durolipons S, Norwich S, Reverse Dublin S,
The foundation of the extent is this 21-lead round block (ie 672 changes),
containing all (=8*7*6*2) possible combinations of bells 1,7,8 in every
position relative to each other in the row, once with each parity:
Having such a block means you can simply ring all 60 possible in-course
tenors fixed courses to generate the extent.
Or in other words, the extent is a neat 60-part.
The 60 in-course courses can be elegantly stitched together with just
block-end calls where the block ends in a 2nds place method. This can be
done with predominately 4ths and 6ths place calls, though a single-change
call (eg 123456, "$") is needed to get all 60 courses on this plan
(Thompson-Rankin theorum). Ander Holroyd helpfully provided this skeleton
60-course framework based on course-end calls:
Austin's 21-lead round block consists just of mx methods, so he transposed
the 60-course block to produce the extent
40320 7-Spliced Surprise Major Op. 4
2345678 1 2 3 4 5 6 7 Methods
4237568 1[x]2[d]3 t t RBMB.B.MW.
3427865 t t s D.DW.N.NWW
2436578 t s t t t B.W.W.MC.M.R
60 part; = 14 Bob; s = 1678 Single; t = 1238 Single; d = 16 Bob; x =
1 Omit in parts 1, 6, 11, 16, 20, 21, 26, 31, 36, 40, 41, 46, 51, 56 and 60.
2 Include in parts 1, 11, 21, 31, 41 and 51.
3 Include in parts 6, 16, 20, 26, 36, 40, 46, 56 and 60.
This is really exciting. Great focus!
Austin has generated a number of (mx) round blocks on this plan, in up to
16 spliced, and hopefully he will provide more context very soon about his
Obviously there is scope to develop the proof-of-concept, including with
more variety of leadhead groups etc. A meaningful extent of spliced
treble-dodging major is now in touching distance! Great work again
Austin, and I look forward to seeing how people can develop this plan...
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