[r-t] Challenge to produce new method - Double Helix Royal

[Philip Earis]

Last Saturday we rang the first handbell peal of Double Helix Major (see www.campanophile.com/view.aspx?131659<http://www.campanophile.com/view.aspx?131659>, and also the brief video at www.youtube.com/watch?v=G-yI6j7QPMQ<http://www.youtube.com/watch?v=G-yI6j7QPMQ>)

As recently discussed on here, Double Helix is a clever major differential that can easily generate the extent.  Double Helix was created by Terry Streeter and consists of a 3-cycle and a 5-cycle: in the 3-cycle, all 8*7*6 = 336 possible different arrangements of the 3 bells are included. The method is therefore split into divisions of 336/3 = 112 rows: in each half-division bells 1,2,3 occupy each possible combination (ie 8!/(5!*3!)) once and once only. The method has conventional double symmetry, no adjacent places in the notation, and is very dynamic (a fishtail is the longest "piece of work").

We're now very keen to see what possibilities there are for an analogous 10 bell method. I'd like to challenge anyone reading this to produce possible method(s).

Such a royal differential would have some very attractive qualities.  Having a 3-cycle and a 7-cycle where the 3-cycle ring all possible arrangements would give 10*9*8 = 720 possible arrangements, ie divisions of 240 changes, equating to a plain course of 5040 changes.

My challenge for people now is to come up with a royal differential (or even a long list of possibilities) matching these constraints:


1.       Consists of a 3-cycle (bells 1,2,3) and a 7-cycle, with 240 change divisions.  In each half division 1,2 and 3 must occupy each of the 10!/(7!*3!) combinations once and once only.  The plain course must therefore be a true 5040 changes



2.       The method should be conventionally double



3.       There should be no adjacent places in the notation (ie available place notations x, 14, 16, 18, 10, 36, 38, 30, 58, 50, 70, possibly 1470)



4.       Preference for making the method as analogous to Double Helix as possible, eg

a.       no more than 2 consecutive blows

b.      the back 7 meet at the front and back in the coursing order

c.       notation for the quarter-section should be "x", notation at the division end should be 14 (and thus 70 at the half division)

d.      no more "staticity" than a fishtail in any position.  Possibly no ordinary dodges except at half-section and section end.

I'm looking forward to seeing what people can produce.

As a parallel question, has an exhaustive list of Double Helix-type (major) candidate methods been generated?  I'd be keen to see this if so.

Ready, steady, go...



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