[r-t] Pitman's 13440 change compositions

Philip Earis pje24 at cantab.net
Wed Aug 9 13:27:53 UTC 2017

> PJE - What scope is there to extend this to a whole extent?
> RRH - The answer is that I think it would be possible, the thinking needs
> extending to having the 7th in 5th and 3rds and then inserting blocks of
> 3 bobs at Fifths in each course. I haven't got the time at the moment but
> I will put it on my list of nobody else comes up with a solution.


Thinking about the whole-extent problem from another angle ("Double
Helix"), I want to use treble-dodging major methods to form a 21-lead
course where bells 1,7,8 appear twice in every possible position in the
change (once +, once -).  This gives (8*7*6)*2 = 672 rows (ie 21 leads of
a treble-dodging major method).  So then if you repeatedly ring this
block, with a composition that stitches together all 60 possible in-course
courses, you'll get a true 40320.

So who can produce some example 21-lead courses that will fit such a plan?
Up to 21 methods, but fewer is fine too.

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