[r-t] Jumpin Jiminy

[Alexander E Holroyd]

This is a very interesting idea, Richard!

Are there other ways of choosing the negative coset that could be more amenable, I wonder?  Presumably you can apply any negative involution instead of pn7, but perhaps it just comes down to the same thing?

Regarding ringability, this does look pretty eccentric to me.  I would not be averse to single changes instead of jumps, if long places could be avoided.

From: ringing-theory <ringing-theory-bounces at bellringers.org> On Behalf Of Richard Pullin
Sent: 12 April 2022 13:23
To: ringing-theory at bellringers.org
Subject: [r-t] Jumpin Jiminy

This challenging new Triples principle might be of interest. The plain course has 336 rows and makes liberal use of jump changes. The conventional changes are all triple, and there are no long places. It uses only three different place notations: 7, 1, and (31)[6475].

As 15 courses are required for a 5040, very simple bobs-only compositions are made possible just by inserting q-sets of 3 bobs (much like in Kidderminster Minor)

5040 Jiminy Jump Triples
RBP (op. 2)
3 4 5
-----
2   3 4132
- -   2314
----------
3 part
Bob = 5

It is rare to find a peal composition of Triples for which adding ordinary q-sets of 3 was the sole technique required to produce it. I can't think of another single-method example.

This project had its origin a little while back. I wanted to find a Triples principle that required an odd number of courses for an extent, and contained only triple changes. I had the idea of using the 168 group for the +tive rows of the plain course, plus 168 -tive rows mapped onto each +tive row by PN 7. The resulting 336 rows are therefore not a group but would still be extentable; and they would partition the extent into an odd number of courses.

Such a principle isn't possible without introducing long places or compromising triple changes, even with the extra 168 -tive rows to dilute things. So I dropped the idea, until realizing last week that jump changes could be used. This is almost completely new territory for me, so I've no idea how Jiminy Jump Triples ranks on the elegance & taste scale -  (31)[6475]  is quite a sledgehammer, but the subtler jump changes aren't an option.

Doubtful of whether 'triple changes throughout' really counts in a jump construct, perhaps a better description would be 'never more than one bell lying still in a row.'

Place Notation: (31)[6475].7.1.7.1.7.1.7.1.7.1.7.(31)[6475].7.1.7.(31)[6475].7.1.7.1.7.(31)[6475].1.(31)[6475].7.1.7.1.7.1.7.(31)[6475].7.(31)[6475].1.(31)[6475].7.1.7.1.7.1.7.(31)[6475].7.(31)[6475].7   3152746

Blue Line: https://complib.org/method/45106








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