[r-t] Infinite Extensions

[Alan Reading]

Essentially it seems that the pivot bell either remains constant or follows
a fixed pattern up the stages e.g. in Bristol 2,3,5,7,...
In all the examples given here (and any others I can think of) it either
follows forward or reverse coursing order.
It seems possible that one might be able to construct examples where the
pivot bell follows a pattern like 2,5,9,..
but clearly there's still going to be a simple formula for describing the
lead head from that of Plain Bob at each stage.

As MBD says it seems to happen like this in all the examples but much
harder to justify that it has to...

Cheers,
Alan






On 23 March 2017 at 07:25, Mark Davies <mark at snowtiger.net> wrote:

> Robert Bennett - I think you're misunderstanding my question. I don't want
> to know which leadhead orders work at a given stage, I want to be able to
> predict which leadhead order a method has at any stage. The thing about
> co-prime stages - I don't particularly care about that, since I believe
> short-course extensions are perfectly valid.
>
> Robin writes,
>
> Newcastle S6 omits stage 8 and
>> goes to all numbers from 10 onwards (seemingly). Why? It is a group 'e'
>> method ('j' in old money) of which the 'lead-number' (-2) increases by
>> two each time so the 8-bell version comes round at the first lead end.
>> On 10, it is group 'b', etc.
>>
>
> So if we accept single-lead methods, and short-course extensions, there
> would be a Major version? That seems pleasant.
>
> On the leadhead order, it sounds like this is simply -7 on all stages. Mod
> the number of working bells, this gives:
>
> -2 Minor
>  0 Major
> +2 Royal
> +4 Maximus
> +6 Fourteen
> -7 Sixteen
> -7 Eighteen
> -7 Twenty
> etc.
>
> I would count that as the same leadhead order on all stages.
>
> I am now strongly suspecting this is always the case for any working
> extension, but can't yet justify this.
>
>
> MBD
>
>
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.net
> http://lists.ringingworld.co.uk/listinfo/ringing-theory
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.ringingworld.co.uk/pipermail/ringing-theory/attachments/20170323/5a55f581/attachment.html>