[r-t] Extension

[Robin Woolley]

Hi All,

There are several things going on since I last posted.

A basic point idenitifed years ago is that change ringing is performed 
on very small numbers - and 16 is a very small number for these 
purposes. JH touches on this with D. Oxford Bob. It is, if you like, a 
paradox, that change ringing starts with 6 bells, say but the patterns 
involved are frequently the limit (as n->0) of a much larger pattern as 
n->infinity. This is part of the justification for the indefinacy rule, 
which is fine for pure theory, but we have to deal with the practical, 
i.e., no peal has been rung for n>22.

As a simple example of this, when 'learning' Cambridge S10, I was given 
a rule - dodge 3, places, dodge 3, miss two (etc). The number of dodges 
is, of course, (n/2)-2 and this gives the basic pattern for all numbers, 
but I don't suppose anyone rings CS6 like this.

MBD asks 'A perhaps more basic question: are there any methods with PB 
leadheads which do extend to an infinite number of stages, and do so 
with different leadhead orders each time?'

I think I have seen at least one, but I can't remember what, when or 
where. Interestingly, this was allowed for in the original Decisions 
were some lead-end sequences were not allowed when the lead-end of the 
parent was taken into account. A brief (mis-?)re-reading of this 
suggests this is a reason why Clyde S10 'is/was not an extension' of 
Glasgow S8.

I remember! Newcastle S6 has such an extension. The unrelatedness of 
this method to Newcastle S8 was discussed at about the time of the 
Cheltenham CC mtg BUT an extension of 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. In a naive way, the lead number increases 
at the same rate as the number of bells so this never happens again. 
Newcastle S8 also extends! Which to choose as the parent? There is a 
free choice on this one - but we 'thought' that, since the Minor was 
rung first, this should be the chosen parent. (They didn't bother 
ringing it!)

Best wishes
R