[r-t] Proposed definition of a peal

Mark Davies mark at snowtiger.net
Thu Aug 7 07:30:45 UTC 2008

Ian A writes,

> I'm not convinced by the last bit.  If you are going to allow part extents
> at the higher stage and part extents at the lower stage, why not both
> provided they are mutually true?

Hmm, yes, I suppose. We need to allow any part of the peal using a method at
a lower stage to be treated as one at the higher stage, rather than just
doing this at the level of the whole peal. This seems to be part of the
thrust of your "recursive definition" and Don's later "sets" definition.

Revising my wording I can get something similar (if a bit woollier):

A peal is true if:

1. It is rung on one stage, and each change in the extent at  this stage is
rung either N or N+1 times in the peal, and no more, for N>=0.

2. It is rung on two stages, A and B, where |B-A|=1, and each change in the
extent on A is rung M times in the peal, and no more, and each change in the
extent on B is rung N or N+1 times, and no more, for M>0 and N>0.

3. In a two-stage peal, methods at the lower stage may be considered to be
rung at the higher stage by including the covering bell.


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